{"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", "readable": false, "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)", "readable": false, "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)", "readable": false, "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", "readable": false, "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)", "readable": false, "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)", "readable": false, "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)", "readable": false, "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)", "readable": false, "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)", "readable": false, "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)", "readable": false, "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)", "readable": false, "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)", "readable": false, "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", "readable": false, "generated": false}, {"id": "card_n_179a4d8207ae", "title": "Augustine, Confessions §aug_conf_01_011: Hear, O God.", "shelf": "classics", "surface": "witness", "snippet": "Hear, O God. Alas, for man's sin! So saith man, and Thou pitiest him; for Thou madest him, but sin in him Thou madest not. Who remindeth me of the sins of my infancy? for in Thy sight none is pure fro", "authority_tier": "father", "source": "Augustine, Confessions (c. AD 400)", "readable": false, "generated": false}, {"id": "card_src_lex_g266", "title": "G266 — ἁμαρτία (hamartia): sin", "shelf": "lexicon", "surface": "secular", "snippet": "ἁμαρτία (hamartia), Strong's G266: sin. ἁμαρτία , -ας, ἡ (ἁμαρτάνω, which see), [in LXX chiefly for חַטָּאת and cogn. forms, also for פֶּשַׁע ,עָוֹן, etc. ;] prop. a missing the mark ; in cl. (see ref", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_n_7b34ae38a3c0", "title": "Psalm 51 — A Broken and Contrite Heart", "shelf": "codex", "surface": "witness", "snippet": "<<For the Chief Musician. A Psalm by David, when Nathan the prophet came to him, after he had gone in to Bathsheba.>> Have mercy on me, God, according to your loving kindness. According to the multitu", "authority_tier": "scripture", "source": "Psalm 51", "readable": false, "generated": false}, {"id": "card_n_6cb382b0b203", "title": "Easton: Sin-offering", "shelf": "dictionary", "surface": "secular", "snippet": "(Heb. hattath), the law of, is given in detail in Lev. 4-6:13; 9:7-11, 22-24; 12:6-8; 15:2, 14, 25-30; 14:19, 31; Num. 6:10-14. On the day of Atonement it was made with special solemnity (Lev. 16:5, 1", "authority_tier": "external_aligned", "source": "Matthew Easton, Illustrated Bible Dictionary (1897)", "readable": false, "generated": false}, {"id": "card_src_book_54291", "title": "Conscience and Sin: Daily Meditations for Lent, Including Week-days and Sundays — S. (Sabine) Baring-Gould", "shelf": "gutenberg", "surface": "secular", "snippet": "Conscience and Sin: Daily Meditations for Lent, Including Week-days and Sundays, by S. (Sabine) Baring-Gould. Subjects: Sin; Conscience; Lent -- Prayers and devotions. Read the full text (public domai", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_n_a6c94441bfe4", "title": "Romans 6", "shelf": "codex", "surface": "witness", "snippet": "1. What shall we say then? Shall we continue in sin, that grace may abound?\n2. May it never be! We who died to sin, how could we live in it any longer?\n3. Or don’t you know that all of us who were bap", "authority_tier": "scripture", "source": "World English Bible · Romans 6", "readable": false, "generated": false}, {"id": "card_works_snell", "title": "Light bends: Snell's law at a glass surface", "shelf": "the-works", "surface": "secular", "snippet": "Passing from air into glass (n = 1.5) at 30°, a ray refracts to 19.47° — n₁ sin θ₁ = n₂ sin θ₂. The same law bends every lens and every rainbow.  Worked & sealed by the engine — sin θ₂ = (1·sin30)/1.5", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}]}