{"query": "Quartz at 32,768 Hz — a power of two on the wrist", "count": 20, "results": [{"id": "card_n_9d42516b140c", "title": "Quartz at 32,768 Hz — a power of two on the wrist", "shelf": "science", "surface": "secular", "snippet": "Every quartz watch cuts a tuning fork to hum at exactly 2^15 = 32,768 Hz, sealed, and\n32768 / 2^15 = 1: run the signal through fifteen binary flip-flops, each halving the frequency,\nand the last ticks", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_domchk_acoustics_claimed_harmonic_hz", "title": "Acoustics: harmonic hz", "shelf": "acoustics", "surface": "secular", "snippet": "A worked check in acoustics: harmonic hz.\n\nGIVEN\n  f_source_hz = 440\n  frequency_hz = 440\n  fundamental_hz = 110\n  harmonic_n = 4\n  speed_medium_mps = 343\n  speed_of_wave = 343\n  v_observer_mps = 10\n ", "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_domchk_acoustics_claimed_f_observed_hz", "title": "Acoustics: f observed hz", "shelf": "acoustics", "surface": "secular", "snippet": "A worked check in acoustics: f observed hz.\n\nGIVEN\n  f_source_hz = 440\n  frequency_hz = 440\n  harmonic_n = 4\n  speed_medium_mps = 343\n  speed_of_wave = 343\n  v_observer_mps = 10\n  v_source_mps = 0\n  v", "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_domchk_music_theory_claimed_frequency_hz", "title": "Music Theory: frequency hz", "shelf": "music_theory", "surface": "secular", "snippet": "A worked check in music theory: frequency hz.\n\nGIVEN\n  freq_a = 440\n  key = C\n  midi_note = 69\n  note = E\n\nCLAIMED\n  claimed_frequency_hz = 440\n\nTHE ENGINE'S VERDICT\n  music.equal_temperament_freq: CO", "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_c_1219a284fc2a", "title": "Quartz at 32,768 Hz — a power of two on the  ↔ Powers of two — the binary ladder", "shelf": "connections", "surface": null, "snippet": "run the signal through fifteen binary flip-flops, each halving the frequency, and the last ticks once per second... Time, on the wrist, is counted in powers of two.  — a concord the card itself states", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_alm_located_midi_to_frequency", "title": "Almanac: MIDI note to frequency: every key is a power of the twelfth root of two from A440", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Every note a synthesizer or piano can play is a single exact frequency, pinned by one anchor and one formula. music_theory confirmed the map on the standard scale: MIDI note 69 (the A abov", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_c_45b1fde0f875", "title": "Quartz at 32,768 Hz — a power of two on the  ↔ Oscillator — LC resonance, the bench's own S", "shelf": "connections", "surface": null, "snippet": "It is the highest power of two that stays low-power and stable — the oscillator meeting the divider chain.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_c_c334ba45e1c7", "title": "Quartz at 32,768 Hz — a power of two on the  ↔ The two clocks — quartz, cesium, and the sec", "shelf": "connections", "surface": null, "snippet": "run the signal through fifteen binary flip-flops, each halving the frequency, and the last ticks once per second.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_src_place_1185121", "title": "Shāhzādpur", "shelf": "geography", "surface": "secular", "snippet": "Shāhzādpur: a place in BD, 83 at 24.177, 89.599, population 102,420. Feature PPL, timezone Asia/Dhaka.", "authority_tier": "reference", "source": "GeoNames (CC-BY 4.0)", "generated": false}, {"id": "card_alm_connection_syntonic_comma", "title": "Almanac: The syntonic comma: the pure third and the Pythagorean third disagree by 81:80", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Music has TWO ways to build a major third, and they do not match. music_theory confirmed the pure (just) major third is the simple ratio 5:4 (64 Hz to 80 Hz) -- the one nature gives in the", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_src_pron_hz", "title": "hz", "shelf": "pronunciation", "surface": "secular", "snippet": "hz: pronounced (ARPABET) HH ER1 T Z. 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", "generated": false}, {"id": "card_src_word_hz", "title": "hz", "shelf": "dictionary", "surface": "secular", "snippet": "hz: (noun) the unit of frequency; one hertz has a periodic interval of one second (named for Heinrich Rudolph Hertz) — syn: hertz, cycle per second, cycles/second, cps, cycle", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_n_91f3b5881075", "title": "Schumann resonance — the Earth-ionosphere cavity, sealed honestly at 7.83 Hz", "shelf": "science", "surface": "secular", "snippet": "The planet is a resonant cavity. Between the ground and the ionosphere, lightning\n(~50 strikes/second worldwide) continuously rings a spherical electromagnetic waveguide; the\nmeasured resonances sit a", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_src_rfc_1843", "title": "RFC1843 — HZ - A Data Format for Exchanging Files of Arbitrarily Mixed Chinese and ASCII characters", "shelf": "rfcs", "surface": "secular", "snippet": "RFC1843: HZ - A Data Format for Exchanging Files of Arbitrarily Mixed Chinese and ASCII characters (August 1995). Status: INFORMATIONAL.", "authority_tier": "reference", "source": "The RFC Index (RFC Editor / IETF) — public domain", "generated": false}, {"id": "card_v_225533310c11", "title": "C → G = 7 semitones (a perfect fifth) · MIDI 69 = A4 = 440 Hz", "shelf": "music_theory", "surface": "secular", "snippet": "Verdict: HOLDS.\n• music.interval_semitones: C → G = 7 semitones (matches claim)\n• music.equal_temperament_freq: MIDI 69 → 440.0000 Hz (matches claim 440.0)\nSealed and independently re-checkable: https", "authority_tier": "engine", "source": "Verified by the engine — music_theory", "generated": false}, {"id": "card_works_music", "title": "The perfect fifth and the pitch of A", "shelf": "the-works", "surface": "secular", "snippet": "From C to G is seven semitones — the perfect fifth; and MIDI note 69 is concert A at exactly 440 Hz. Where mathematics becomes music.  Worked & sealed by the engine — C → G = 7 semitones (a perfect fi", "authority_tier": "verified", "source": "The Works — worked & sealed", "generated": false}, {"id": "card_alm_connection_pythagorean_comma", "title": "Almanac: The Pythagorean comma: twelve pure fifths overshoot seven octaves", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Climb the circle of fifths twelve times -- C, G, D, A, E, B, F#, C#, G#, D#, A#, E#, and back toward C -- and you should land seven octaves above where you began. You do not, and the engin", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_domchk_acoustics_claimed_db", "title": "Acoustics: db", "shelf": "acoustics", "surface": "secular", "snippet": "A worked check in acoustics: db.\n\nGIVEN\n  f_source_hz = 440\n  frequency_hz = 440\n  harmonic_n = 4\n  reference = 1e-12\n  speed_medium_mps = 343\n  speed_of_wave = 343\n  v_observer_mps = 10\n  v_source_mp", "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_alm_connection_major_triad_is_overtone_ratios", "title": "Almanac: The major chord is built into sound: harmonics 4:5:6 are the major triad", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  The major chord is not a human invention but a fact of physics that the engine confirmed across three domains. Any vibrating string or air column sounds a fundamental plus a series of harm", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "generated": false}, {"id": "card_c_9b4f831bc355", "title": "The spectrum walk begins at the Schumann cavity", "shelf": "connections", "surface": null, "snippet": "The first rung: the 7.83 Hz fundamental's 38,287 km wave — the planet-sized bottom of the dial.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}]}