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Three independent checks, and the third is the one the legacy envelope cannot offer: the claim carries its own recipe, so the value is re-derived here and compared. 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Applied only if the revision is newer.","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/identity/peer/presence/{zid}":{"get":{"tags":["Other"],"summary":"node-to-node","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"zid","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"identityDirectory.ts"}},"/api/kernel":{"get":{"tags":["Operators & Kernel"],"summary":"GET /api/kernel — full structured JSON","responses":{"200":{"description":"OK"}},"x-zeq-tier":"public","x-zeq-source":"kernel.ts"}},"/api/kernel/demo":{"get":{"tags":["Operators & Kernel"],"summary":"GET /api/kernel/demo — cached three-body computation result","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"kernel.ts"}},"/api/kernel/live":{"get":{"tags":["Operators & Kernel"],"summary":"GET /api/kernel/live — re-run three-body computation, refresh cache","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"kernel.ts"}},"/api/kernel/prompt":{"get":{"tags":["Operators & Kernel"],"summary":"Full Zeq kernel prompt (LLM bootstrap).","responses":{"200":{"description":"Kernel markdown"}}}},"/api/kernel/skill":{"get":{"tags":["Operators & Kernel"],"summary":"GET /api/kernel/skill — JSON manifest with install instructions Programmatic install path: client GETs this, reads the install commands for its platform (claude-code / cowork / cursor / openai), and writes","responses":{"200":{"description":"OK"}},"x-zeq-tier":"public","x-zeq-source":"kernel.ts"}},"/api/kernel/skill.md":{"get":{"tags":["Operators & Kernel"],"summary":"other skill-aware LLM clients can drop into their skills directory verbatim. 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So adding it cannot lock out the legacy cookie path, and the handler keeps its own 401 for the genuinely-unauthenticated case.","responses":{"201":{"description":"Created"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"keys.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/keys/list":{"get":{"tags":["Accounts & Keys"],"summary":"GET /api/keys/list","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"keys.ts","description":"GET /api/keys/list — owner's active keys (cookie-auth, no Bearer required). F16 — the Portal Hub key panel needs to render BEFORE the user has any key to issue. /keys/me is gated behind authenticateKey (requires existing key); this thin endpoint mirrors the same cookie-auth path as /keys/issue and /keys/revoke so the panel can list, generate, revoke without ever needing the user to paste a key back."}},"/api/keys/me":{"get":{"tags":["Accounts & Keys"],"summary":"GET /api/keys/me","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"keys.ts","security":[{"bearerAuth":[]}]}},"/api/keys/revoke":{"post":{"tags":["Accounts & Keys"],"summary":"POST /api/keys/revoke","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"keys.ts","description":"POST /api/keys/revoke — kill an api key by id (cookie-auth, owner-checked). F16 — needed so the Portal can offer Generate / Delete on each key.","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/keys/rotate":{"post":{"tags":["Accounts & Keys"],"summary":"POST /api/keys/rotate","responses":{"201":{"description":"Created"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"keys.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/llm/chat":{"post":{"tags":["Other"],"summary":"authed browser sessions (the canonical /apps/skills/ chatbot path) can reach this endpoint without minting a Bearer key on the client. The authenticateKey middleware short-circuits when both req.user and req.zeqAuth are","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"502":{"description":"Upstream error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"504":{"description":"Upstream timeout","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"llmGateway.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/llm/key":{"post":{"tags":["Other"],"summary":"A10-F1 FIX: req.body guard protects destructure against empty body (500 → 400). async as of 2026-08-02: storing a key is now a durable write to ZSC rather than a synchronous Map.set, so this handler has to await it — and","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"llmGateway.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/llm/models":{"get":{"tags":["Other"],"summary":"GET /api/llm/models?provider=xxx","responses":{"200":{"description":"OK"},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"provider","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"llmGateway.ts"}},"/api/llm/providers":{"get":{"tags":["Other"],"summary":"Async now: hasKey is a question about the vault, not about this process's memory. It was the only signal a user had for \"is the LLM configured?\", and it answered for one container out of fourteen.","responses":{"200":{"description":"OK"}},"x-zeq-tier":"public","x-zeq-source":"llmGateway.ts"}},"/api/machine/allocation":{"get":{"tags":["Other"],"summary":"GET /api/machine/allocation","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"allocation.ts","security":[{"bearerAuth":[]}]}},"/api/machines/top":{"get":{"tags":["Other"],"summary":"GET /api/machines/top","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"limit","in":"query","required":false,"schema":{"type":"string"}},{"name":"offset","in":"query","required":false,"schema":{"type":"string"}},{"name":"window","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"machinesLeaderboard.ts"}},"/api/mail/ai/compose-html":{"post":{"tags":["Other"],"summary":"POST /api/mail/ai/compose-html","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"502":{"description":"Upstream error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","description":"MAIL.HTML1 — generate an HTML email body from a description. Runs on the SENDER'S OWN provider and key. Nothing is proxied through a Foundation account and no Foundation quota is consumed: the prompt and the generated markup go to whichever provider that user configured in BYOK. If they have not configured one we say so explicitly (code NO_BYOK) rather than failing vaguely, because \"nothing happened\" is the worst possible answer. The model's output is sanitised with the same function used on send and on render. A model can be talked into emitting a <script> — by a hostile instruction pasted into the prompt, or simply by being asked — and that must not survive into anyone's inbox.","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/aliases":{"get":{"tags":["Other"],"summary":"GET /mail/aliases","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]},"post":{"tags":["Other"],"summary":"POST /mail/aliases","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/aliases/{id}":{"delete":{"tags":["Other"],"summary":"DELETE /mail/aliases/:id","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]}},"/api/mail/blocklist":{"get":{"tags":["Other"],"summary":"GET /mail/blocklist","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]},"post":{"tags":["Other"],"summary":"POST /mail/blocklist { kind: \"address\"|\"domain\"|\"pattern\", value, reason? }","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/blocklist/{id}":{"delete":{"tags":["Other"],"summary":"DELETE /mail/blocklist/:id","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]}},"/api/mail/contacts":{"get":{"tags":["Other"],"summary":"GET /mail/contacts Derived from message history: every distinct address the owner has sent to OR received from. No separate persistence — keeps the mail schema lean and cont","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]},"put":{"tags":["Other"],"summary":"PUT /mail/contacts Save or update the detail for one address. Upsert, so the client does not have to know whether a record already exists.","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/contacts/{id}":{"delete":{"tags":["Other"],"summary":"Removes the SAVED DETAIL, not the contact. The person reappears from message history with their bare address — we cannot honestly forget someone you have exchanged mail with while that mail still exists, and pretending o","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]}},"/api/mail/foundation/daily":{"post":{"tags":["Other"],"summary":"POST /api/mail/foundation/daily","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/foundation/unsubscribe":{"get":{"tags":["Other"],"summary":"GET /mail/foundation/unsubscribe?zid=&t= — one click, no login.","responses":{"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"t","in":"query","required":false,"schema":{"type":"string"}},{"name":"zid","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mail.ts"}},"/api/mail/inbound":{"post":{"tags":["Other"],"summary":"POST /api/mail/inbound","responses":{"200":{"description":"OK"},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/inbox":{"get":{"tags":["Other"],"summary":"GET /mail/inbox","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]}},"/api/mail/message/{id}":{"get":{"tags":["Other"],"summary":"GET /mail/message/:id","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]},"patch":{"tags":["Other"],"summary":"PATCH /mail/message/:id","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/message/{id}/block":{"post":{"tags":["Other"],"summary":"POST /mail/message/:id/block One-click block from an open message or a card. Blocks the sender and sweeps their existing mail into spam so the inbox is clean immediately.","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/send":{"post":{"tags":["Other"],"summary":"Internal routing: alias-table OR ZID-derived address → local zid. Both sender's sent-copy and (if internal) recipient's inbox-copy are inserted as separate rows, each independently encrypted under the owner's encryption","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"413":{"description":"Payload too large","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/sent":{"get":{"tags":["Other"],"summary":"GET /mail/sent","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]}},"/api/mail/signatures":{"get":{"tags":["Other"],"summary":"GET /mail/signatures","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]},"put":{"tags":["Other"],"summary":"PUT /mail/signatures Upsert the signature for one address you own. Stored server-side so it is appended on send no matter which client sent the message.","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mail/spam":{"get":{"tags":["Other"],"summary":"GET /mail/spam Quarantine. Nothing here was rejected — it was scored, filed and kept, so a false positive is always recoverable by moving it back to the inbox.","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]}},"/api/mail/stats":{"get":{"tags":["Other"],"summary":"GET /mail/stats Auth-gate bootstrap. Returns counts + identity card. The UI checks {ok:true} to hide the auth-gate div and render the mailbox.","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mail.ts","security":[{"bearerAuth":[]}]}},"/api/mcp":{"get":{"tags":["MCP"],"summary":"MCP discovery document — per-node name/url, machine_hash, surface stats and tool list.","responses":{"200":{"description":"Discovery JSON"}}},"post":{"tags":["MCP"],"summary":"MCP Streamable HTTP endpoint (JSON-RPC 2.0): initialize, tools/list, tools/call. Every tool is listed under x-mcp-tools at the document root; zeq_api_catalog maps the surface and zeq_http calls any endpoint.","requestBody":{"required":true,"content":{"application/json":{"schema":{"type":"object","properties":{"jsonrpc":{"type":"string"},"id":{},"method":{"type":"string"},"params":{"type":"object"}},"required":["jsonrpc","method"]}}}},"responses":{"200":{"description":"JSON-RPC result"}}}},"/api/mesh":{"get":{"tags":["Mesh & Nodes"],"summary":"GET /api/mesh","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mesh.ts"}},"/api/mesh/announce":{"post":{"tags":["Mesh & Nodes"],"summary":"POST /api/mesh/announce","responses":{"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zeqMesh.ts","description":"POST /mesh/announce — SUPER-MACHINE P3: