{"query": "sin θ₂ = (1·sin30)/1.5 → θ₂ ≈ 19.47°", "count": 20, "results": [{"id": "card_v_1cfd6b96477b", "title": "sin θ₂ = (1·sin30)/1.5 → θ₂ ≈ 19.47°", "shelf": "optics", "surface": "secular", "snippet": "Verdict: HOLDS.\n• optics.snell_law: θ₂ = arcsin((1.0/1.5)·sin(30.0°)) = 19.471° (matches claim 19.471220634490688)\nSealed and independently re-checkable: https://narrowhighway.com/s/7e0717dfc554e1bf11", "authority_tier": "engine", "source": "Verified by the engine — optics", "generated": false}, {"id": "card_theory_wave_optics", "title": "Wave optics (Huygens, Snell's law, diffraction)", "shelf": "theories", "surface": "secular", "snippet": "Wave optics (Huygens, Snell's law, diffraction) — an engine domain that can touch it: optics. Calibration: seals — refraction, lens and diffraction relations compute. Light behaves as a wave: it refra", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "generated": false}, {"id": "card_n_8832cd0d54b2", "title": "Aurelius, Meditations 2.7: Theophrastus, where he compares sin with sin (as after a vulgar sense such th...", "shelf": "classics", "surface": "secular", "snippet": "Theophrastus, where he compares sin with sin (as after a vulgar sense such things I grant may be compared:) says well and like a philosopher, that those sins are greater which are committed through lu", "authority_tier": "external_aligned", "source": "Marcus Aurelius, Meditations (c. AD 170)", "generated": false}, {"id": "card_n_50196c35c878", "title": "1 John 3", "shelf": "codex", "surface": "witness", "snippet": "1. See how great a love the Father has given to us, that we should be called children of God! For this cause the world doesn’t know us, because it didn’t know him.\n2. Beloved, now we are children of G", "authority_tier": "scripture", "source": "World English Bible · 1 John 3", "generated": false}, {"id": "card_n_8d1c964dd9c3", "title": "Easton: Sin", "shelf": "dictionary", "surface": "secular", "snippet": "Is “any want of conformity unto or transgression of the law of God” (1 John 3:4; Rom. 4:15), in the inward state and habit of the soul, as well as in the outward conduct of the life, whether by omissi", "authority_tier": "external_aligned", "source": "Matthew Easton, Illustrated Bible Dictionary (1897)", "generated": false}, {"id": "card_n_b487d6767744", "title": "Pirkei Avot §avot_05_18: Whoever causes the multitudes to be righteous, sin will not occur on his acco...", "shelf": "classics", "surface": "secular", "snippet": "Whoever causes the multitudes to be righteous, sin will not occur on his account; And whoever causes the multitudes to sin, they do not give him the ability to repent. Moses was righteous and caused t", "authority_tier": "external_aligned", "source": "Pirkei Avot — Ethics of the Fathers (Mishnah, c. AD 200)", "generated": false}, {"id": "card_src_lex_h2399", "title": "H2399 — חֵטְא (chet): sin", "shelf": "lexicon", "surface": "secular", "snippet": "חֵטְא (chet), Strong's H2399: sin. 1) sin 1a) sin 1b) guilt for sin 1c) punishment for sin Aramaic equivalent: cha.ti (חֲטָי \"sin\" H2408)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_src_lex_h2398", "title": "H2398 — חָטָא (cha.ta): to sin", "shelf": "lexicon", "surface": "secular", "snippet": "חָטָא (cha.ta), Strong's H2398: to sin. 1) to sin, miss, miss the way, go wrong, incur guilt, forfeit, purify from uncleanness 1a) (Qal) 1a1) to miss 1a2) to sin, miss the goal or path of right and du", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_enc_easton_forgiveness-of-sin", "title": "Forgiveness of sin", "shelf": "encyclopedia", "surface": "witness", "snippet": "One of the constituent parts of justification. In pardoning sin, God absolves the sinner from the