{"query": "pH — the logarithm of the proton", "count": 20, "results": [{"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", "generated": false}, {"id": "card_theory_statistical_mechanics", "title": "Statistical mechanics (Boltzmann — why the second law is a counting argument)", "shelf": "theories", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) — an engine domain that can touch it: thermodynamics. Calibration: seals — Boltzmann distributions, partition functions an", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_src_word_napierian_logarithm", "title": "napierian logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "napierian logarithm: (noun) a logarithm to the base e — syn: natural logarithm", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_natural_logarithm", "title": "natural logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "natural logarithm: (noun) a logarithm to the base e — syn: Napierian logarithm", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_c_9d6917fca9f5", "title": "pH — the logarithm of the proton ↔ Logarithms — multiplication made addition, a", "shelf": "connections", "surface": null, "snippet": "−log₁₀(10⁻⁴) = 4 sealed on the logarithm card. This is chemistry borrowing the grammar of the senses  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "generated": false}, {"id": "card_src_word_common_logarithm", "title": "common logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "common logarithm: (noun) a logarithm to the base 10", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_c_857eed5a5e82", "title": "Logarithms — multiplication made addition, a ↔ pH — the logarithm of the proton", "shelf": "connections", "surface": null, "snippet": "All sealed: ... acidity by pH (-log10(10^-4) = 4).  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "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", "generated": false}, {"id": "card_src_word_logarithm", "title": "logarithm", "shelf": "dictionary", "surface": "secular", "snippet": "logarithm: (noun) the exponent required to produce a given number — syn: log", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_pron_logarithms", "title": "logarithms", "shelf": "pronunciation", "surface": "secular", "snippet": "logarithms: pronounced (ARPABET) L AA1 G ER0 IH2 DH AH0 M 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_c_60eaf1dc310a", "title": "The logarithm inverts radioactive decay", "shelf": "connections", "surface": null, "snippet": "Half-life is a logarithm of the surviving fraction — the carbon clock read backward.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_c_6b353b6912b0", "title": "The logarithm inverts the capacitor's exponential clock", "shelf": "connections", "surface": null, "snippet": "Exponential rises by multiplying; the logarithm returns by adding. One law, two directions.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_src_word_ph", "title": "ph", "shelf": "dictionary", "surface": "secular", "snippet": "ph: (noun) (from potential of Hydrogen) the logarithm of the reciprocal of hydrogen-ion concentration in gram atoms per liter; provides a measure on a scale from 0 to 14 of the acidity or alkalinity o", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_ph_scale", "title": "ph scale", "shelf": "dictionary", "surface": "secular", "snippet": "ph scale: (noun) (from potential of Hydrogen) the logarithm of the reciprocal of hydrogen-ion concentration in gram atoms per liter; provides a measure on a scale from 0 to 14 of the acidity or alkali", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_pron_logarithm", "title": "logarithm", "shelf": "pronunciation", "surface": "secular", "snippet": "logarithm: pronounced (ARPABET) L AA1 G ER0 IH2 DH AH0 M. 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_book_42342", "title": "Encyclopaedia Britannica, 11th Edition, \"Logarithm\" to \"Lord Advocate\" Volume 16, Slice 8 — Various", "shelf": "gutenberg", "surface": "secular", "snippet": "Encyclopaedia Britannica, 11th Edition, \"Logarithm\" to \"Lord Advocate\" Volume 16, Slice 8, by Various. Subjects: Encyclopedias and dictionaries. Read the full text (public domain): https://www.gutenbe", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_c_27e331f56531", "title": "pH is a logarithm", "shelf": "connections", "surface": null, "snippet": "pH = -log10[H+] — chemistry using the exact log scale of the senses.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}, {"id": "card_alm_connection_cents_are_logarithmic", "title": "Almanac: Cents are logarithmic: pitch ratios multiply, but intervals add", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Pitch is multiplicative -- you go UP an octave by DOUBLING frequency, up two octaves by quadrupling -- yet musicians count intervals by ADDING (a fifth plus a fourth makes an octave). The ", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "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)", "generated": false}, {"id": "card_c_0706824b5f9f", "title": "Information IS a logarithm", "shelf": "connections", "surface": null, "snippet": "2 bits per DNA base = log2(4), sealed in the genome card — Shannon's measure is a log.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "generated": false}]}