peer discovery. A peer POSTs its self-descriptor { node_id, base_url, tcp_host, tcp_port }, HMAC-signed over the same body via x-node-handshake (meshHandshake). We register it and return our full peer set, so the caller learns the whole known mesh in one round-trip and a fresh node converges from ONE bootstrap peer with no env surgery on the others. handleAnnounce does the HMAC check. Auth: node handshake (verified inside handleAnnounce) Rate limit: 60/min (shares the gossip limiter budget shape)","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mesh/gossip":{"post":{"tags":["Mesh & Nodes"],"summary":"POST /api/mesh/gossip","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zeqMesh.ts","description":"POST /mesh/gossip Receive gossip from a peer node Input: { event, sourceNodeId, zeqond, signature } Auth: Node handshake required Rate limit: 60/min","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mesh/issuance/at":{"get":{"tags":["Mesh & Nodes"],"summary":"value with no coordination. This endpoint simply exposes what THIS node computes for a given Zeqond — public, verifiable, non-secret observability. There is deliberately no voting/quorum: determinism needs none, and exac","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"z","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"mesh.ts"}},"/api/mesh/join":{"post":{"tags":["Mesh & Nodes"],"summary":"POST /api/mesh/join","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"429":{"description":"Rate limited","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zeqMesh.ts","description":"SUPER-MACHINE — OPEN JOIN over HTTPS. Any machine earns read access to the shared federated log by solving a Landauer proof-of-compute challenge (no shared secret needed). On success we mint a fleet-signed join token (valid on ANY node) and hand back the peer roster + genesis anchor. Loopback callers are exempt (0 bits). The token is presented to GET /api/worm/fed/stream.","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/mesh/peers":{"get":{"tags":["Mesh & Nodes"],"summary":"GET /api/mesh/peers","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zeqMesh.ts","description":"SUPER-MACHINE — public peer roster: a fresh joiner GETs this to learn who is in the mesh (bootstrap seed). Descriptors only (hostnames/ports) — no secrets."}},"/api/mesh/self":{"get":{"tags":["Mesh & Nodes"],"summary":"GET /api/mesh/self","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"mesh.ts"}},"/api/mesh/status":{"get":{"tags":["Mesh & Nodes"],"summary":"GET /api/mesh/status","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zeqMesh.ts","description":"GET /mesh/status Get mesh health information Output: { meshSize, activeNodes, coherenceScore, lastGossip, zeqond } Auth: None (public endpoint) Rate limit: Built-in (trust via IP)"}},"/api/mesh/verify":{"post":{"tags":["Mesh & Nodes"],"summary":"POST /api/mesh/verify","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zeqMesh.ts","description":"POST /mesh/verify Verify an identity across the mesh Input: { zid: string, nodes?: string[] } Output: { zid, verified, meshNodes[], coherenceScore, consensusReached, quorum } Auth: API key required Rate limit: 30/min","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/msg/ai/chat":{"post":{"tags":["Other"],"summary":"POST /api/msg/ai/chat","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"428":{"description":"Precondition required","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"502":{"description":"Upstream error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"msgAi.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/msg/ai/history":{"get":{"tags":["Other"],"summary":"GET /api/msg/ai/history","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"convId","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"msgAi.ts","description":"GET /msg/ai/history?convId=… — this conversation, rebuilt from the server. The client's history is localStorage plus an encrypted transcript it writes itself. Both depend on a device having been there. This does not: every completed turn is already sealed in msg_ai_turns, so a fresh device — or one whose storage was cleared — can be handed the conversation back. Returns messages in the shape the client already renders, so it can merge without a translation layer: a user message from the prompt, an assistant message from the reply, computations and builds attached to the reply where the turn produced them. Ids are DERIVED FROM THE TURN ID rather than generated, so merging is idempotent — a client that already has these messages recognises them instead of duplicating the whole conversation on every open.","security":[{"bearerAuth":[]}]}},"/api/msg/ai/key":{"get":{"tags":["Other"],"summary":"GET /msg/ai/key — which credentials exist? 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WHY THIS EXISTS. AI chats were HITE-encrypted with a passphrase the user typed into ONE browser. That made cross-device sync impossible: a second device fetched the ciphertext from the repo (which is server-side and does sync) but had no passphrase to read it. The key must therefore come from the server, available to any authenticated session — never from something the user carries between devices. It is a DETERMINISTIC per-ZID key: HMAC-SHA256(\"zeq-chat-archive:\" + ZID, ZEQ_FIELD_KEY). Every node shares ZEQ_FIELD_KEY, so the key is identical on every device and every node, and it is never stored — it is recomputed from the authenticated ZID on each request. 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The message AUTHOR or a channel admin may pin; the pin is shared (everyone sees the pinned bar). 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Stored in the `reactions` jsonb ({ emoji: [zids] }); returns the updated map","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"slug","in":"path","required":true,"schema":{"type":"string"}},{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"channels.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/msg/channels/{slug}/search":{"get":{"tags":["Other"],"summary":"GET /msg/channels/:slug/search?q= Search a channel's full history by content (case-insensitive). 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allows this","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"vpn.ts","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/vpn/tunnel/handshake-request":{"post":{"tags":["Other"],"summary":"POST /api/vpn/tunnel/handshake-request","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"402":{"description":"Insufficient compute credit","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"409":{"description":"Conflict — the resource is not in a state that allows this","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"vpn.ts","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/vpn/tunnels":{"get":{"tags":["Other"],"summary":"GET /api/vpn/tunnels?slug=X","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"slug","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"vpn.ts"}},"/api/waitlist":{"post":{"tags":["Other"],"summary":"POST /api/waitlist","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"marketing.ts","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/worm/anchor":{"get":{"tags":["Other"],"summary":"GET /api/worm/anchor","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/anchor — this node's own live anchor."}},"/api/worm/anchor-of/{peer}":{"get":{"tags":["Other"],"summary":"GET /api/worm/anchor-of/:peer","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"peer","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/anchor-of/:peer — THIS node's last-stored record of a given peer's root. Lets an HTTP-federated peer ask \"what root did you record for X?\" (the cross-observation quorum needs), without the ZeqSSH channel."}},"/api/worm/anchors":{"get":{"tags":["Other"],"summary":"GET /api/worm/anchors","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/anchors — stored peer anchors."}},"/api/worm/anchors/verify":{"get":{"tags":["Other"],"summary":"GET /api/worm/anchors/verify","responses":{"200":{"description":"OK"}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/anchors/verify — for each peer, re-pull its LIVE anchor over ZeqSSH and compare against the stored anchor. A mismatch means the peer's WORM state changed since we anchored it → tamper flagged (the W5 gate)."}},"/api/worm/balances":{"get":{"tags":["Other"],"summary":"GET /api/worm/balances","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/balances — the derived projection + status."}},"/api/worm/fed/stream":{"get":{"tags":["Other"],"summary":"GET /api/worm/fed/stream","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"after_seq","in":"query","required":false,"schema":{"type":"string"}},{"name":"limit","in":"query","required":false,"schema":{"type":"string"}},{"name":"origin","in":"query","required":false,"schema":{"type":"string"}},{"name":"token","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"SUPER-MACHINE — HTTPS federated-log transport. The TCP replication port (18870) is internal to the zeqmesh network; this serves the SAME federated sub-chain over 443 so an off-host / NAT'd machine can converge. Gated by a PoW-earned join token (see POST /api/mesh/join). Optional ?origin=X serves this node's stored replica of X, so a joiner can pull the WHOLE mesh from a single hub."}},"/api/worm/kernel":{"get":{"tags":["Other"],"summary":"GET /api/worm/kernel","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts"}},"/api/worm/network-mode":{"get":{"tags":["Other"],"summary":"GET /api/worm/network-mode","responses":{"200":{"description":"OK"}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/network-mode — this node's federation posture (public, read-only). `solo` (default) = private: seals its own worm_ledger locally, never pulls or serves a peer's ledger. `networked` = participates in the shared economy log. The enterprise-safe default is solo; the operator opts in via ZEQ_NETWORK_MODE."}},"/api/worm/quorum":{"get":{"tags":["Other"],"summary":"GET /api/worm/quorum","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts"}},"/api/worm/replica/{origin}":{"get":{"tags":["Other"],"summary":"GET /api/worm/replica/:origin","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"origin","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/replica/:origin — this node's verified replica snapshot of a peer (root, count, cursor, integrity, folded balances). Read-only; what this node can serve on the peer's behalf."}},"/api/worm/replication":{"get":{"tags":["Other"],"summary":"GET /api/worm/replication","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts"}},"/api/worm/resolve/{origin}":{"get":{"tags":["Other"],"summary":"GET /api/worm/resolve/:origin","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"origin","in":"path","required":true,"schema":{"type":"string"}},{"name":"host","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/resolve/:origin — failover resolve. Serves local if origin is this node; otherwise probes the origin over ZeqSSH and serves its live state if reachable, else this node's verified replica with stale:true."}},"/api/worm/root":{"get":{"tags":["Other"],"summary":"GET /api/worm/root","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts"}},"/api/worm/status":{"get":{"tags":["Other"],"summary":"GET /api/worm/status","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts"}},"/api/worm/tombstone":{"post":{"tags":["Other"],"summary":"POST /api/worm/tombstone","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"409":{"description":"Conflict — the resource is not in a state that allows this","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"POST /api/worm/tombstone — the ONLY delete in a WORM domain. Owner proves ownership by presenting their account equation; the server recomputes the frozen HITE HMAC and timing-safe compares it to the stored equation_hash. On success it appends a hash-linked, ZeqProof-sealed tombstone. The equation is used transiently and is NEVER stored, logged, or echoed. The original event stays intact (append-only) — reads redact tombstoned tokens. Body: { token_id, owner_zid, equation, reason? } 200 → { ok:true, seq, hash, zeqproof, zeqond, already_tombstoned } 403 → wrong equation / not the owner (enumeration-flat message)","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/worm/tombstones/{owner_zid}":{"get":{"tags":["Other"],"summary":"GET /api/worm/tombstones/:owner_zid","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"owner_zid","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/tombstones/:owner_zid — the token_ids an owner has deleted."