{"query": "3²   4² = 5² → a true right angle", "count": 20, "results": [{"id": "card_theory_non_euclidean_hyperbolic_elliptic_geometry", "title": "Non-Euclidean (hyperbolic / elliptic) geometry", "shelf": "theories", "surface": "secular", "snippet": "Non-Euclidean (hyperbolic / elliptic) geometry — an engine domain that can touch it: geometry. Calibration: partial — curvature relations verify; the choice of axioms is map-only. Deny Euclid's fifth ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_golden_ratio_phyllotaxis", "title": "The golden ratio & phyllotaxis", "shelf": "theories", "surface": "secular", "snippet": "The golden ratio & phyllotaxis — an engine domain that can touch it: mathematics. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and seal them. phi ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_vsepr_theory", "title": "VSEPR theory (molecular geometry)", "shelf": "theories", "surface": "secular", "snippet": "VSEPR theory (molecular geometry) — an engine domain that can touch it: molecular_geometry. Calibration: seals — shapes and bond angles predict directly. Valence Shell Electron Pair Repulsion: electro", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_physical_oceanography", "title": "Physical oceanography (hydrostatics, tides)", "shelf": "theories", "surface": "secular", "snippet": "Physical oceanography (hydrostatics, tides) — an engine domain that can touch it: oceanography. Calibration: seals — pressure with depth and tidal periods compute. Pressure rises about one atmosphere ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_differential_geometry", "title": "Differential geometry (curvature measured from inside)", "shelf": "theories", "surface": "secular", "snippet": "Differential geometry (curvature measured from inside) — an engine domain that can touch it: geometry. Calibration: map-only — specific curvature and geodesic computations verify; the framework is bro", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_map_projections", "title": "Map projections (why no flat map is honest)", "shelf": "theories", "surface": "secular", "snippet": "Map projections (why no flat map is honest) — an engine domain that can touch it: geography. Calibration: seals — projected coordinates and distortion factors compute exactly. NO FLAT MAP OF A SPHERE ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_projective_geometry", "title": "Projective geometry (perspective & the cross-ratio)", "shelf": "theories", "surface": "secular", "snippet": "Projective geometry (perspective & the cross-ratio) — an engine domain that can touch it: geometry. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_biomechanics_human_movement", "title": "Biomechanics of human movement (levers, torque, ground reaction)", "shelf": "theories", "surface": "secular", "snippet": "Biomechanics of human movement (levers, torque, ground reaction) — an engine domain that can touch it: exercise_science. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable cl", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_v_b7cf152660c4", "title": "3² + 4² = 5² → a true right angle", "shelf": "geometry", "surface": "secular", "snippet": "Verdict: HOLDS.\n• geometry.pythagorean: (3.0,4.0,5.0) right-triangle=True (matches claim)\nSealed and independently re-checkable: https://narrowhighway.com/s/aa3f89f2bd9378be920cc301b665a6de98b4b1c0ec2", "authority_tier": "engine", "source": "Verified by the engine — geometry", "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_nav_compass", "title": "The compass — magnetic north vs true north", "shelf": "navigation", "surface": "secular", "snippet": "A compass needle points to MAGNETIC north, which differs from TRUE (map) north by an angle called DECLINATION — printed on the map's margin, and different for every region and slowly changing. To be a", "authority_tier": "reference", "source": "U.S. Army FM 3-25.26 — Map Reading and Land Navigation (public domain)", "readable": false, "generated": false}, {"id": "card_bridge_theory_euclidean_geometry_the_parallel_postulate__cell_theory", "title": "Bridge: Euclidean geometry & the parallel postulate  ↔  Cell theory", "shelf": "bridges", "surface": "secular", "snippet": "Euclidean geometry & the parallel postulate and Cell theory are the same form in different domains. the honeycomb theorem (Hales 1999): the hexagonal grid minimizes total perimeter per area, and the i", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_standard_model", "title": "The floor of the Standard Model - where two trees meet", "shelf": "codex", "surface": "secular", "snippet": "The Standard Model of particle physics stands on two roots: Maxwell's electromagnetism (the electromagnetic tree) and Fermi's 1933 theory of the weak interaction (the weak tree), both on quantum mecha", "authority_tier": "engine_derived", "source": "Narrow Highway - the Standard-Model chain (operator seed)", "readable": false, "generated": false}, {"id": "card_src_fed_nasa_techdoc_19980227352", "title": "A Method of Solution with Tabulated Results for the Attached Oblique Shock-Wave System for Surfaces at Various Angles of Attack, Sweep, and Dihedral in an Equilibrium Real Gas Incl", "shelf": "science", "surface": "secular", "snippet": "A Method of Solution with Tabulated Results for the Attached Oblique Shock-Wave System for Surfaces at Various Angles of Attack, Sweep, and Dihedral in an Equilibrium Real Gas Including the Atmosphere", "authority_tier": "reference", "source": "NASA technical documents (PD, 17 USC 105)", "readable": true, "generated": false}, {"id": "card_domchk_molecular_geometry_claimed_geometry", "title": "Molecular Geometry: geometry", "shelf": "molecular_geometry", "surface": "secular", "snippet": "A worked check in molecular geometry: geometry.\n\nGIVEN\n  bonding_domains = 4\n  lone_pairs = 0\n\nCLAIMED\n  claimed_geometry = tetrahedral\n\nTHE ENGINE'S VERDICT\n  molecular_geometry.vsepr: CONFIRMED — st", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "readable": false, "generated": false}, {"id": "card_works_trig_identities", "title": "From the unit circle to the double-angle law", "shelf": "the-works", "surface": "secular", "snippet": "The Pythagorean identity is the unit circle written as algebra; the double-angle law for cosine follows in its train. Both are confirmed exactly (not sampled), for all x.  Worked & sealed by the engin", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_span_0e5e7a4144b9", "title": "I will close this discursive chapter by offering a bit of advice", "shelf": "practical", "surface": "secular", "snippet": "I will close this discursive chapter by offering a bit of advice. Do not\r\ngo into the woods on a fishing tour without a stock of well cleansed\r\nangle-worms. Keep them in a tin can partly filled with d", "authority_tier": "primary_pd", "source": "Woodcraft and Camping", "readable": true, "generated": false}, {"id": "card_works_polygon", "title": "The angles inside a hexagon", "shelf": "the-works", "surface": "secular", "snippet": "The interior angles of any n-sided polygon sum to (n−2)·180°. For a hexagon that is 720° — the reason six equilateral triangles, or a honeycomb, tile the plane.  Worked & sealed by the engine — (6−2)·", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_works_vsepr", "title": "Why methane is a tetrahedron", "shelf": "the-works", "surface": "secular", "snippet": "Four bonding pairs and no lone pairs around a central atom push apart into a tetrahedron with 109.47° angles — the shape of methane, and of carbon's whole architecture.  Worked & sealed by the engine ", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_domchk_geometry_claimed_interior_angle_sum_deg", "title": "Geometry: interior angle sum deg", "shelf": "geometry", "surface": "secular", "snippet": "A worked check in geometry: interior angle sum deg.\n\nGIVEN\n  polygon_n = 6\n\nCLAIMED\n  claimed_interior_angle_sum_deg = 720\n\nTHE ENGINE'S VERDICT\n  geometry.polygon_interior_angle_sum: CONFIRMED — 6-go", "authority_tier": "reference", "source": "The verifier's own documented relation, and a run this engine performed against it (deterministic; re-runnable with tools/domain_goldens.py)", "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_theory_non_euclidean_hyperbolic_elliptic_geometry"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}