{"query": "p ∨ ¬p is a tautology · ¬(p ∧ q) ≡ ¬p ∨ ¬q  (De Morgan)", "count": 11, "results": [{"id": "card_v_f4b827f56b3c", "title": "p ∨ ¬p is a tautology · ¬(p ∧ q) ≡ ¬p ∨ ¬q  (De Morgan)", "shelf": "formal_logic", "surface": "secular", "snippet": "Verdict: HOLDS.\n• formal_logic.tautology: formula 'p | ~p' tautology=True, matches claim\n• formal_logic.equivalence: '~(p & q)' ≡ '~p | ~q' = True, matches claim\nSealed and independently re-checkable:", "authority_tier": "engine", "source": "Verified by the engine — formal_logic", "readable": false, "generated": false}, {"id": "card_theory_darwinian_evolution_by_natural_selection", "title": "Darwinian evolution by natural selection", "shelf": "theories", "surface": "secular", "snippet": "Darwinian evolution by natural selection — an engine domain that can touch it: biology. Calibration: map-only — historical and empirical; population genetics computes. Three conditions and one consequ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_50a5aa72df98", "title": "The three doors the disease framework could escape through — and how they were shut", "shelf": "science", "surface": "secular", "snippet": "The honest part. A framework earns trust by naming where it could be WRONG. The red-team found three\ndoors this one could slip through to avoid ever being falsified — and each was shut, sealed as logi", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-10", "readable": false, "generated": false}, {"id": "card_bridge_theory_boolean_algebra_propositional_logic__formal_logic_epistemology", "title": "Bridge: Boolean algebra / propositional logic  ↔  Formal logic & epistemology (validity, inference)", "shelf": "bridges", "surface": "secular", "snippet": "Boolean algebra / propositional logic and Formal logic & epistemology (validity, inference) are the same form in different domains. Boole's algebra IS propositional inference in arithmetic dress: AND/", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_master_boolean_algebra", "title": "Master equation: (a AND b), (a OR b), NOT a  —  the two-valued algebra", "shelf": "bridges", "surface": "secular", "snippet": "the law of thought made algebra: the same AND/OR/NOT structure is propositional logic, a network of switches, and the algebra of sets. Boole titled it The Laws of Thought; Shannon showed a circuit IS ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_domchk_formal_logic_claimed_tautology", "title": "Formal Logic: tautology", "shelf": "formal_logic", "surface": "secular", "snippet": "A worked check in formal logic: tautology.\n\nGIVEN\n  conclusion = q\n  formula = p & q\n\nCLAIMED\n  claimed_tautology = False\n\nTHE ENGINE'S VERDICT\n  formal_logic.tautology: CONFIRMED — formula 'p & q' ta", "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_logic", "title": "Two laws of thought, checked over every case", "shelf": "the-works", "surface": "secular", "snippet": "The law of excluded middle (p or not-p is always true) and De Morgan's law are verified across the entire truth table — not argued, exhaustively decided.  Worked & sealed by the engine — p ∨ ¬p is a t", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_calc_v_formal_logic_tautology", "title": "Tautology", "shelf": "calculations", "surface": "secular", "snippet": "Tautology — formal_logic. Formula: phi true under every assignment. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier formal_logic.tautology — the deterministic check the", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_mathematics_set_algebra", "title": "Set algebra", "shelf": "calculations", "surface": "secular", "snippet": "Set algebra — mathematics. Formula: set identity iff Boolean formula is a tautology. Canonical FORM: boolean_logic (phi is SAT / valid / entailed) — engine verifier mathematics.set_algebra — the deter", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_src_openstax_contemporary_mathematics_key_terms_7cc30378", "title": "Key Terms — Contemporary Mathematics", "shelf": "reference", "surface": "secular", "snippet": "Key Terms\n\n2.1\n\nStatements and Quantifiers\n\nlogic\n\nlogical statement\n\ntruth values\n\nsymbolic form\n\nnegation of a logical statement\n\nquantifier\n\npremises\n\nconclusion\n\ninductive logical arguments\n\n2.2\n\n", "authority_tier": "reference", "source": "OpenStax: Contemporary Mathematics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_src_etym_tautology", "title": "tautology", "shelf": "etymology", "surface": "secular", "snippet": "tautology: etymology (Webster 1913) — n.: [L. tautologia, Gr. tautologie.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "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_f4b827f56b3c"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}