{"query": "H(½,½) = 1 bit · Hamming(1011, 1001) = 1", "count": 4, "results": [{"id": "card_v_a2c57d5d0b2a", "title": "H(½,½) = 1 bit · Hamming(1011, 1001) = 1", "shelf": "information_theory", "surface": "secular", "snippet": "Verdict: HOLDS.\n• info_theory.shannon_entropy: H = 1.000000 bits (matches claim 1.0)\n• info_theory.hamming_distance: Hamming('1011', '1001') = 1 (matches claim)\nSealed and independently re-checkable: ", "authority_tier": "engine", "source": "Verified by the engine — information_theory", "generated": false}, {"id": "card_theory_error_correcting_codes", "title": "Error-correcting codes (Hamming, Reed–Solomon)", "shelf": "theories", "surface": "secular", "snippet": "Error-correcting codes (Hamming, Reed–Solomon) — an engine domain that can touch it: information_theory. Calibration: seals — code distances, correctable error counts and parity all compute exactly. A", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_works_information", "title": "Measuring information: one bit, and a distance", "shelf": "the-works", "surface": "secular", "snippet": "A single fair coin carries exactly one bit of Shannon entropy; the Hamming distance counts how many positions two codewords differ in — the ground of error correction.  Worked & sealed by the engine —", "authority_tier": "verified", "source": "The Works — worked & sealed", "generated": false}, {"id": "card_src_word_hamming", "title": "hamming", "shelf": "dictionary", "surface": "secular", "snippet": "hamming: (noun) poor acting by a ham actor — syn: overacting", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}]}