condemnation of the law, and that on account of the work of Christ, i.e., he removes the guilt of sin,", "authority_tier": "reference", "source": "Easton's Bible Dictionary (1897, public domain)", "generated": false}, {"id": "card_src_lex_h2401", "title": "H2401 — חֲטָאָה (cha.ta.ah): sin", "shelf": "lexicon", "surface": "secular", "snippet": "חֲטָאָה (cha.ta.ah), Strong's H2401: sin. 1) sin, sin offering 1a) sin 1b) sin offering Aramaic equivalent: chat.ta.ah (חַטָּאָה \"sin offering\" H2402)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_n_d186ec88bbd9", "title": "Easton: Forgiveness of sin", "shelf": "dictionary", "surface": "secular", "snippet": "One of the constituent parts of justification. In pardoning sin, God absolves the sinner from the condemnation of the law, and that on account of the work of Christ, i.e., he removes the guilt of sin,", "authority_tier": "external_aligned", "source": "Matthew Easton, Illustrated Bible Dictionary (1897)", "generated": false}, {"id": "card_src_lex_g21497", "title": "G21497 — σ, Σεν (sin/shin): Sin/Shin", "shelf": "lexicon", "surface": "secular", "snippet": "σ, Σεν (sin/shin), Strong's G21497: Sin/Shin. Sin/Shin, the 21st letter of the Hebrew alphabet; used in LXX for acrostic Psalms such as Psa.119", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_fk_fk1_29", "title": "Run with Patience", "shelf": "fieldkit", "surface": "secular", "snippet": "Run with Patience — anchor: Hebrews 12:1-2 (lay aside every weight, and the sin which doth so easily beset us).  Source: Two things to lay down: weights, and the besetting sin.  Floor: Carrying both, ", "authority_tier": "reference", "source": "The Lighthouse Field Kit v1 (authored deck)", "generated": false}, {"id": "card_n_293819220cd4", "title": "Hebrews 10", "shelf": "codex", "surface": "witness", "snippet": "1. For the law, having a shadow of the good to come, not the very image of the things, can never with the same sacrifices year by year, which they offer continually, make perfect those who draw near.\n", "authority_tier": "scripture", "source": "World English Bible · Hebrews 10", "generated": false}, {"id": "card_src_word_deadly_sin", "title": "deadly sin", "shelf": "dictionary", "surface": "secular", "snippet": "deadly sin: (noun) an unpardonable sin entailing a total loss of grace — syn: mortal sin", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_mortal_sin", "title": "mortal sin", "shelf": "dictionary", "surface": "secular", "snippet": "mortal sin: (noun) an unpardonable sin entailing a total loss of grace — syn: deadly sin", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_actual_sin", "title": "actual sin", "shelf": "dictionary", "surface": "secular", "snippet": "actual sin: (noun) a sin committed of your own free will (as contrasted with original sin)", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_lex_h2408", "title": "H2408 — חֲטָי (cha.ti): sin", "shelf": "lexicon", "surface": "secular", "snippet": "חֲטָי (cha.ti), Strong's H2408: sin. sin Aramaic of chet (חֵטְא \"sin\" H2399)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_src_lex_h2409", "title": "H2409 — חַטָּיָא (cha.t.ta.ya): sin offering", "shelf": "lexicon", "surface": "secular", "snippet": "חַטָּיָא (cha.t.ta.ya), Strong's H2409: sin offering. sin offering Aramaic of chat.tat (חַטָּאת \": sin\" H2403B)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}, {"id": "card_src_lex_h2402", "title": "H2402 — חַטָּאָה (chat.ta.ah): sin offering", "shelf": "lexicon", "surface": "secular", "snippet": "חַטָּאָה (chat.ta.ah), Strong's H2402: sin offering. sin offering Aramaic of cha.ta.ah (חֲטָאָה \"sin\" H2401)", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "generated": false}]}