}},"/api/worm/verify":{"get":{"tags":["Other"],"summary":"GET /api/worm/verify","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/verify — recompute the ledger hash chain, report integrity."}},"/api/worm/xfers":{"get":{"tags":["Other"],"summary":"GET /api/worm/xfers","responses":{"200":{"description":"OK"},"503":{"description":"Unavailable","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"worm.ts","description":"GET /api/worm/xfers — this node's cross-shard transfers + settlement status."}},"/api/zeq-auth/api-key":{"delete":{"tags":["Other"],"summary":"DELETE /api/zeq-auth/api-key","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"zeqAuth.ts"},"get":{"tags":["Other"],"summary":"GET /api/zeq-auth/api-key","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"zeqAuth.ts"},"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/api-key","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server 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malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"zeqAuth.ts","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zeq-auth/approve/decide":{"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/approve/decide","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"approvals.ts","description":"Approve or deny. Signed by a bound device when the identity has one; a session alone otherwise.","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zeq-auth/approve/lookup":{"get":{"tags":["Other"],"summary":"GET /api/zeq-auth/approve/lookup","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"user_code","in":"query","required":false,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"approvals.ts","description":"A TV/IoT code the person typed: what is asking, before they approve it.","security":[{"bearerAuth":[]}]}},"/api/zeq-auth/approve/pending":{"get":{"tags":["Other"],"summary":"GET /api/zeq-auth/approve/pending","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"approvals.ts","description":"What a trusted launcher shows: my pending sign-in requests (TV codes are entered, not listed).","security":[{"bearerAuth":[]}]}},"/api/zeq-auth/approve/poll":{"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/approve/poll","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"410":{"description":"Gone — retired endpoint","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"429":{"description":"Rate limited","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"approvals.ts","description":"The requester polls. approved → the session (cookie + token), once.","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zeq-auth/approve/start":{"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/approve/start","responses":{"200":{"description":"OK"},"429":{"description":"Rate limited","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"approvals.ts","description":"A new device asks to sign in. Never reveals whether the ZID/slug exists.","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zeq-auth/device/session":{"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/device/session","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"zeqAuthV3.ts","description":"Exchange a launcher's device key for a short session (PL2 Phase 1). Auth: `Authorization: Bearer zsm_…` — the per-device admin-scope machine key minted by `session-key/mint` with a `device`. Body: `{ device_id }` (the uuid enrolled with that key). The launcher never posts an equation; \"forget this device\" (DELETE /zeq-auth/devices/:id) ends this door immediately. Audited as `login_device`. Sets the session cookie too. @returns {ok:true, token, zid, device_id, expires_in} @error 401 UNAUTHORIZED (bad/revoked key) · 403 DEVICE_REVOKED / DEVICE_UNKNOWN · 400 INVALID_INPUT","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zeq-auth/devices":{"get":{"tags":["Other"],"summary":"GET /api/zeq-auth/devices","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"devices.ts","description":"Your devices. @returns {devices:[{id,label,platform,created_at,last_seen_at,revoked_at,has_key}]}","security":[{"bearerAuth":[]}]}},"/api/zeq-auth/devices/{id}":{"delete":{"tags":["Other"],"summary":"DELETE /api/zeq-auth/devices/:id","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"parameters":[{"name":"id","in":"path","required":true,"schema":{"type":"string"}}],"x-zeq-tier":"public","x-zeq-source":"devices.ts","description":"Forget a device: its machine key is revoked NOW; the row stays, marked revoked (revision-ordered).","security":[{"bearerAuth":[]}]}},"/api/zeq-auth/devices/policy":{"get":{"tags":["Other"],"summary":"GET /api/zeq-auth/devices/policy","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"devices.ts","description":"PL2 Phase 4 — launcher-only sign-in status for the signed-in identity.","security":[{"bearerAuth":[]}]},"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/devices/policy","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"devices.ts","description":"Switch launcher-only sign-in. Needs a session AND the device headers signed by one of this identity's bound devices (a stolen session alone cannot lock the owner out; only a device that can still sign in can turn it on or off). Replicated to the mesh like Protected Login.","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zeq-auth/devices/register":{"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/devices/register","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"404":{"description":"Not found","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"409":{"description":"Conflict — the resource is not in a state that allows this","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"owner","x-zeq-source":"devices.ts","description":"PL2 Phase 4 — bind this device to its own Ed25519 key (first registration wins). Auth: `Bearer zsm_…` (the device key) + the device headers signed with the CANDIDATE key over this very request (proof of possession). Body: { device_id, pubkey } — pubkey = raw Ed25519 public key, 64 hex chars. Once bound, POST /zeq-auth/device/session must carry a signature by this key: a copied .zeqkey on another device (no private key) is refused with DEVICE_BOUND. Re-binding to a different key is refused (409 DEVICE_BOUND); forget the device to start over.","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zeq-auth/devices/self":{"get":{"tags":["Other"],"summary":"GET /api/zeq-auth/devices/self","responses":{"200":{"description":"OK"},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"403":{"description":"Forbidden — authenticated, but not permitted for this resource","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"devices.ts","description":"Who am I, as a device. Auth: `Bearer zsm_…` (the device key). The launcher's reachability probe and the replacement for GET /session-key, which needs a session. @returns {ok:true, zid, device:{id,label,platform,last_seen_at,revoked_at}|null}"}},"/api/zeq-auth/equation-reissue":{"post":{"tags":["Other"],"summary":"POST /api/zeq-auth/equation-reissue","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"409":{"description":"Conflict — the resource is not in a state that allows this","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server 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error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zsp.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zsp/scan":{"post":{"tags":["Other"],"summary":"POST /api/zsp/scan","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zsp.ts","requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}},"/api/zsp/status":{"get":{"tags":["Other"],"summary":"Phase C completion (TODO-2 from phase-c-report.md) — public read-only status snapshot used by apps/zeq-dev/public/apps/zsp/index.html. No secret material is exposed; this surface only describes current health of the prot","responses":{"200":{"description":"OK"},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zsp.ts"}},"/api/zsp/unprotect":{"post":{"tags":["Other"],"summary":"AU2: auth-gated like protect. The zid used for the temporal HMAC stays body→env.zid resolution (backward compat — old envelopes were stamped with the zid they carry; forcing the session zid here would break them).","responses":{"200":{"description":"OK"},"400":{"description":"Bad request — a parameter or body field is missing or malformed","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"401":{"description":"Missing or invalid credentials","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}},"500":{"description":"Server error","content":{"application/json":{"schema":{"$ref":"#/components/schemas/ZeqError"}}}}},"x-zeq-tier":"public","x-zeq-source":"zsp.ts","security":[{"bearerAuth":[]}],"requestBody":{"required":false,"content":{"application/json":{"schema":{"type":"object"}}}}}}},"x-mcp":{"endpoint":"/api/mcp","protocol":"JSON-RPC 2.0 (MCP Streamable HTTP)","toolCount":60,"map":"zeq_api_catalog","door":"zeq_http"},"x-mcp-tools":[{"name":"zeq_hpz","description":"HulyaPulse-Zeqond solver — ONE solver over everything, in natural units where c = ħ = k_B = ε₀ = 1 and time is counted in Zeqonds (f₀ = 1287/1000 Hz exactly, definitional). It dispatches on mathematical FORM, not on subject area, and there are only three:\n  • closed     — evaluate a finite expression. `expression` plus `inputs` for every free symbol. Constants (c, hbar, h, k_B, eps0, mu0, G, e, m_e, m_p, m_n, sigma_SB, b_Wien, N_A, alpha, M_Planck, pi, two_pi, euler) resolve automatically as PURE NUMBERS; an unbound symbol is REFUSED by name, never defaulted. Pass `dim` [M,L,T,I,Θ,N,J] to get the SI value back.\n  • dynamical  — integrate the HULYAS master equation ϕ̈ = −3Hϕ̇ − μ²ϕ − λϕ³ − e^{−ϕ/ϕ_c} + ϕ_c²ΣC_k − T^μ_μ − βF² − J_ext, on a Minkowski or cubic-sine FLRW background. Returns the trajectory, the residual of the published equation on it, and both HULYAS runtime equations: the Functional Equation E = P_ϕ·Z(M,R,δ,C,X) and the Spectral-Topological propagator Ψ = ∭K·ϕ.\n  • geometry   — sample a closed-form invariant of the cyclic FLRW reference spacetime a(t) = 1 + ε sin³(πt): a, H, HDot, R, K, rho, P, V, rhoPlusP.\n  • integral   — a DEFINITE INTEGRAL by adaptive Gauss–Kronrod (G7/K15), with the error MEASURED from the embedded pair. `expression`, `variable`, `from`, `to`. A singular integrand is refused with the abscissa where it blew up.\n  • ode        — dy/d<var> = f(var, y) from an initial value, adaptive DP54.\n  • series     — Σ or ∏ over an INTEGER index, by Kahan compensated summation, so the answer does not depend on the order the terms were added in. The residual compensation IS the reported uncertainty. A fractional limit is refused and points at the integral form; an overflowing product is refused rather than returned as Infinity.\n  • pde        — a FIELD EQUATION by the method of lines: wave, heat, klein-gordon, schrodinger, or **hulyas** — the HULYAS master equation with ∇²ϕ ACTUALLY PRESENT, which no other implementation in this framework carries (they all drop the spatial term and integrate the homogeneous reduction). The uncertainty is the drift of the equation's own conserved quantity — field energy, mass, or norm — because a scheme can take small steps and still not be solving the equation.\n  • operator   — evaluate one of the **1,612 registry operators** from ITS OWN published equation. `operator` is the id (GR37, HOHMANN_TRANSFER, …) plus `inputs` for its free symbols. 805 of the 1,612 are closed-form algebra and evaluate here; the other 807 are integrals, partial differential equations, series, systems, asymptotic growth classes and tensor expressions, and are REFUSED BY SHAPE with the kind named — never answered with a neighbouring solver's formula. Σ C_k in the master equation couples to these same ids, and an id that is not in the registry is refused with near misses.