{"query": "Luhn(4532 0151 1283 0366) is valid · ISBN-13 978-0-306-40615", "count": 11, "results": [{"id": "card_v_50597b7a3831", "title": "Luhn(4532 0151 1283 0366) is valid · ISBN-13 978-0-306-40615-7 is valid", "shelf": "document_validation", "surface": "secular", "snippet": "Verdict: HOLDS.\n• doc_validation.luhn: Luhn '4532015112830366' valid=True (matches claim)\n• doc_validation.isbn13: ISBN-13 '9780306406157' valid=True (matches claim)\nSealed and independently re-checka", "authority_tier": "engine", "source": "Verified by the engine — document_validation", "readable": false, "generated": false}, {"id": "card_calc_v_doc_validation_luhn", "title": "Luhn", "shelf": "calculations", "surface": "secular", "snippet": "Luhn — document_validation. Formula: Luhn checksum mod 10 = 0. Canonical FORM: check_digit (weighted sum mod n = 0) — engine verifier doc_validation.luhn — the deterministic check the concordance runs", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_checksum_mod", "title": "Checksums (mod arithmetic)", "shelf": "calculations", "surface": "secular", "snippet": "Checksums (mod arithmetic) — cybersecurity. Formula: sum * w mod m. Canonical FORM: check_digit (weighted sum mod n = 0) — ISBN, Luhn and CRC all catch errors by a modulus. Same form, different domain", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_form_check_digit", "title": "Canonical form: check_digit  (weighted sum mod n = 0)", "shelf": "forms", "surface": "secular", "snippet": "A canonical mathematical FORM: weighted sum mod n = 0 — error-detecting checksums — ISBN, Luhn, EAN. Every calculation joined here is this same computation under a change of variable; the domains diff", "authority_tier": "reference", "source": "The Calculation Map — canonical forms", "readable": false, "generated": false}, {"id": "card_domchk_document_validation_claimed_luhn_valid", "title": "Document Validation: luhn valid", "shelf": "document_validation", "surface": "secular", "snippet": "A worked check in document validation: luhn valid.\n\nGIVEN\n  luhn_number = 4532015112830366\n\nCLAIMED\n  claimed_luhn_valid = True\n\nTHE ENGINE'S VERDICT\n  doc_validation.luhn: CONFIRMED — Luhn '453201511", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_works_luhn", "title": "The check digit that catches a mistyped number", "shelf": "the-works", "surface": "secular", "snippet": "The Luhn and ISBN algorithms embed a check digit so a single wrong digit is caught before it becomes a wrong order or a wrong book. Two standards, both verified.  Worked & sealed by the engine — Luhn(", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_src_pron_luhn", "title": "luhn", "shelf": "pronunciation", "surface": "secular", "snippet": "luhn: pronounced (ARPABET) L AH1 N. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_seal_0605e158229e877a0a51b348301ed30c7e453b684d1c3f1dc0f4a89d3b12a406", "title": "Receipt 0605e158229e… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"document_validation\",\n  \"dimensions\": [\n   \"authority_trust\",\n   \"encoding\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"co", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_seal_33359dd81e2f9a3f9e1dad39e2cf65afc845c0a687ac3398c245e70a78b51c31", "title": "Receipt 33359dd81e2f… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"document_validation\",\n  \"dimensions\": [\n   \"authority_trust\",\n   \"encoding\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"co", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_seal_d5fef05d88fdbcc324c7f00dbf4773ade276d09157e28ea69aa9c80e4f789658", "title": "Receipt d5fef05d88fd… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"document_validation\",\n  \"dimensions\": [\n   \"authority_trust\",\n   \"encoding\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"co", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_bridge_master_modular_reduction", "title": "Master equation: x mod m", "shelf": "bridges", "surface": "secular", "snippet": "the wrap-around: reduce to a residue class in Z/mZ and the line becomes a circle. A clock is Z/12, a week is Z/7, an octave is Z/12, a check digit is the residue chosen to make a weighted sum vanish. ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_v_50597b7a3831"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}