{"query": "Counting: how many ways to choose and to arrange", "count": 17, "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", "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)", "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)", "generated": false}, {"id": "card_src_lex_g2885", "title": "G2885 — κοσμέω (kosmeō): to arrange", "shelf": "lexicon", "surface": "secular", "snippet": "κοσμέω (kosmeō), Strong's G2885: to arrange. κοσμέω , -ῶ (κόσμος), [in LXX for עָדָה, תָּקַן, etc. ;] __1. to order, arrange, prepare (in Hom. esp. of marshalling armies): Mat.25:7 (cf. Sir.50:9 , al.", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "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)", "generated": false}, {"id": "card_src_word_arrange", "title": "arrange", "shelf": "dictionary", "surface": "secular", "snippet": "arrange: (verb) put into a proper or systematic order — syn: set up · (verb) make arrangements for — syn: fix up · (verb) plan, organize, and carry out (an event) — syn: stage · (verb) set (printed ma", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "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)", "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)", "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)", "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", "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", "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", "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", "generated": false}, {"id": "card_n_71e537de3407", "title": "La Rochefoucauld 001: What we term virtue is often but a mass of various actions and divers interes...", "shelf": "classics", "surface": "secular", "snippet": "What we term virtue is often but a mass of various actions and divers interests, which fortune, or our own industry, manage to arrange; and it is not always from valour or from chastity that men are b", "authority_tier": "external_aligned", "source": "François de La Rochefoucauld, Maxims (1665)", "generated": false}, {"id": "card_n_22453f2203b2", "title": "Augustine, Confessions §aug_conf_12_023: For they say, \"Though these things be true, yet did not Moses intend those tw...", "shelf": "classics", "surface": "witness", "snippet": "For they say, \"Though these things be true, yet did not Moses intend those two, when, by revelation of the Spirit, he said, In the beginning God created heaven and earth. He did not under the name of ", "authority_tier": "father", "source": "Augustine, Confessions (c. AD 400)", "generated": false}, {"id": "card_src_pron_arranges", "title": "arranges", "shelf": "pronunciation", "surface": "secular", "snippet": "", "authority_tier": "", "source": "", "generated": false}, {"id": "card_src_pron_arrange", "title": "arrange", "shelf": "pronunciation", "surface": "secular", "snippet": "", "authority_tier": "", "source": "", "generated": false}]}