\n  • vector     — VECTOR ALGEBRA and VECTOR CALCULUS. `vector: {op, …}`. Algebra: dot, cross, norm, unit, add, sub, scale, triple, angle, project — each checked against an identity (Lagrange for the cross product, ‖â‖ = 1 for the unit vector, (a − proj)·b = 0 for the projection) and each carrying an ABSOLUTE rounding bound, so two near-perpendicular vectors whose dot product cancels to nothing come back OUT OF TOLERANCE instead of as a confident 0. Calculus: gradient, divergence, curl and laplacian of a field given as EXPRESSIONS, evaluated at a point — `{op:'curl', field:['-y','x','0'], at:{x:1,y:2,z:0}}`. The derivative is a central difference Richardson-extrapolated to O(h⁴), and the extrapolation's own disagreement IS the reported uncertainty. The step is scaled to the point, so a derivative at x = 1e8 is not pure rounding noise. cross and curl exist only in three dimensions and refuse anything else BY NAME rather than padding with zeros.\n  • quantum    — HILBERT-SPACE vectors and the operators on them. `quantum: {op, psi, phi, a, b, rho}`; amplitudes are numbers or [re, im] pairs. inner (⟨φ|ψ⟩, conjugating the LEFT argument), probability (the Born rule), norm, normalise, apply (Â|ψ⟩), expectation (⟨ψ|Â|ψ⟩/⟨ψ|ψ⟩), variance (⟨²⟩ − ⟨Â⟩²), commutator and anticommutator, outer (ρ = |ψ⟩⟨ψ|), trace, purity Tr(ρ²), the von Neumann entropy −Tr(ρ log ρ) by Jacobi on the real 2n × 2n embedding, and the Kronecker product |ψ⟩⊗|φ⟩. EVERY ONE IS CROSS-CHECKED against a property a wrong implementation cannot fake — Cauchy–Schwarz on the inner product, ⟨Â⟩ real for a Hermitian  with ‖ − †‖ reported so a non-observable cannot pass itself off as one, Var ≥ 0, ρ² = ρ for a pure state, Σλᵢ = Tr ρ — and the check must PASS for `verified`, because an expectation value that comes out complex is wrong however tight its rounding bound. A non-Hermitian ρ is REFUSED for the entropy rather than returned as a number that would look like one.\nTHE UNCERTAINTY IS MEASURED, NOT STAMPED — a closed-form cross-check against an independent numerical route, a Richardson step-doubling estimate, or the exact arithmetic bound — so `verified` means the bound was actually met. Every result is SEALED with an Ed25519 claim that carries its own recipe, so `zeq_hpz_verify` can RE-DERIVE the value offline instead of trusting this node. The claim also carries a `repro_digest` — SHA-256 over everything but the tick — so two claims of the SAME computation made at different times share it, and reproducibility is checkable with a hash rather than asserted. No API key required.","inputSchema":{"type":"object","properties":{"form":{"type":"string","description":"closed | operator | geometry | dynamical | integral | ode | pde | series | vector | quantum"},"expression":{"type":"string","description":"closed: e.g. \"2*G*M/c^2\" or \"sqrt(hbar*c/G)\""},"inputs":{"type":"object","description":"closed: a value for every free symbol, in HPZ units"},"dim":{"type":"array","description":"closed: SI dimensions [M,L,T,I,Θ,N,J] to convert the answer back","items":{"type":"number"}},"unit":{"type":"string","description":"a label for the receipt; never read by the maths"},"quantity":{"type":"string","description":"geometry: a | H | HDot | R | K | rho | P | V | rhoPlusP"},"t":{"type":"number","description":"geometry: time in Zeqonds (the geometry has period 2)"},"epsilon":{"type":"number","description":"geometry/dynamical: 0 < ε < 1, default 0.3"},"operator":{"type":"string","description":"operator: a registry id, e.g. GR37 or HOHMANN_TRANSFER"},"variable":{"type":"string","description":"integral/ode: the variable of integration (default x / t)"},"from":{"type":"number","description":"integral/ode: lower limit"},"to":{"type":"number","description":"integral/ode: upper limit"},"y0":{"type":"number","description":"ode: the initial value"},"product":{"type":"boolean","description":"series: true for the product instead of the sum"},"rtol":{"type":"number","description":"the tolerance the solver must hold; it is signed into the claim"},"atol":{"type":"number"},"pde":{"type":"object","description":"pde: {equation:'wave'|'heat'|'klein-gordon'|'schrodinger'|'hulyas', nx, length, boundary, tMax, frames, speed, diffusivity, muSq, lambda, phiC, couplingSum, jExt, background, potential, initial, mode, amplitude}"},"master":{"type":"object","description":"dynamical: {background:'minkowski'|'cubic-sine', muSq, lambda, phiC, beta, jExt, phi0, phiDot0, tMax, dt, rtol, atol, couplings:{<operatorId>: weight}}"},"quantum":{"type":"object","description":"quantum: {op:'inner'|'probability'|'norm'|'normalise'|'apply'|'expectation'|'variance'|'commutator'|'anticommutator'|'outer'|'trace'|'purity'|'entropy'|'tensor', psi, phi (states: arrays of numbers or [re,im] pairs), a, b (square matrices), rho (a density matrix)}"},"vector":{"type":"object","description":"vector: {op:'dot'|'cross'|'norm'|'unit'|'add'|'sub'|'scale'|'triple'|'angle'|'project'|'gradient'|'divergence'|'curl'|'laplacian', a, b, c, k, field (a string, or one string per coordinate), at (the point), vars (default x,y,z), h (the step)}"},"couplingCount":{"type":"number","description":"operators on the chain — the C term of the Functional Equation"},"wizard":{"type":"boolean","description":"true → run the seven-step wizard and return every step"}}}},{"name":"zeq_hpz_auto","description":"HulyaPulse-Zeqond AUTO — say what you want computed in plain English and it is routed, bound, computed and sealed. The query is scored against ALL 1,612 registry operators (id, name, description, category, equation, founder), quantities are extracted from the text with their units (\"1.989e30 kg\", \"5x10^14 Hz\", \"6371 km\") and bound to the chosen operator's symbols BY DIMENSION.\nIT REFUSES RATHER THAN GUESSES. If two symbols could take the same quantity it says so and returns the candidates; if the query supplies nothing for a symbol it names the symbol. The ranked candidate list is always returned, so the routing is inspectable instead of magical. Supply `inputs` to bind symbols the sentence does not carry. No API key required.","inputSchema":{"type":"object","properties":{"query":{"type":"string","description":"e.g. \"Schwarzschild radius of a 1.989e30 kg star\""},"inputs":{"type":"object","description":"explicit symbol bindings, in HPZ units, for anything the sentence does not say"}},"required":["query"]}},{"name":"zeq_hpz_verify","description":"Verify a sealed HulyaPulse-Zeqond claim WITHOUT trusting the node that produced it. Three independent checks: the Ed25519 signature over canonicalJson(claim); the claim's own inequality (precision_actual ≤ precision_bound, asserted only when verification is \"verified\"); and — the check a conventional receipt cannot offer — the VALUE, by re-running the recipe the claim carries inside its signature and comparing to 1e-12. Pass the `sealed` block from zeq_hpz verbatim. A value altered and then validly re-signed still fails, because the recipe no longer produces it. No API key required.","inputSchema":{"type":"object","properties":{"sealed":{"type":"object","description":"the {alg, public_key, claim, signature} block from zeq_hpz"}},"required":["sealed"]}},{"name":"zeq_protect","description":"ZeqPulseGuard — the PROTECT solver: a sealed protection heartbeat. Computes ZEQ-PROTECT-001 |sin(5ϕ)|/f_pulse and ZEQ-PROTECT-002 0.5+0.3·sin(t/30) from the live Zeqond phase, maps a liveness signal to a branch (healthy→bounded harmonic guard; down→hyperbolic alarm), applies the Zeq proper-time modulation R(t)=S(t)[1+α·sin(2π·1.287·t)], and returns guardState OK/DEGRADED/BREACH. Give t (unix seconds) or phase (radians), and health (up|slow|down) or liveness [0,1] or an HTTP status. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"t":{"type":"number","description":"unix seconds"},"phase":{"type":"number","description":"phase in radians"},"health":{"type":"string","description":"up | slow | down"},"liveness":{"type":"number","description":"0..1"},"status":{"type":"number","description":"HTTP status (200=up)"}}}},{"name":"zeq_api_catalog","description":"THE MAP - search the FULL public API surface of this Zeq node (883 public endpoints; admin routes are not exposed). Filter by q (substring across path+description), method, auth. Use this to discover endpoints, then call them with zeq_http.","inputSchema":{"type":"object","properties":{"q":{"type":"string","description":"Substring filter across path + description (e.g. 'tally envelopes', 'observer', 'state-machines')."},"method":{"type":"string","description":"Filter: GET | POST | PUT | PATCH | DELETE."},"auth":{"type":"string","description":"Filter: public | user | key | admin."},"limit":{"type":"number","description":"Max entries returned (default 40, max 200)."}}}},{"name":"zeq_http","description":"THE DOOR - call ANY public /api/* endpoint on this node directly (the full 883-endpoint public surface, not just the curated tools). Supports GET/POST/PUT/PATCH/DELETE and the new HTTP QUERY method (RFC 10008, June 2026): the safe, idempotent GET-with-a-body for complex data grabs - pass method QUERY with a JSON body and the node merges it into query params per the RFC semantics. Your Authorization bearer key is forwarded. Admin routes and /api/mcp itself are blocked. Discover endpoints with zeq_api_catalog first.","inputSchema":{"type":"object","required":["method","path"],"properties":{"method":{"type":"string","description":"GET | POST | PUT | PATCH | DELETE | QUERY (RFC 10008: safe GET-with-body - use for complex searches)"},"path":{"type":"string","description":"Endpoint path starting /api/ (e.g. /api/zeq/pulse, /api/mesh, /api/chain/state-machines/foundation)."},"query":{"type":"object","description":"Optional query params as a flat object."},"body":{"type":"object","description":"Optional JSON body for non-GET requests."}}}},{"name":"zeq_spin_up","description":"Spin up your own ZeqVM state machine and get a REAL, account-backed API key. REQUIRES authentication: pass a demo key as Authorization: Bearer zeq_ak_demo_… — if you have no key yet, first POST /api/demo-key/mint (free, no signup) to get one, then call this with it. Provisions a fresh machine (unique ZID), seeds its audit chain, and mints an active zeq_ak_ compute key on the free tier. Returns your ZID, recovery equation + salt (SHOWN ONCE — save them, there is no password reset), the machine slug, and the API key (SHOWN ONCE). Put the returned apiKey in your connector's Authorization header and every subsequent zeq_compute / zeq_solve / contract call runs on YOUR machine. (Every API key belongs to an account — there is no keyless minting.)","inputSchema":{"type":"object","properties":{"displayName":{"type":"string","description":"Optional label for your machine (e.g. your agent's name). Defaults to 'mcp-agent'."}}}},{"name":"zeq_contract_generate","description":"Draft a state contract from a plain-English description. The framework turns your intent into an operator-grounded contract definition on YOUR machine. Returns the definition — pass it to zeq_contract_deploy. Requires your zeq_ak_ key (from zeq_spin_up).","inputSchema":{"type":"object","required":["query"],"properties":{"query":{"type":"string","description":"8-600 chars: what the contract should do, its states, and transition conditions."}}}},{"name":"zeq_contract_templates","description":"List the 321 built-in state-contract templates (id + name) across every industry category. Deploy any with zeq_contract_deploy { templateId } — no LLM credential needed. Requires your zeq_ak_ key.","inputSchema":{"type":"object","properties":{}}},{"name":"zeq_contract_deploy","description":"Deploy a state contract to your machine. Every transition is ZeqProof-anchored on the entangled-state chain and visible in the Observer. Pass EITHER `templateId` (from zeq_contract_templates — works with no LLM credential) OR a full `definition` object (must include a version; from zeq_contract_generate). Requires your zeq_ak_ key.","inputSchema":{"type":"object","properties":{"templateId":{"type":"string","description":"Built-in template id to deploy (see zeq_contract_templates)."