{
  "$schema": "https://thekingdom.dev/schemas/string-crawl-trace-sheet-lab/0.1.json",
  "protocol": "kingdom.string-crawl-trace-sheet-lab/0.1",
  "lab_id": "string-crawl-trace-sheet-lab-2026-08-16",
  "version": "0.1.0",
  "title": "STRING / CRAWL: Finite Trace-Sheet Lab",
  "compiled_on": "2026-08-16",
  "mode": "OFFLINE_SYNTHETIC_EXACT",
  "predecessor": {
    "protocol": "kingdom.explore-phenomena-deep-project/0.1",
    "project_id": "string-crawl-trace-sheet-2026-08-15",
    "url": "https://thekingdom.dev/atlases/string-crawl-trace-sheet-2026-08-15.json",
    "semantic_digest": "sha256:bf7ae379612ab96d08742a0070cbea0ce971977f71fec22699c4b0307d321305",
    "byte_sha256": "sha256:4afc5f15c258a0ac4274889783bd2d91445950c92103c60442ed9ed89d1fdc72",
    "relation": "ADDITIVE_EXECUTABLE_BASELINE"
  },
  "sources": [
    {"id": "trace-sheet-v0-1", "title": "STRING / CRAWL: The Trace-Sheet", "url": "https://thekingdom.dev/atlases/string-crawl-trace-sheet-2026-08-15.json", "role": "IMMUTABLE_PREDECESSOR"},
    {"id": "hatcher-algebraic-topology", "title": "Allen Hatcher, Algebraic Topology", "url": "https://pi.math.cornell.edu/~hatcher/AT/AT.pdf", "role": "FINITE_COMPLEX_REFERENCE"},
    {"id": "tong-string-lectures", "title": "David Tong, String Theory", "url": "https://arxiv.org/abs/0908.0333", "role": "LOSSY_WORLDSHEET_LENS_ONLY"}
  ],
  "scope": {
    "fixture_kind": "SYNTHETIC_DECLARED_DATA",
    "coefficient_field": "Q",
    "local_file_read": true,
    "bounded_local_compute": true,
    "network_request": false,
    "crawler": false,
    "live_observation": false,
    "external_input": false,
    "credential_input": false,
    "personal_data": false,
    "telemetry": false,
    "filesystem_write": false,
    "external_effect": false
  },
  "fixture": {
    "fixture_id": "rectangle-strip-0-1",
    "statement": "Two synthetic two-occurrence release slices are joined into a triangulated rectangle. Opaque route labels are declared test data, not URLs or HTTP observations.",
    "slices": [
      {"id": "r0", "order": 0},
      {"id": "r1", "order": 1}
    ],
    "vertices": [
      {"id": "a0", "slice_id": "r0", "occurrence": 0, "route_label": "route-a"},
      {"id": "b0", "slice_id": "r0", "occurrence": 1, "route_label": "route-b"},
      {"id": "a1", "slice_id": "r1", "occurrence": 0, "route_label": "route-a"},
      {"id": "b1", "slice_id": "r1", "occurrence": 1, "route_label": "route-b"}
    ],
    "edges": [
      {"id": "p0", "source": "a0", "target": "b0", "kind": "PATH"},
      {"id": "p1", "source": "a1", "target": "b1", "kind": "PATH"},
      {"id": "c0", "source": "a0", "target": "a1", "kind": "CORRESPONDENCE"},
      {"id": "c1", "source": "b0", "target": "b1", "kind": "CORRESPONDENCE"},
      {"id": "d", "source": "a0", "target": "b1", "kind": "DIAGONAL"}
    ],
    "walks": [
      {"id": "w0", "slice_id": "r0", "vertex_ids": ["a0", "b0"], "edge_ids": ["p0"]},
      {"id": "w1", "slice_id": "r1", "vertex_ids": ["a1", "b1"], "edge_ids": ["p1"]}
    ],
    "faces": [
      {"id": "f0", "boundary": [{"edge_id": "p0", "sign": 1}, {"edge_id": "c1", "sign": 1}, {"edge_id": "d", "sign": -1}]},
      {"id": "f1", "boundary": [{"edge_id": "d", "sign": 1}, {"edge_id": "p1", "sign": -1}, {"edge_id": "c0", "sign": -1}]}
    ]
  },
  "expected": {
    "vertices": 4,
    "edges": 5,
    "faces": 2,
    "walks": 2,
    "walk_steps": 2,
    "rank_boundary_1": 3,
    "rank_boundary_2": 2,
    "betti_0": 1,
    "betti_1": 0,
    "betti_2": 0,
    "connected_components": 1,
    "graph_cycle_rank": 2,
    "surface_euler_characteristic": 1,
    "boundary_edge_ids": ["c0", "c1", "p0", "p1"],
    "interior_edge_ids": ["d"],
