{"query": "Counting: how many ways to choose and to arrange", "count": 20, "results": [{"id": "card_works_counting", "title": "Counting: how many ways to choose and to arrange", "shelf": "the-works", "surface": "secular", "snippet": "From five things, there are 20 ordered pairs but only 10 unordered pairs — order is the whole difference between a permutation and a combination.  Worked & sealed by the engine — P(5,2) = 5!/3! = 20 ·", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_theory_central_place_theory", "title": "Central place theory (Christaller)", "shelf": "theories", "surface": "secular", "snippet": "Central place theory (Christaller) — an engine domain that can touch it: geography. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation. Settlements a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_periodic_law", "title": "Periodic law (Mendeleev)", "shelf": "theories", "surface": "secular", "snippet": "Periodic law (Mendeleev) — an engine domain that can touch it: periodic_table. Calibration: seals — element properties and group trends look up and compute. Arrange elements by atomic number and their", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_c_130ff92ca772", "title": "Supersymmetry — pairing as the map's arrange ↔ The periodic table — the map of the elements", "shelf": "connections", "surface": null, "snippet": "the symmetry then PREDICTS the missing partner — a broken pair is a gap that tells us what to look for, the way SUSY predicts a superpartner.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_n_0be5414e0c37", "title": "Supersymmetry — pairing as the map's arrangement", "shelf": "concepts", "surface": "secular", "snippet": "Arrange the map so each axis/node has a dual; the symmetry then PREDICTS the missing partner — a broken pair is a gap that tells us what to look for, the way SUSY predicts a superpartner.\n\nHONEST STAT", "authority_tier": "matt", "source": "Operator's seed (Matt) — honest grade: resonance", "readable": false, "generated": false}, {"id": "card_bridge_master_binomial_counting", "title": "Master equation: C(n,k) = n! / (k!(n-k)!)", "shelf": "bridges", "surface": "secular", "snippet": "the atom of counting: n! is the number of orderings of n things, and every way to arrange or select is that factorial divided by the orderings that don't matter. Permutations keep order, combinations ", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_c_275d2a32f646", "title": "Supersymmetry — pairing as the map's arrange ↔ Two poles — abstract/formal vs material/embo", "shelf": "connections", "surface": null, "snippet": "Held on for the general method (seek complementary structure) and the refined direction the data points to — NOT the stated pairs.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_a9e92568df8b", "title": "Two poles — abstract/formal vs material/embo ↔ Supersymmetry — pairing as the map's arrange", "shelf": "connections", "surface": null, "snippet": "The strongest anti-correlations run ACROSS this divide (reasoning <-> physical_substance, reasoning <-> metabolism), NOT within the proposed supersymmetry duals.  — a concord the card itself states; m", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_principle_benjamin_franklin_22f9047542", "title": "Benjamin Franklin: Our sensations being very much fixed to the moment, we are apt to forget that more moments are to follow the f", "shelf": "strategy", "surface": "secular", "snippet": "Our sensations being very much fixed to the moment, we are apt to forget that more moments are to follow the first, and consequently that man should arrange his conduct so as to suit the whole of a li", "authority_tier": "primary", "source": "Benjamin Franklin, The Autobiography of Benjamin Franklin (1791) — Project Gutenberg #148, public domain", "readable": true, "generated": false}, {"id": "card_src_lex_h6186", "title": "H6186 — עָרַךְ (a.rakh): to arrange", "shelf": "lexicon", "surface": "secular", "snippet": "עָרַךְ (a.rakh), Strong's H6186: to arrange. 1) to arrange, set or put or lay in order, set in array, prepare, order, ordain, handle, furnish, esteem, equal, direct, compare 1a) (Qal) 1a1) to arrange ", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_src_pron_arranges", "title": "arranges", "shelf": "pronunciation", "surface": "secular", "snippet": "arranges: pronounced (ARPABET) ER0 EY1 N JH IH0 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", "readable": false, "generated": false}, {"id": "card_src_pron_arrange", "title": "arrange", "shelf": "pronunciation", "surface": "secular", "snippet": "arrange: pronounced (ARPABET) ER0 EY1 N JH. 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", "readable": false, "generated": false}, {"id": "card_src_etym_arrange", "title": "arrange", "shelf": "etymology", "surface": "secular", "snippet": "arrange: etymology (Webster 1913) — v. t.: [OE. arayngen, OF. arengier, F. arranger, fr. a (L. ad) + OF. rengier, rangier, F. ranger. See Range, v. t.]. From Webster's Revised Unabridged Dictionary (1", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_lex_g7262", "title": "G7262 — ἐντάσσω (entassō): to arrange in", "shelf": "lexicon", "surface": "secular", "snippet": "ἐντάσσω (entassō), Strong's G7262: to arrange in. to place or post in :—;Pass., σφενδονᾶν ἐντεταγμένος posted to use the sling, (Xenophon Historicus) (ML)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_src_lex_g20234", "title": "G20234 — διαρρυθμίζω (diarruthmizō): to arrange in order", "shelf": "lexicon", "surface": "secular", "snippet": "διαρρυθμίζω (diarruthmizō), Strong's G20234: to arrange in order. arrange in order", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_src_etym_classify", "title": "classify", "shelf": "etymology", "surface": "secular", "snippet": "classify: etymology (Webster 1913) — v. t.: [L. classis class + Defn: To distribute into classes; to arrange according to a system; to arrnge in sets according to some method founded on common propert", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_lex_g21133", "title": "G21133 — στιχίζω (stichizō): to arrange", "shelf": "lexicon", "surface": "secular", "snippet": "στιχίζω (stichizō), Strong's G21133: to arrange. arranged in a row", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_src_lex_g4294", "title": "G4294 — προκαταρτίζω (prokatartizō): to arrange", "shelf": "lexicon", "surface": "secular", "snippet": "προκαταρτίζω (prokatartizō), Strong's G4294: to arrange. προ-κατ-αρτίζω to make ready beforehand : 2Co.9:5. † (AS)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_src_etym_assessor", "title": "assessor", "shelf": "etymology", "surface": "secular", "snippet": "assessor: etymology (Webster 1913) — n.: [L., one who sits beside, the assistant of a judge, fr. assid. See Assession. LL., one who arranges of determines the taxes, fr. assid. See Assess, v., and cf.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_etym_disarrange", "title": "disarrange", "shelf": "etymology", "surface": "secular", "snippet": "disarrange: etymology (Webster 1913) — v. t.: [Pref. dis- + arrange: cf. F. désarranger.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "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_works_counting"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}