},"definition":{"type":"object","description":"A full custom contract definition (states, transitions, operators, conditions, version)."}}}},{"name":"zeq_contract_list","description":"List the state contracts on your machine — id, name, current state, and fire count. Requires your zeq_ak_ key.","inputSchema":{"type":"object","properties":{}}},{"name":"zeq_contract_get","description":"Get one contract's full state + definition by id. Requires your zeq_ak_ key.","inputSchema":{"type":"object","required":["id"],"properties":{"id":{"type":"string","description":"Contract id (from zeq_contract_list)."}}}},{"name":"zeq_contract_fire","description":"Fire a contract's next transition now. Returns a ZeqProof receipt; guarded transitions report their reason instead of firing. Requires your zeq_ak_ key.","inputSchema":{"type":"object","required":["id"],"properties":{"id":{"type":"string","description":"Contract id to advance."}}}},{"name":"zeq_observer","description":"Read the live entangled-state chain — your proof-of-computation feed. With no key it returns the global recent feed; with your zeq_ak_ key it focuses on YOUR machine's state. Each entry links to the Explorer.","inputSchema":{"type":"object","properties":{"limit":{"type":"number","description":"How many entries (1-50, default 15)."}}}},{"name":"zeq_publish_page","description":"Publish a live HTML page/app to your machine — instantly hosted at /s/<machine>/p/<pageSlug>/ and added to your machine launcher. Pass `title` and full `html` (optional `pageSlug`). Owner-authenticated. Requires your zeq_ak_ key (from zeq_spin_up).","inputSchema":{"type":"object","required":["title","html"],"properties":{"title":{"type":"string","description":"Page title."},"html":{"type":"string","description":"Full HTML markup of the page/app."},"pageSlug":{"type":"string","description":"URL slug (a-z0-9-, defaults to 'app')."}}}},{"name":"zeq_mail_html","description":"Build an HTML email and deliver it straight to YOUR OWN Zeq Mail inbox (<zid>@<your node's mail domain>), where you can review it and forward it on to anyone. This does NOT send to third parties — it only ever delivers to the mailbox of the identity making the call, so an agent cannot be talked into mailing strangers. Use it to draft newsletters, announcements and campaigns: compose the markup, deliver it here, open Zeq Mail, then hit Forward. Write email HTML, not web-page HTML — table layout, all CSS inline, absolute https:// links, max 600px wide. Scripts, forms and iframes are stripped on arrival. Owner-authenticated: requires your zeq_ak_ key (from zeq_spin_up).","inputSchema":{"type":"object","required":["subject","html"],"properties":{"subject":{"type":"string","description":"Subject line of the email."},"html":{"type":"string","description":"The email body as HTML (fragment or full document)."},"text":{"type":"string","description":"Optional plain-text alternative. Generated from the HTML if omitted — always sent, because an empty text part reads blank in text-only clients."},"from":{"type":"string","description":"Optional display name to attribute the draft to, e.g. 'Campaign Builder'. Cosmetic only; delivery is always to your own mailbox."}}}},{"name":"zeq_compute","description":"Compute physics results using the Zeq.dev HulyaSync framework. Applies 1,600+ catalogued operators across 67 domains (19 closed-form solvers; coverage map published). Every result is phase-stamped to the HulyaPulse (1.287 Hz system clock) and returned as a ZeqState envelope with masterSum R(t), phase φ, Zeqond τ, and an explicit numeric-accuracy bound. KO42 is always included. Response includes a zeqProof HMAC for tamper-evident verification. Requires a valid zeq_ak_ API key in the Authorization header.","inputSchema":{"type":"object","required":["domain","inputs"],"properties":{"domain":{"type":"string","description":"Physics domain to compute in. Examples: quantum-mechanics, classical-mechanics, thermodynamics, fluid-dynamics, aerospace, electromagnetism, astrophysics, biomedical, materials-science. 67 domains are available — use zeq_list_operators to see all."},"inputs":{"type":"object","description":"Key-value pairs of numeric domain inputs — use the keys the solver actually reads. Example for quantum-mechanics (particle in a box): {\"n\": 1, \"L\": 1e-10, \"m\": 9.109e-31} → E_n eigenvalue. Unrecognized keys are rejected by the dimensional gate (value: NaN), so match the domain's documented inputs. Values must be finite numbers.","additionalProperties":{"type":"number"}},"operators":{"type":"array","items":{"type":"string"},"description":"Optional list of specific operator IDs to apply (e.g. ['QM01', 'QM03']). KO42 is always added automatically. If omitted, the domain default operator is used. Use zeq_list_operators to discover available IDs per domain."},"folder":{"type":"string","description":"Optional folder name to file this computation under (e.g. 'Orbital Mechanics'). Computations sharing a folder group together: each folder becomes a tab in the state explorer and a directory in the user's ZeqGit 'computations' repo (open in Zeq Studio). Reuse the same name to keep adding to it; omit for the 'unfiled' catch-all. When a user is running several related computes, ask if they want to name a folder."}}}},{"name":"zeq_list_operators","description":"List available Zeq.dev physics operators for a given domain, or list all 67 domains. Use this to discover operator IDs before calling zeq_compute. No API key required.","inputSchema":{"type":"object","properties":{"domain":{"type":"string","description":"Domain to list operators for. Omit or pass empty string to list all 67 domains."}}}},{"name":"zeq_paper_search","description":"Search the scientific literature across arXiv, OpenAlex, Crossref and Europe PMC in one call. Returns deduplicated results with a canonical id (arxiv:… / doi:… / pmid:…), title, authors, date, venue and abstract snippet. Use this INSTEAD of answering a literature question from memory — a citation you did not look up is a guess. No API key required.","inputSchema":{"type":"object","required":["q"],"properties":{"q":{"type":"string","description":"Search query, e.g. 'AlphaFold protein structure prediction'."},"sources":{"type":"array","items":{"type":"string"},"description":"Optional subset of: arxiv, openalex, crossref, europepmc, semanticscholar, biorxiv. Defaults to the four that work without a key."},"limit":{"type":"number","description":"Max results, 1-50. Default 20."}}}},{"name":"zeq_paper_fetch","description":"Fetch one scientific record by canonical id — 'arxiv:1706.03762', 'doi:10.1038/s41586-021-03819-2', 'pmid:34265844'. Returns the full record including abstract where the source provides one. Use this to verify a citation before repeating it. No API key required.","inputSchema":{"type":"object","required":["id"],"properties":{"id":{"type":"string","description":"Canonical id in 'scheme:local' form. Schemes: arxiv, doi, pmid, openalex, s2, biorxiv."}}}},{"name":"zeq_domain_match","description":"Given a paper (canonical id) or any text, return which of the 67 Zeq operator domains it plausibly falls in, with the exact vocabulary terms that fired as evidence. Use this to ask 'could the framework compute this?' before claiming it can. IMPORTANT: this is deterministic term overlap, NOT a solvability proof — 258 of 1,612 operators (16%) have their own equation evaluated, so a domain match means 'worth testing with zeq_solve', never 'solvable'.","inputSchema":{"type":"object","properties":{"id":{"type":"string","description":"Canonical id — arxiv:1706.03762, doi:10.1038/…, pmid:…"},"text":{"type":"string","description":"Raw text to classify, if you have no id."},"limit":{"type":"number","description":"Max domains to return, 1-12. Default 5."}}}},{"name":"zeq_science_domains","description":"List the 67 Zeq operator domains and which literature sources serve each. Use before zeq_paper_search to scope a search: applied/industry domains (ENERGY, FIN, ENG, MAT) are served by Crossref + OpenAlex, physics and CS by arXiv, biomedical by Europe PMC. Scoping measurably improves precision. No API key required.","inputSchema":{"type":"object","properties":{}}},{"name":"zeq_find_operator","description":"Find operators by name, id, equation or description — ONE call instead of paging through domains. Returns id, domain, PREFIX (what zeq_compute takes), tier, equation and the domain's accepted input keys. No API key required.","inputSchema":{"type":"object","required":["term"],"properties":{"term":{"type":"string","description":"Search term, e.g. 'schwarzschild', 'kinetic', 'QM9', 'entropy'."},"limit":{"type":"number","description":"Max matches (default 12, max 40)."}}}},{"name":"zeq_pulse","description":"Get the current ZeqPulse state — live Zeqond counter, HulyaPulse phase φ, and R(t) value. No API key required. Use this to read the real-time 1.287 Hz heartbeat of the Zeq.dev framework and synchronize agent operations to the HulyaPulse clock.","inputSchema":{"type":"object","properties":{}}},{"name":"zeq_verify","description":"Verify a ZeqProof HMAC returned by zeq_compute. Confirms the response (including the physics value, for v2 receipts) reached you unmodified — integrity, not independent re-derivation of the physics. Pass the proof string along with operatorIds, R_t, zeqond, value, unit, and the keyPrefix from the original response. Returns valid: true/false. Requires API key.","inputSchema":{"type":"object","required":["proof","operatorIds","R_t","zeqond"],"properties":{"proof":{"type":"string","description":"The 64-character hex zeqProof HMAC from the compute response (field: zeqProof)."},"operatorIds":{"type":"array","items":{"type":"string"},"description":"Operator IDs array from the original zeqState.operators field."},"R_t":{"type":"number","description":"The masterSum value from the original zeqState.masterSum field."},"zeqond":{"type":"number","description":"The zeqond value from the original zeqState.zeqond field."},"keyPrefix":{"type":"string","description":"Optional keyPrefix from the original response. Defaults to the API key user ID prefix."},"value":{"type":"number","description":"The physics value from the original response (required for v2 receipts, which sign the value)."},"unit":{"type":"string","description":"The unit string from the original response (v2 receipts)."}}}},{"name":"zeq_lattice","description":"Compute a ZeqLattice — a multi-node coherence grid. Pass an array of 2–5 node specs, each with optional { domain, inputs }. All nodes share one Date.now() timestamp but run at staggered HulyaPulse phases. Returns per-node R_t, coherenceScore (0–1), and lattice equation. Counts as N compute tokens (one per node). Requires API key.","inputSchema":{"type":"object","required":["nodes"],"properties":{"nodes":{"type":"array","description":"Array of 2–5 node specifications, each with optional domain and inputs.","minItems":2,"maxItems":5,"items":{"type":"object","properties":{"domain":{"type":"string","description":"Physics domain for this node (same options as zeq_compute)."},"inputs":{"type":"object","description":"Numeric key-value physics inputs for this node.","additionalProperties":{"type":"number"}}}}}}}},{"name":"zeq_shift","description":"Compute a ZeqShift — a deterministic forward time-series projection of R(t) across up to 64 Zeqond steps. Each step advances by 0.777 s (one Zeqond) and returns t (absolute seconds), phase φ, zeqond τ, R_t, and delta (R_t change from previous step; 0 for step 0). Counts as N compute tokens (one per step). Requires API key.","inputSchema":{"type":"object","properties":{"steps":{"type":"number","description":"Number of Zeqond steps to project forward (1–64, default 16)."},"domain":{"type":"string","description":"Physics domain (optional, defaults to Quantum Mechanics)."