{"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_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}, {"id": "card_n_fa0acd9a1b33", "title": "Polycarp to the Philippians VIII", "shelf": "patristics", "surface": "witness", "snippet": "Let us then continually persevere in our hope, and the earnest of our righteousness, which is Jesus Christ, “who bore our sins in His own body on the tree,” “who did no sin, neither was guile found in", "authority_tier": "father", "source": "Epistle of Polycarp to the Philippians (trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_n_9b276ed995a5", "title": "Sermon: Restoration Through the Blood", "shelf": "codex", "surface": "witness", "snippet": "Restoration Through the Blood\nMain Text: 1 Peter 5:9–11 NKJV\nIntroduction\nGod designed us to live in love — with Him, one another, and creation.\nSin corrupted the code, introducing viruses: lust, gree", "authority_tier": "matt", "source": "Operator-authored sermon", "readable": false, "generated": false}, {"id": "card_n_1d1f032bf9d3", "title": "Westminster Shorter Q20", "shelf": "codex", "surface": "witness", "snippet": "Did God leave all mankind to perish in the estate of sin and misery?\n\nGod having, out of his mere good pleasure, from all eternity, elected some to everlasting life, did enter into a covenant of grace", "authority_tier": "catechism", "source": "Westminster Shorter Catechism (1647)", "readable": false, "generated": false}, {"id": "card_alm_connection_shape_and_number_are_one", "title": "Almanac: Shape and number are one -- coordinates turn every figure into arithmetic and back, with the right triangle as the master key", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Capstone of the geometry cluster. Lay a grid on space and shape becomes number: a point is its coordinates, a length is a calculation, an angle is a ratio -- and the sealed cards of this c", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_n_7f2f52140183", "title": "Devotional: Restoration", "shelf": "codex", "surface": "witness", "snippet": "God created us to live in love. In love with Him, those around us, and our environment. We were programmed for that state, but the world has corrupted that programming. Sin is a virus in the code. It ", "authority_tier": "matt", "source": "Operator-authored devotional", "readable": false, "generated": false}, {"id": "card_n_899f1c38d0c8", "title": "James 5:16", "shelf": "codex", "surface": "witness", "snippet": "Confess your sins to one another and pray for one another, that you may be healed. The insistent prayer of a righteous person is powerfully effective.", "authority_tier": "scripture", "source": "World English Bible · James 5:16", "readable": false, "generated": false}, {"id": "card_n_4529cf87e2d4", "title": "Heidelberg Q23", "shelf": "codex", "surface": "witness", "snippet": "What are these articles?\n\nI believe in God the Father almighty, Maker of heaven and earth. And in Jesus Christ, his only begotten Son, our Lord; who was conceived by the Holy Ghost, born of the Virgin", "authority_tier": "catechism", "source": "Heidelberg Catechism (1563)", "readable": false, "generated": false}, {"id": "card_n_564bb97c946f", "title": "The Apostles' Creed", "shelf": "codex", "surface": "witness", "snippet": "I believe in God, the Father almighty,\ncreator of heaven and earth.\n\nI believe in Jesus Christ, his only Son, our Lord,\nwho was conceived by the Holy Spirit,\nborn of the Virgin Mary,\nsuffered under Po", "authority_tier": "creed", "source": "The Apostles' Creed · c. 2nd–8th centuries (final form ~700 AD)", "readable": false, "generated": false}, {"id": "card_n_d598a2d34ecb", "title": "Belgic Art. 24: Man's Sanctification and Good Works", "shelf": "codex", "surface": "witness", "snippet": "We believe that this true faith, being wrought in man by the hearing of the Word of God and the operation of the Holy Ghost, regenerates and makes him a new man, causing him to live a new life and fre", "authority_tier": "creed", "source": "Belgic Confession (1561)", "readable": false, "generated": false}, {"id": "card_n_eea82058b82d", "title": "Ignatius to the Smyrnaeans VII", "shelf": "patristics", "surface": "witness", "snippet": "They abstain from the Eucharist and from prayer, because they confess not the Eucharist to be the flesh of our Saviour Jesus Christ, which suffered for our sins, and which the Father, of His goodness,", "authority_tier": "father", "source": "Ignatius to the Smyrnaeans (shorter recension; trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_n_339e73de8bc6", "title": "2 Timothy 3", "shelf": "codex", "surface": "witness", "snippet": "1. But know this: that in the last days, grievous times will come.\n2. For men will be lovers of self, lovers of money, boastful, arrogant, blasphemers, disobedient to parents, unthankful, unholy,\n3. w", "authority_tier": "scripture", "source": "World English Bible · 2 Timothy 3", "readable": false, "generated": false}, {"id": "card_n_3a794cd9373c", "title": "Polycarp to the Philippians I", "shelf": "patristics", "surface": "witness", "snippet": "I have greatly rejoiced with you in our Lord Jesus Christ, because ye have followed the example of true love [as displayed by God], and have accompanied, as became you, those who were bound in chains,", "authority_tier": "father", "source": "Epistle of Polycarp to the Philippians (trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_n_c3b2790c36e5", "title": "Psalm 25 — Psalm 25", "shelf": "codex", "surface": "witness", "snippet": "<<By David.>> To you, Yahweh, do I lift up my soul. My God, I have trusted in you. Don't let me be shamed. Don't let my enemies triumph over me. Yes, no one who waits for you shall be shamed. They sha", "authority_tier": "scripture", "source": "Psalm 25", "readable": false, "generated": false}, {"id": "card_n_a0b8e603f03c", "title": "Psalm 65 — Psalm 65", "shelf": "codex", "surface": "witness", "snippet": "<<For the Chief Musician. A Psalm by David. A song.>> Praise waits for you, God, in Zion. To you shall vows be performed. You who hear prayer, to you all men will come. Sins overwhelmed me, but you at", "authority_tier": "scripture", "source": "Psalm 65", "readable": false, "generated": false}, {"id": "card_n_20a9445137c0", "title": "Revelation 1", "shelf": "codex", "surface": "witness", "snippet": "1. This is the Revelation of Jesus Christ, which God gave him to show to his servants the things which must happen soon, which he sent and made known by his angel to his servant, John,\n2. who testifie", "authority_tier": "scripture", "source": "World English Bible · Revelation 1", "readable": false, "generated": false}, {"id": "card_n_98aaf9f16770", "title": "Hebrews 1", "shelf": "codex", "surface": "witness", "snippet": "1. God, having in the past spoken to the fathers through the prophets at many times and in various ways,\n2. has at the end of these days spoken to us by his Son, whom he appointed heir of all things, ", "authority_tier": "scripture", "source": "World English Bible · Hebrews 1", "readable": false, "generated": false}, {"id": "card_n_8caf4ba1d131", "title": "Barnabas XII", "shelf": "patristics", "surface": "witness", "snippet": "Testament._ In like manner He points to the cross of Christ in another prophet, who saith, “And when shall these things be accomplished? And the Lord saith, When a tree shall be bent down, and again a", "authority_tier": "father", "source": "Epistle of Barnabas (trans. Roberts-Donaldson, 1885)", "readable": false, "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_v_1cfd6b96477b"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}