{"query": "p ∨ ¬p is a tautology · ¬(p ∧ q) ≡ ¬p ∨ ¬q  (De Morgan)", "count": 6, "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", "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)", "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)", "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", "generated": false}, {"id": "card_src_word_tautology", "title": "tautology", "shelf": "dictionary", "surface": "secular", "snippet": "tautology: (noun) (logic) a statement that is necessarily true · (noun) useless repetition", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "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", "generated": false}]}