},"inputs":{"type":"object","description":"Numeric key-value physics inputs for S(t) computation.","additionalProperties":{"type":"number"}}}}},{"name":"zeq_field_status","description":"Query the ZeqField security system status — cipher algorithm, key source, and protocol versions. Returns whether ZEQ_FIELD_KEY is configured, current PBKDF2 parameters, and ZeqProof HMAC settings. No API key required.","inputSchema":{"type":"object","properties":{}}},{"name":"zeq_solve","description":"Integrates the geodesic in the KO42-tensioned metric  ds² = gμν dxμ dxν + α·sin(2π·1.287·t)·dt²  and returns the trajectory φ(t), the register dump, the HULYAS functional energy E = P_φ · Z(M,R,δ,C,X), and the term-by-term diagnostic. The base metric carries the REAL physics selected by the operators (7-step SELECT→BIND): NM19/NM24 → free-fall −g; NM21 (+ real `position` in metres) → radial gravity −GM/x²; NM30 → SHM −ω²x; GR33–38 add the weak-field g₀₀ factor √(1−2GM/xc²) (relativity, in the metric). The KO42 metric tension rides on top for every domain — the unification — so R(t)=S(t)[1+α·sin] reduces to textbook mechanics within the α≈1.29e-3 band and its Zeqond-average recovers S(t) exactly. `errorPct` is a TOLERANCE CEILING (≤0.1% confirms 'computed within physical law'), not an error rate. Use REAL numbers and REAL positions. (`zeq_compute` is the exact static closed-form path.) Requires zeq_ak_ API key.","inputSchema":{"type":"object","required":["prompt"],"properties":{"prompt":{"type":"string","description":"Label only — never read by math. Max 500 chars."},"mass":{"type":"number","description":"Object mass in kg. Default 1.0."},"location":{"type":"string","description":"Categorical: earth | mars | moon | jupiter | sun."},"medium":{"type":"string","description":"Categorical: air | water | vacuum."},"object":{"type":"string","description":"Free-form object label — not read by math."},"alpha":{"type":"number","description":"KO42.1 amplitude. Default 1.0."},"beta":{"type":"number","description":"KO42.2 amplitude. Default 0.0."},"koSettings":{"type":"object","description":"Operator weights, keyed by operator ID (e.g. { KO42: 1.0, NM21: 0.5, GR35: 0.3 }).","additionalProperties":{"type":"number"}},"tMax":{"type":"number","description":"Simulation horizon in seconds. Clamped to [0.1, 30]. Default 5.0."},"position":{"type":"number","description":"Real starting position/radius in METRES for gravity mode (a=−GM/x²). Real numbers only — not toy units."},"dt":{"type":"number","description":"Integrator timestep. Clamped to [0.001, 0.1]. Default 0.01."},"useOperatorModules":{"type":"boolean","description":"Use operator-specific physics values (SDK formula path)."},"normalizeOperators":{"type":"boolean","description":"Default true: normalise operator values by reference scale."},"coreOnly":{"type":"boolean","description":"Restrict coupling to the 8 Core Operator Families."},"referenceMode":{"type":"string","enum":["free-fall","shm","gravity","model"],"description":"Base-metric law: free-fall (−g), shm (−ω²x), gravity (−GM/x², needs `position`), or model. Operators (NM19/NM21/NM24/NM30, GR33–38) also select it automatically."},"strict":{"type":"boolean","description":"ALWAYS ON (2026-08-10 — same rule as the REST route since 2026-08-01): every solve autotunes β + operator weights to drive the precision bound vs the chosen referenceMode to ≤ 0.1 %, and REFUSES to seal anything still outside it. This flag is accepted and ignored; there is no opt-out. Honest — returns tuneStatus 'converged' (tolerance met) or a refusal (never a faked pass)."},"maxIterations":{"type":"number","description":"Strict-mode autotune budget (1–40). Default 40."},"folder":{"type":"string","description":"Optional folder name to file this solve under. Computations sharing a folder group into a tab in the state explorer and a directory in the user's ZeqGit 'computations' repo (open in Zeq Studio). Reuse the name to append; omit for the 'unfiled' catch-all."}}}},{"name":"zeq_multibody","description":"Run the vector master equation: N coupled φ_i(t) trajectories with pairwise inverse-square coupling. Each body gets its own register dump; every pair returns mean/final force magnitude + separation statistics. Use for Sun-Earth-Moon-style three-body experiments. Strictly mathematical — math reads only the numerical/categorical fields. Requires zeq_ak_ API key.","inputSchema":{"type":"object","required":["prompt","bodies"],"properties":{"prompt":{"type":"string","description":"Label only — never read by math."},"bodies":{"type":"array","minItems":2,"maxItems":16,"description":"Array of body specs (2–16 bodies).","items":{"type":"object","required":["mass"],"properties":{"mass":{"type":"number","description":"Body mass in kg."},"location":{"type":"string","description":"earth | mars | moon | jupiter | sun."},"medium":{"type":"string","description":"air | water | vacuum."},"object":{"type":"string","description":"Free-form label."},"phi0":{"type":"number","description":"Optional explicit initial φ."},"dphi0":{"type":"number","description":"Optional explicit initial dφ/dt."},"position":{"type":"number","description":"Real 1-D position in METRES. If every body has one, runs REAL Newtonian gravity (G, real r) instead of the dimensionless φ-field."}}}},"alpha":{"type":"number"},"beta":{"type":"number"},"koSettings":{"type":"object","additionalProperties":{"type":"number"},"description":"Operator weights shared across all bodies."},"tMax":{"type":"number"},"dt":{"type":"number"},"pairwiseCoupling":{"type":"number","description":"γ in the pairwise term. Default 0.05."},"pairwiseSoftening":{"type":"number","description":"ε² softening. Default 1e-6."},"useOperatorModules":{"type":"boolean"},"normalizeOperators":{"type":"boolean"},"coreOnly":{"type":"boolean"},"folder":{"type":"string","description":"Optional folder name to file this multibody run under. Computations sharing a folder group into a tab in the state explorer and a directory in the user's ZeqGit 'computations' repo (open in Zeq Studio). Reuse the name to append; omit for 'unfiled'."}}}},{"name":"zeq_evolve","description":"Run ZeqEvolve — deterministic Nano-Zeqond MOLECULAR DYNAMICS: velocity-Verlet (2nd-order symplectic) integration of a Lennard-Jones system (NM19) with optional harmonic bonds (NM30) in the NVE ensemble. Presets: lj-liquid, lj-gas, crystal, polymer. Returns the energy-conservation drift (the ≤0.1% reality check), temperature, virial pressure and total momentum, plus a ZEQOND_RECEIPT of the real fields it produced. Same inputs reproduce the same run (seeded). Real physics for materials/soft-matter/biology sandboxes. Requires zeq_ak_ API key.","inputSchema":{"type":"object","properties":{"preset":{"type":"string","description":"lj-liquid | lj-gas | crystal | polymer. Default lj-liquid."},"N":{"type":"number","description":"Particle count (2–2000). Default from preset."},"rho":{"type":"number","description":"Number density N/area (reduced units)."},"T0":{"type":"number","description":"Initial temperature (reduced units)."},"steps":{"type":"number","description":"Velocity-Verlet steps (10–200000). Default 2000."},"dtSim":{"type":"number","description":"MD time step, reduced units. Default 0.003 (VV-stable)."},"eps":{"type":"number","description":"Lennard-Jones ε. Default 1."},"sig":{"type":"number","description":"Lennard-Jones σ. Default 1."},"rc":{"type":"number","description":"Cutoff in units of σ. Default 2.5."},"kBond":{"type":"number","description":"Harmonic bond stiffness (polymer). Default 30."},"r0Bond":{"type":"number","description":"Bond rest length. Default 1."},"seed":{"type":"number","description":"Seed for reproducibility. Omit → deterministic seed derived from the inputs."},"sample":{"type":"number","description":"Energy samples in the returned series (2–500). Default 40."},"folder":{"type":"string","description":"Optional folder to file this run under (groups in the explorer + ZeqGit)."}}}},{"name":"zeq_action","description":"Run ZeqAction — a least-action, HIGH-ORDER SYMPLECTIC integrator (Störmer-Verlet → Yoshida triple-jump, order 4/6/8, fixed dt, Kahan-compensated). Structure-preserving, so energy has NO secular drift. Systems: kepler (orbit), oscillator (anharmonic), pendulum. It ALSO runs classical RK4 on the same system and returns both drifts, proving the difference — symplectic stays bounded, RK4 drifts (the orbit decays). The reality check for long-horizon dynamics. Requires zeq_ak_ API key.","inputSchema":{"type":"object","properties":{"system":{"type":"string","description":"kepler | oscillator | pendulum. Default kepler."},"order":{"type":"number","description":"Symplectic composition order: 2 | 4 | 6 | 8. Default 4."},"steps":{"type":"number","description":"Integration steps (10–2,000,000). Default 20000."},"dt":{"type":"number","description":"Fixed time step (symplecticity needs it constant). Default 0.01."},"eccentricity":{"type":"number","description":"Kepler orbit eccentricity 0–0.98. Default 0.6."},"mu":{"type":"number","description":"Kepler gravitational parameter. Default 1."},"omega":{"type":"number","description":"Oscillator frequency. Default 1."},"lambda":{"type":"number","description":"Oscillator quartic anharmonicity. Default 1."},"q0":{"type":"number","description":"Initial coordinate (oscillator/pendulum)."},"p0":{"type":"number","description":"Initial momentum (oscillator/pendulum)."},"compare":{"type":"boolean","description":"Also run RK4 to show the drift difference. Default true."},"sample":{"type":"number","description":"Series points returned (2–500). Default 60."},"folder":{"type":"string","description":"Optional folder to file this run under."}}}},{"name":"zeq_heat","description":"ZeqHeat — 2-D heat/diffusion ∂T/∂t=α(∂²T/∂x²+∂²T/∂y²) on a grid (the default). method 'explicit' (FTCS, conditionally stable — blows up past the 2-D CFL r=α·dt·(1/dx²+1/dy²)=½) or 'implicit' (ADI Peaceman–Rachford, UNCONDITIONALLY stable). Compared to the exact 2-D Fourier-mode decay. Fills temperature_field + heat_flux_vector. Pass dim:1 (or L, or the 1-D `mode`) for the original 1-D bar. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"method":{"type":"string","description":"explicit | implicit (default)"},"nx":{"type":"number","description":"grid points in x (8–128)"},"ny":{"type":"number","description":"grid points in y (8–128)"},"kx":{"type":"number","description":"Fourier mode in x"},"ky":{"type":"number","description":"Fourier mode in y"},"alpha":{"type":"number"},"dt":{"type":"number"},"steps":{"type":"number"},"dim":{"type":"number","description":"1 for the 1-D bar"},"mode":{"type":"number","description":"1-D Fourier mode (selects the 1-D bar)"},"folder":{"type":"string"}}}},{"name":"zeq_lorenz","description":"ZeqLorenz — the Lorenz attractor (RK4), deterministic chaos. Checks the exact phase-volume contraction −(σ+1+β) and measures the Lyapunov exponent (butterfly effect) from a twin trajectory. Bounded strange attractor, reproduced bit-for-bit. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"sigma":{"type":"number"},"rho":{"type":"number"},"beta":{"type":"number"},"dt":{"type":"number"},"steps":{"type":"number"},"delta":{"type":"number","description":"twin separation for the Lyapunov estimate"},"folder":{"type":"string"}}}},{"name":"zeq_wave","description":"ZeqWave — 2-D MEMBRANE wave ∂²u/∂t²=c²(∂²u/∂x²+∂²u/∂y²) by leapfrog (the default), reality-checked by EXACT discrete-energy conservation (drift ~1e-13) and against the standing mode ω=cπ√(kx²/Lx²+ky²/Ly²). 2-D Courant C=c·dt·√(1/dx²+1/dy²)≤1 or it explodes. Pass mode:'maxwell' for 1-D Maxwell (Yee FDTD), or dim:1 / mode_k for the 1-D scalar wave. Fills displacement/velocity (or E,B in maxwell). Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"mode":{"type":"string","description":"membrane (default) | maxwell | wave1d"},"nx":{"type":"number","description":"grid x (16–128)"},"ny":{"type":"number","description":"grid y (16–128)"},"kx":{"type":"number","description":"2-D mode in x"},"ky":{"type":"number","description":"2-D mode in y"},"c":{"type":"number"},"dt":{"type":"number"},"courant":{"type":"number","description":"target 2-D Courant (default 0.5)"},"steps":{"type":"number"},"dim":{"type":"number","description":"1 for the 1-D scalar wave"},"mode_k":{"type":"number","description":"1-D Fourier mode (selects 1-D)"},"eps":{"type":"number"},"mu":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_flow","description":"ZeqFlow — 2-D incompressible Navier–Stokes (Stam stable fluids): advect + diffuse + pressure PROJECTION so ∇·u→0. Reports divergence before/after projection. Fills velocity/pressure/viscosity. