{"query": "Loudness — the decibel, a logarithm", "count": 20, "results": [{"id": "card_acoustics_loudness", "title": "Loudness — the decibel, a logarithm", "shelf": "codex", "surface": "secular", "snippet": "The ear spans a trillion-fold range, so loudness is measured in decibels: every 10 dB is a tenfold power ratio, 30 dB a thousandfold (sealed). Perception compresses huge ranges logarithmically. Rests ", "authority_tier": "engine_derived", "source": "Narrow Highway — acoustics", "readable": false, "generated": false}, {"id": "card_bridge_master_logarithmic_scale", "title": "Master equation: L = k * log10(x / x_ref)", "shelf": "bridges", "surface": "secular", "snippet": "put a ratio on a log scale — the same operation, wherever a range spans many orders of magnitude. ONE equation, 8 domains, connected by a change of variable: acoustics [k = 10, x = intensity, x_ref = ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_acoustics", "title": "Acoustics — waves, loudness, and harmonics", "shelf": "codex", "surface": "secular", "snippet": "The physics of sound and hearing, standing between matter and mind. Sound is a pressure wave in a medium (v = f lambda); loudness is logarithmic (the decibel); pitch is frequency and timbre is the har", "authority_tier": "engine_derived", "source": "Narrow Highway — acoustics", "readable": false, "generated": false}, {"id": "card_src_openstax_physics_concept_items_5f3c157f", "title": "Concept Items — Physics", "shelf": "physics", "surface": "secular", "snippet": "Concept Items\n\n14.1\n\nSpeed of Sound, Frequency, and Wavelength\n\n1.\n\nWhat is the amplitude of a sound wave perceived by the human ear?\n\nloudness\n\npitch\n\nintensity\n\ntimbre\n\n2.\n\nThe compressibility of ai", "authority_tier": "reference", "source": "OpenStax: Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_n_5d1c28bd4ea5", "title": "Logarithms — multiplication made addition, and the grammar of the senses", "shelf": "science", "surface": "secular", "snippet": "The logarithm turns multiplication into addition: log(15) = log(3)+log(5), sealed. That\none property made calculation possible before computers (Napier 1614 -> slide rules -> every\nengineer until 1970", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_n_789214dd088e", "title": "pH — the logarithm of the proton", "shelf": "science", "surface": "secular", "snippet": "pH = −log₁₀[H⁺]: acidity is literally a logarithm, so each unit is a tenfold change in\nproton concentration — pH 4 is ten times more acidic than pH 5, a hundred times more than\npH 6. Sealed in-domain:", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_alm_connection_logarithmic_scales_two_witnesses", "title": "Almanac: Decibels and star magnitudes: one logarithm, two senses", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  How loud a sound is and how bright a star is are measured on scales that look unrelated, yet two independent verifiers found the same machinery underneath. The acoustics verifier confirmed", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_calc_v_acoustics_decibel_ratio", "title": "Decibel ratio", "shelf": "calculations", "surface": "secular", "snippet": "Decibel ratio — acoustics. Formula: dB = 10 log10(I/I_ref). Canonical FORM: logarithmic (y = k * log(x / x0)) — engine verifier acoustics.decibel_ratio — the deterministic check the concordance runs. ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "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)", "readable": false, "generated": false}, {"id": "card_form_logarithmic", "title": "Canonical form: logarithmic  (y = k * log(x / x0))", "shelf": "forms", "surface": "secular", "snippet": "A canonical mathematical FORM: y = k * log(x / x0) — a ratio compressed onto a log scale — decibels, pH, magnitude, entropy, half-life. Every calculation joined here is this same computation under a c", "authority_tier": "reference", "source": "The Calculation Map — canonical forms", "readable": false, "generated": false}, {"id": "card_calc_ph_scale", "title": "pH scale", "shelf": "calculations", "surface": "secular", "snippet": "pH scale — chemistry. Formula: pH = -log10[H+]. Canonical FORM: logarithmic (y = k * log(x / x0)) — acidity on a log scale — a hydrogen-ion ratio compressed, like decibels and magnitude. Same form, di", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_seal_479e62486f99015c43659c75ae1d787303dbcc6f5749f723aec095b5352712b3", "title": "Receipt 479e62486f99… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_seal_3df57212c5d571ba80ccd1a6420dc83564d744fa4e9a0e0c4521ad6f2c10a652", "title": "Receipt 3df57212c5d5… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_seal_90cdade55796f9d2e9ab2b4d771b8b12eda91b458f6bee81941410e03327ef6d", "title": "Receipt 90cdade55796… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_seal_0ae414b87c68cc7b1c637fbf6d37ca748cb542456d2e4abe54d6f50f485e209f", "title": "Receipt 0ae414b87c68… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_src_word_db", "title": "db", "shelf": "dictionary", "surface": "secular", "snippet": "db: (noun) a transuranic element — syn: dubnium, hahnium, element 105, atomic number 105 · (noun) a logarithmic unit of sound intensity; 10 times the logarithm of the ratio of the sound intensity to s", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_theory_room_acoustics_sabine", "title": "Room acoustics & reverberation (Sabine)", "shelf": "theories", "surface": "secular", "snippet": "Room acoustics & reverberation (Sabine) — an engine domain that can touch it: acoustics. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and seal the", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_n_18b53f98f008", "title": "The mole — counting the uncountable", "shelf": "science", "surface": "secular", "snippet": "A mole is 6.02214076×10²³ things — exact since the 2019 SI redefinition — the bridge\nfrom atoms you cannot see to grams you can weigh. The molar mass is just the atomic weights\nadded up, sealed: water", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_n_6e7a5b14e556", "title": "The periodic table — the map of the elements", "shelf": "science", "surface": "secular", "snippet": "118 elements, ordered by proton count, and their properties RECUR in periods — the\nsingle most predictive table in science. Sealed in-domain: carbon is element 6, symbol C\n(https://narrowhighway.com/s", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_n_f69fb7c82462", "title": "The counter-pattern — when persecution grows what force cannot", "shelf": "science", "surface": "secular", "snippet": "There are universal patterns — natural law among them: the same moral precepts recur\nacross Babylonian, Egyptian, Chinese, Greek, and Hebrew sources (C.S. Lewis catalogued them as\n'the Tao'; Paul call", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "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_acoustics_loudness"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}