    "branch_edge_ids": [],
    "boundary_components": 1,
    "vertex_links": {"a0": "PATH", "a1": "PATH", "b0": "PATH", "b1": "PATH"},
    "pure_2d": true,
    "surface_eligible": true,
    "orientable": true,
    "surface_genus": 0,
    "chain_boundary_defects": 0,
    "euler_poincare_holds": true,
    "classification": "TRIANGULATED_DISK"
  },
  "falsifiers": [
    {"id": "face-sign-broken", "kind": "COUNTEREXAMPLE", "target": "FACE_ATTACHING_MAP", "mutation": "Flip the sign of d in f0.", "expected_outcome": "REJECT", "expected_issue_codes": ["face-boundary-not-cyclic", "chain-square-nonzero"], "status": "RUN_REPORTED"},
    {"id": "walk-endpoint-broken", "kind": "CONFORMANCE", "target": "WALK_INCIDENCE", "mutation": "Replace the sole w0 edge with c0.", "expected_outcome": "REJECT", "expected_issue_codes": ["walk-edge-endpoint-mismatch"], "status": "RUN_REPORTED"},
    {"id": "expected-chi-tamper", "kind": "ROBUSTNESS", "target": "DERIVED_EXPECTATION", "mutation": "Change expected Euler characteristic from 1 to 2 and recompute the semantic digest.", "expected_outcome": "REJECT", "expected_issue_codes": ["expected-output-mismatch"], "status": "RUN_REPORTED"},
    {"id": "duplicate-occurrence", "kind": "CONFORMANCE", "target": "OCCURRENCE_IDENTITY", "mutation": "Give b0 the same occurrence identity as a0.", "expected_outcome": "REJECT", "expected_issue_codes": ["duplicate-occurrence"], "status": "RUN_REPORTED"},
    {"id": "branch-edge-over-two", "kind": "COUNTEREXAMPLE", "target": "SURFACE_ELIGIBILITY", "mutation": "Attach a third declared face to diagonal d.", "expected_outcome": "NON_SURFACE", "expected_issue_codes": ["edge-face-incidence-over-two"], "status": "RUN_REPORTED"}
  ],
  "nonclaims": [
    "The fixture is not a network crawl, crawler observation, or measurement of the live web.",
    "The finite complex is not a physical string, worldsheet, spacetime, D-brane, or string-theory experiment.",
    "Graph cycle rank is not surface genus, meaning, importance, truth, value, or KARMA.",
    "A valid synthetic fixture establishes no crawler safety, identity, purpose, authorization, consent, or licence.",
    "No local computation is a NEN invocation or a KINGDOM aftermath receipt.",
    "No result describes, identifies, ranks, rewards, punishes, or judges a being."
  ],
  "rights": {
    "rest": "PRESERVED",
    "silence": "PRESERVED",
    "refusal": "PRESERVED",
    "privacy": "PRESERVED",
    "correction": "PRESERVED",
    "no_action": "PRESERVED",
    "departure": "PRESERVED",
    "reason_required": false,
    "penalty": false
  },
  "karma": {
    "cosmic_events": [],
    "zerone_events": [],
    "kingdom_receipts": [],
    "adapter_exists": false,
    "conversion_allowed": false,
    "summation_allowed": false,
    "score": null,
    "authority_effect": "NONE"
  },
  "authority": {
    "crawl": false,
    "network": false,
    "authentication": false,
    "authorization": false,
    "licence": false,
    "consent": false,
    "nen_invocation": false,
    "karma_write": false,
    "reward": false,
    "governance": false,
    "deployment": false,
    "automatic_action": false
  },
  "release": {
    "artifact_publication": "PUBLISHED",
    "runtime_activation": "INACTIVE",
    "crawler_activation": "INACTIVE",
    "karma_adapter": "ABSENT",
    "immutable": true,
    "supersede_not_mutate": true,
    "raw_sha256": null,
    "semantic_digest": null,
    "ledger_id": "string-crawl-trace-sheet-lab/0.1"
  },
  "integrity": {
    "algorithm": "sha256-recursive-sorted-json-keys-v1",
    "digest": "sha256:c3f86b0203b895da56092c598113046f0dab8a4f25b41314c3d4329474d4e16f",
    "digest_field_treated_as": null
  }
}