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"N":{"type":"number","description":"grid size (8–160)"},"steps":{"type":"number"},"dt":{"type":"number"},"visc":{"type":"number"},"iters":{"type":"number","description":"Poisson iterations"},"folder":{"type":"string"}}}},{"name":"zeq_fracture","description":"ZeqFracture — 2-D bond-based peridynamic CRACK PROPAGATION (mode-I SENT, the default): a seeded edge notch either holds below a critical far-field strain, or the crack initiates at the tip and runs across the specimen above it (unstable fracture). Reports crack tip, advance, whether it spanned, critical strain. Fills the material+boundary receipt tier: stress, strain, damage, elasticity, boundary_traction, contact. Pass mode:\"bar\" (or an N) for the 1-D cohesive bar. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"mode":{"type":"string","description":"\"2d\" (default, crack propagation) | \"bar\" (1-D)"},"nx":{"type":"number","description":"2-D grid width (16–64)"},"ny":{"type":"number","description":"2-D grid height (8–40)"},"notchFrac":{"type":"number","description":"2-D starter-notch length as a fraction of width (0.1–0.6)"},"horizonM":{"type":"number","description":"peridynamic horizon in grid spacings (2–4)"},"N":{"type":"number","description":"1-D bar node count (selects mode:bar)"},"E":{"type":"number"},"strain":{"type":"number","description":"max applied far-field strain"},"s0":{"type":"number","description":"critical bond stretch"},"sf":{"type":"number","description":"1-D full-failure stretch"},"loadSteps":{"type":"number"},"relaxIters":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_react","description":"ZeqReact — reaction–diffusion (biology). model 'gray-scott' (Turing morphogenesis: spots/stripes/worms self-organise) or 'fitzhugh-nagumo' (excitable media: cardiac/neural travelling & spiral waves). 2-D grid, explicit. Stability D·dt/dx²≤¼ or it blows up. Fills the chemical/biological receipt tier (concentration + reaction rate). Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"model":{"type":"string","description":"gray-scott | fitzhugh-nagumo"},"N":{"type":"number","description":"grid size (16–400)"},"steps":{"type":"number"},"dt":{"type":"number"},"Du":{"type":"number"},"Dv":{"type":"number"},"F":{"type":"number","description":"Gray-Scott feed"},"k":{"type":"number","description":"Gray-Scott kill"},"epsilon":{"type":"number"},"a":{"type":"number"},"b":{"type":"number"},"I":{"type":"number","description":"FitzHugh-Nagumo stimulus"},"folder":{"type":"string"}}}},{"name":"zeq_epi","description":"ZeqEpi — SIR/SEIR epidemic dynamics (RK4). Reality check: population conserved. Reports R₀, peak infected, peak day, final size (Kermack–McKendrick). Public-health domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"model":{"type":"string","description":"sir | seir"},"beta":{"type":"number"},"gamma":{"type":"number"},"sigma":{"type":"number"},"N":{"type":"number"},"I0":{"type":"number"},"days":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_quant","description":"ZeqQuant — European option price by Monte-Carlo, verified against the closed-form Black–Scholes. Reports price, standard error, delta. Quant-finance domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"type":{"type":"string","description":"call | put"},"S0":{"type":"number"},"K":{"type":"number"},"r":{"type":"number"},"sigma":{"type":"number"},"T":{"type":"number"},"paths":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_zeta","description":"ZeqZeta — locate Riemann zeta nontrivial zeros on the ½-line (Riemann–Siegel) and VERIFY the count against N(T)=θ(T)/π+1 up to height T. Verifies RH in range; does NOT prove it. Number-theory domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"T":{"type":"number","description":"height up to which to verify (15–2000)"},"dt":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_sat","description":"ZeqSAT — DPLL 3-SAT solver on a seeded random instance at ratio α=m/n (hardness peaks ≈4.26). Certifies SAT assignments; reports decisions/propagations (the NP-hard scaling). Solves instances; does NOT resolve P vs NP. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"n":{"type":"number","description":"variables (3–120)"},"alpha":{"type":"number","description":"clause/variable ratio"},"m":{"type":"number"},"seed":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_gauge","description":"ZeqGauge — 2-D compact U(1) lattice gauge theory (Metropolis). Mean plaquette verified against the EXACT Bessel result I₁(β)/I₀(β). The method used to study Yang–Mills numerically; does NOT prove the mass-gap theorem. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"L":{"type":"number","description":"lattice size (4–64)"},"beta":{"type":"number"},"sweeps":{"type":"number"},"seed":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_fea","description":"ZeqFEA — 2-D plane-stress finite-element cantilever (Q4, matrix-free element-by-element Jacobi-preconditioned CG — memory O(dof), so LARGE meshes run: up to ~9000 elements). Tip deflection vs Euler–Bernoulli beam theory; refine the mesh and the ratio CONVERGES to ~1.00 (coarse 24×6 is ~0.94, refined 120×30 is ~1.00). Reports von Mises stress, CG residual. Fills stress/strain/displacement/elasticity. Structural-engineering domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"nx":{"type":"number","description":"elements along length (4–220, default 120)"},"ny":{"type":"number","description":"elements through depth (2–80, default 30)"},"Lx":{"type":"number"},"Ly":{"type":"number"},"E":{"type":"number"},"P":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_grid","description":"ZeqGrid — DC power-flow on an N-bus network (B·θ=P). Reality check: Kirchhoff's current law + power balance. Reports bus angles, line flows, max loading. Power-systems domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"N":{"type":"number","description":"buses (3–300)"},"chords":{"type":"number"},"reactance":{"type":"number"},"seed":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_device","description":"ZeqDevice — 2-D device ELECTROSTATICS (the default): the potential + field in a semiconductor cross-section under an electrode, solving ∇²φ=0 by matrix-free Jacobi-preconditioned CG, verified against the EXACT analytic solution (a sinh Fourier mode) to ~0.004% — the peak |E| sets breakdown (MOSFET/HEMT/diode design). Pass dim:1 (or Na/Nd) for the 1-D PN junction (built-in voltage V_bi=V_T·ln(NaNd/ni²) vs Poisson). Fills potential + E-field. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"nx":{"type":"number","description":"2-D grid x (16–220)"},"ny":{"type":"number","description":"2-D grid y (16–220)"},"Lx":{"type":"number"},"Ly":{"type":"number"},"V":{"type":"number","description":"electrode voltage"},"kx":{"type":"number","description":"electrode mode"},"dim":{"type":"number","description":"1 for the PN junction"},"Na":{"type":"number","description":"1-D acceptor doping (m⁻³) — selects PN junction"},"Nd":{"type":"number","description":"1-D donor doping (m⁻³)"},"ni":{"type":"number"},"T":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_opt","description":"ZeqOpt — nonlinear optimization: minimise a test function (sphere, rosenbrock, rastrigin, beale) by Nelder–Mead or gradient descent, checked against the KNOWN global minimum. Operations-research / ML / design domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"fn":{"type":"string","description":"sphere | rosenbrock | rastrigin | beale"},"method":{"type":"string","description":"nelder-mead | gradient"},"dim":{"type":"number"},"maxIter":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_climate","description":"ZeqClimate — 2-D shallow-water equations (Lax–Friedrichs), a droplet radiating gravity waves. Reality check: total mass conserved; CFL √(gH)dt/dx≤1. Fills velocity + height. Climate / geophysics / oceanography domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"N":{"type":"number"},"steps":{"type":"number"},"g":{"type":"number"},"H":{"type":"number"},"dt":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_unified","description":"ZeqUnifiedComposer -- compose MULTIPLE operators in ONE call. Give an operator chain (KO42 is auto-prepended) plus numeric inputs; each operator is evaluated formula-as-data (no eval) and composed: Strategy A (algebraic product under the KO42 frame), B (sequential Zeqond timeline, RK4 for ODE operators), or C (single-operator fallback). Operators may be ids (GR37, NM19, NM21, QM9, ORBIT_PERIOD, NM23/24/26, GR35/36/41, QM10) or {id, equation, unit?, kind?} objects for ANY formula-as-data expression. Returns the composed value, the method, per-operator intermediates and the compiled expression, sealed like every solver. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"operators":{"type":"array","description":"operator ids and/or {id, equation, unit?, kind?} objects; KO42 auto-prepended","items":{}},"inputs":{"type":"object","description":"numeric inputs used by the operator equations (mass, m, v, r, a, ...)"},"consts":{"type":"object","description":"optional overrides: t, alpha, f_H, T_Z"},"folder":{"type":"string"}}}},{"name":"zeq_dock","description":"ZeqDock — rigid-body molecular docking: minimise a Lennard-Jones + Coulomb score over the ligand's 6 DOF against a receptor pocket, from seeded restarts. Reports binding energy + pose. Drug-discovery / comp-chem domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"restarts":{"type":"number"},"iters":{"type":"number"},"seed":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_buckling","description":"ZeqBuckling — the Euler critical buckling load of a compressed column/strut: the axial load P_cr at which a slender member collapses (columns, struts, landing gear, rocket interstages, scaffolding). Solves the beam-column buckling generalised eigenproblem K φ=P·K_g φ from Hermitian Euler–Bernoulli beam finite elements (Cholesky reduction + Jacobi), the smallest positive P being P_cr. Checked against EULER's exact P_cr=π²·EI/(K·L)² for the end condition — pinned-pinned K=1, fixed-fixed K=0.5, fixed-free K=2, fixed-pinned K≈0.699. RMS error vs Euler is the seal (a coarse mesh seals observable-differential). Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"ends":{"type":"string","description":"\"pinned-pinned\" (default), \"fixed-fixed\", \"fixed-free\", \"fixed-pinned\""},"EI":{"type":"number","description":"flexural rigidity E·I (N·m²)"},"E":{"type":"number","description":"Young's modulus (Pa)"},"I":{"type":"number","description":"second moment of area (m⁴)"},"L":{"type":"number","description":"column length (m)"},"ne":{"type":"number","description":"elements (4–80)"},"folder":{"type":"string"}}}},{"name":"zeq_acoustic","description":"ZeqAcoustic — the resonant modes of a 1-D acoustic resonator (Helmholtz −p″=k²p): the standing-wave frequencies of an organ pipe, wind instrument, exhaust/HVAC duct or muffler. Each end is OPEN (pressure-release) or CLOSED (rigid); a finite-volume + half-cell-mass discretisation gives a symmetric tridiagonal solved by Sturm bisection, and the frequencies f=kc/2π are checked against the EXACT closed forms — open–open n·c/2L, open–closed (2n−1)·c/4L, closed–closed n·c/2L. RMS error vs exact is the seal (a coarse grid seals observable-differential). Reports the fundamental + overtones in Hz. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"ends":{"type":"string","description":"\"open-open\" (default), \"open-closed\", or \"closed-closed\""},"L":{"type":"number","description":"resonator length (m)"},"c":{"type":"number","description":"sound speed (m/s), default 343"},"N":{"type":"number","description":"cells (64–6000)"},"modes":{"type":"number","description":"resonances to return (1–16)"},"folder":{"type":"string"}}}},{"name":"zeq_schrodinger","description":"ZeqSchrodinger — the time-independent Schrödinger eigenvalue problem Ĥψ=Eψ, Ĥ=−(ℏ²/2m)d²/dx²+V(x): the quantum bound-state ENERGY LEVELS behind atoms, quantum wells/dots, molecular vibration and the qubit. A finite-difference tridiagonal Hamiltonian is diagonalised by Sturm-sequence bisection (robust, deterministic) and its lowest levels are checked against the EXACT analytic spectrum — harmonic oscillator Eₙ=ℏω(n+½), infinite square well Eₙ=n²π²ℏ²/2mL². The RMS error vs exact is the seal (life-or-death: too coarse a grid or too small a box gives WRONG levels and seals observable-differential). Natural units ℏ=m=1. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"potential":{"type":"string","description":"\"harmonic\" (default) or \"square-well\""},"N":{"type":"number","description":"grid points (64–4000)"},"levels":{"type":"number","description":"eigenvalues to return (1–12)"},"omega":{"type":"number","description":"harmonic frequency ω"},"L":{"type":"number","description":"square-well width"},"folder":{"type":"string"}}}},{"name":"zeq_tumor","description":"ZeqTumor — Fisher–KPP growth front ∂u/∂t=D u_xx+r u(1−u): a population/tumor/gene that grows AND spreads, invading as a travelling front (oncology, invasion biology, gene spread, spatial epidemics). Reality checks: the density stays in [0,1] (the seal — a stable scheme holds it, an unstable one past CFL D·dt/dx²≤½ violates it and explodes), and the front advances at the EXACT Ablowitz–Zeppetella speed c=5√(rD/6) (verified to ~0.2%). Reports front speed, boundedness, pointwise error vs the exact wave. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"D":{"type":"number","description":"diffusion (spread rate)"},"r":{"type":"number","description":"growth rate"},"nx":{"type":"number","description":"grid points (50–2000)"},"L":{"type":"number","description":"domain length"},"x0":{"type":"number","description":"initial front position"},"dt":{"type":"number"},"steps":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_lotka","description":"ZeqLotka — predator–prey / ecosystem dynamics (Lotka–Volterra). dx/dt=αx−βxy, dy/dt=δxy−γy. Reality check: the first integral H=δx−γ·ln x+βy−α·ln y is conserved on every orbit — RK4 (default) holds it to ~1e-9 (the seal), forward-Euler drifts and the populations spiral to a FALSE extinction/explosion (the life-or-death). Reports the boom-bust extremes, cycle period, and coexistence fixed point (γ/δ, α/β). Fisheries, pest control, conservation biology. method 'rk4'|'symplectic'|'euler'. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"method":{"type":"string","description":"rk4 (default) | symplectic | euler"},"alpha":{"type":"number","description":"prey growth"},"beta":{"type":"number","description":"predation rate"},"delta":{"type":"number","description":"predator growth from prey"},"gamma":{"type":"number","description":"predator death"},"x0":{"type":"number","description":"initial prey"},"y0":{"type":"number","description":"initial predator"},"dt":{"type":"number"},"steps":{"type":"number"},"folder":{"type":"string"}}}},{"name":"zeq_kalman","description":"ZeqKalman — optimal state estimation (the Kalman filter): track a constant-velocity target from noisy position measurements (GPS/radar/robotics/sensor-fusion/navigation). Reality checks: the error covariance converges to the steady-state Riccati/DARE solution (the seal, → machine precision); empirical RMSE → √P∞ (optimality); innovation variance ≈ HP⁻Hᵀ+R (whiteness); the Joseph-form update keeps the covariance positive-definite (a naive update diverges). Deterministic (seeded). State-estimation / control domain. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"steps":{"type":"number","description":"filter steps (50–20000)"},"dt":{"type":"number"},"sigmaA":{"type":"number","description":"process (acceleration) noise σ"},"sigmaZ":{"type":"number","description":"measurement noise σ"},"seed":{"type":"number"},"v0":{"type":"number","description":"true target velocity"},"folder":{"type":"string"}}}},{"name":"zeq_auto","description":"ZeqAuto — FRICTIONLESS: send a natural-language `query` + `constants` and the right solver is auto-selected, run, and sealed. Covers molecular dynamics, orbits, heat, chaos, waves/EM, fluids, fracture, reaction-diffusion, epidemics, option pricing, Riemann zeros, SAT, lattice gauge, FEA, power flow, semiconductors, optimization, shallow-water, docking. No operators or endpoint to pick. Requires zeq_ak_ key.","inputSchema":{"type":"object","required":["query"],"properties":{"query":{"type":"string","description":"e.g. 'simulate a Lennard-Jones liquid', 'price a call S0=100 K=100 sigma=0.2', 'shallow-water tsunami', 'SIR epidemic R0=3'"},"constants":{"type":"object","description":"solver parameters (S0, K, sigma, preset, steps, beta, gamma, …)"},"solver":{"type":"string","description":"optional: force a specific solver key"},"folder":{"type":"string"}}}},{"name":"zeq_stream","description":"ZeqStream — hosted, ticking solver channels. A channel is a solver wrapped as a live endpoint with its OWN key that a game/sensor/instrument ticks. action=create makes one (returns its key, shown once); action=tick advances ONE Zeqond and seals an envelope + receipt; action=get/list/close manage it. Each seal is one credit-compute; `tickIntervalZeqonds` sets the fair cadence (≈111197 ≈ a 24-hour tick). Requires zeq_ak_ key.","inputSchema":{"type":"object","required":["action"],"properties":{"action":{"type":"string","description":"create | tick | get | list | close | link | secure. link = a keyless signed pull URL (no API key/.env). secure = open a ZeqSSH AES-256-GCM encrypted line (returns a one-time sessionSecret)."},"solver":{"type":"string","description":"create: solver key (lorenz, quant, evolve, heat, …) — or use query"},"query":{"type":"string","description":"create: natural-language, auto-classified like zeq_auto"},"constants":{"type":"object","description":"create: base constants merged into every tick"},"label":{"type":"string"},"autotick":{"type":"boolean","description":"create: server advances it every cadence (spends credits)"},"tickIntervalZeqonds":{"type":"number","description":"create: Zeqonds between seals; ~111197 ≈ 24h"},"ttlSeconds":{"type":"number","description":"link: how long the keyless URL stays valid (default 30d)"},"channel":{"type":"string","description":"tick/get/close/link/secure: the channel id"},"inputs":{"type":"object","description":"tick: values merged over the channel constants"}}}},{"name":"zeq_closedform","description":"ZeqClosedForm — the CLOSED-FORM master-equation solver, the analytic counterpart to the open-form RK4 (/api/solve). Compiles polynomial couplings a+bϕ+dϕ³ into effective (μ²_eff,λ_eff,F_eff) and writes the EXACT branch solution of ϕ̈=μ²_eff·ϕ+λ_eff·ϕ³+F_eff (÷ KO42 tensioner): free / uniform-accel / harmonic / hyperbolic / driven, and Duffing ϕ₀·cn(Ωt,k) via AGM (hardening & softening). KO42 enters first-order in α on the linear branches. Ships an independent RK4 closed-vs-open cross-check. ϕ² / √ / exp shapes are REFUSED by name, never approximated. Give effective coeffs directly (mu2_eff,lambda_eff,F_eff) OR couplings [{a,b,c,d}] / [{samples:[[x,y],...]}]; phi0/phidot0 (else equilibrium launch), t, ko42, alpha. Requires zeq_ak_ key.","inputSchema":{"type":"object","properties":{"mu2_eff":{"type":"number","description":"effective μ² (skip compile)"},"lambda_eff":{"type":"number","description":"effective λ (cubic)"},"F_eff":{"type":"number","description":"effective constant forcing"},"couplings":{"type":"array","description":"couplings to compile: {a,b,c,d} cubics or {samples:[[x,y],...]} (≥4 pts; c≠0 → refused QUADRATIC)","items":{}},"mu2":{"type":"number"},"lambda":{"type":"number"},"Jext":{"type":"number"},"phi42":{"type":"number"},"phi0":{"type":"number"},"phidot0":{"type":"number"},"t":{"type":"number","description":"evaluation time"},"ko42":{"type":"boolean","description":"apply the KO42 tensioner (default true)"},"alpha":{"type":"number","description":"KO42.1 amplitude (default 1e-3)"},"mode":{"type":"string","description":"auto | manual"},"beta":{"type":"number","description":"manual-mode tensioner amplitude"},"folder":{"type":"string"}}}},{"name":"zeq_reactor","description":"ZeqReactor — recursive, sealed, environment-driven compute loops. Where zeq_stream BROADCASTS one sealed envelope, a reactor CLOSES THE LOOP: the sealed output of step n plus a live environment observation become the inputs for step n+1 — xₙ₊₁ = seal(Solver(T(xₙ, uₙ))), each step hash-linked to the previous. action=create builds one from a transition contract (a solver + initialInput + a transition.inputs map whose values are literals or dot-paths over {output, env, step}, e.g. sigmaZ:'env.noise', v0:'output.rmse'); action=step advances one step (a credit-compute, sealed + receipt), optional inline env; action=observe pushes an environment reading and steps immediately if the contract's trigger is 'on-observe'; action=state/trajectory/telemetry/get read it (owner-scoped); action=close stops it. Any of the 26 solvers can drive a reactor. Field-carry makes a stateful digital twin — set transition.inputs.initialState:'output.finalDensity' (e.g. a tumour front that keeps advancing). Each step is reality-gated: a step that fails its ≤0.1% check seals observable-differential and the onUnverified guard can halt the loop, so a blown-up state can never seed the next. Requires zeq_ak_ key (step/observe burn credit, tied to your ZID).","inputSchema":{"type":"object","required":["action"],"properties":{"action":{"type":"string","description":"create | list | step | observe | state | trajectory | telemetry | secure | get | close. secure = open a keyless ZeqSSH encrypted line to consume sealed states (no API key)."},"solver":{"type":"string","description":"create: solver key (kalman, lorenz, tumor, heat, …) or 'auto'"},"initialInput":{"type":"object","description":"create: x₀ base inputs, e.g. { steps: 60, sigmaZ: 0.5 }"},"transition":{"type":"object","description":"create: { inputs: { nextKey: 'env.x' | 'output.y' | literal } }"},"trigger":{"type":"object","description":"create: { mode: 'on-request' | 'on-observe' }"},"guards":{"type":"object","description":"create: { maxSteps, creditBudget, until, onUnverified: 'halt'|'continue' }"},"contract":{"type":"object","description":"create: a full contract object (overrides solver/initialInput/transition/trigger/guards)"},"reactor":{"type":"string","description":"step/observe/state/trajectory/telemetry/get/close: the reactor id"},"env":{"type":"object","description":"step/observe: the environment observation uₙ, e.g. { noise: 0.8 }"},"folder":{"type":"string","description":"create: seal folder for this reactor's steps"}}}}],"components":{"securitySchemes":{"bearerAuth":{"type":"http","scheme":"bearer","description":"A Zeq API key (zeq_ak_…) or machine key (zsm_…) as a bearer token."},"adminSession":{"type":"apiKey","in":"cookie","name":"zeq_auth_token","description":"An admin principal's session cookie. Admin routes are cookie-gated; there is no bearer path."}},"schemas":{"ZeqError":{"type":"object","description":"The uniform failure shape. `ok` is false on every error path; `code` is the machine-readable reason and `error` the human one.","properties":{"ok":{"type":"boolean","enum":[false]},"error":{"type":"string","description":"Human-readable message."},"code":{"type":"string","description":"Stable machine-readable code, e.g. ADMIN_REQUIRED, INVALID_ZID, ZID_NOT_LINKED."}},"required":["ok"]},"ZeqProof":{"type":"object","description":"The seal carried by every verified computation: HMAC over the operator chain and the result, bound to the Zeqond it was computed at.","properties":{"zeqProof":{"type":"string","description":"HMAC-SHA256 seal."},"operatorChain":{"type":"array","items":{"type":"string"},"description":"Operators applied, KO42 first."},"masterSum":{"type":"number","description":"R(t) — the HulyaPulse modulation at that tick."},"phase":{"type":"number","description":"Phase in [0,1)."},"zeqondTick":{"type":"integer","description":"The Zeqond the result was sealed at."},"precisionBound":{"type":"number","description":"Numeric-accuracy bound; the gate is <= 0.001."}}},"ZeqondClock":{"type":"object","description":"The machine's clock reading. One Zeqond is 0.777000777 s; the pulse is 1.287 Hz.","properties":{"zeqond":{"type":"integer"},"phase":{"type":"number"},"sinceGenesis":{"type":"integer","description":"Ticks since this network's genesis."}}}}}}