{"query": "The great-circle distance from New York to London", "count": 20, "results": [{"id": "card_works_haversine", "title": "The great-circle distance from New York to London", "shelf": "the-works", "surface": "secular", "snippet": "Across the curved Earth, the shortest path (the haversine great-circle distance) from New York to London is about 5,570 km — the number behind every flight plan and GPS fix.  Worked & sealed by the en", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_theory_depth_of_field", "title": "Depth of field & hyperfocal distance", "shelf": "theories", "surface": "secular", "snippet": "Depth of field & hyperfocal distance — an engine domain that can touch it: photography. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and seal them", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "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_heliocentrism_kepler_s_laws", "title": "Heliocentrism & Kepler's laws", "shelf": "theories", "surface": "secular", "snippet": "Heliocentrism & Kepler's laws — an engine domain that can touch it: astronomy. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it. Three laws, from Tycho", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_algebraic_geometry", "title": "Algebraic geometry (solution sets as shapes)", "shelf": "theories", "surface": "secular", "snippet": "Algebraic geometry (solution sets as shapes) — an engine domain that can touch it: mathematics. Calibration: map-only — specific curve computations verify; the theory is abstract. The study of the sha", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_honeycomb_conjecture", "title": "Optimal packing & the honeycomb conjecture (Hales)", "shelf": "theories", "surface": "secular", "snippet": "The hexagonal grid is the most efficient way to divide a surface into regions of equal area with the LEAST TOTAL PERIMETER. Stated by Pappus of Alexandria around 300 AD as an observation about bees, i", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_hermeneutics__the_theory_of_interpretation", "title": "Hermeneutics (the theory of interpretation)", "shelf": "theories", "surface": "secular", "snippet": "Hermeneutics (the theory of interpretation) — an engine domain that can touch it: philosophy. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RESONANCE); fo", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_depth_of_field__wave_optics", "title": "Bridge: Depth of field & hyperfocal distance  ↔  Wave optics (Huygens, Snell's law, diffraction)", "shelf": "bridges", "surface": "secular", "snippet": "Depth of field & hyperfocal distance and Wave optics (Huygens, Snell's law, diffraction) are the same form in different domains. focus and the circle of confusion are optics — the lens equation on a s", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_alm_connection_reality_is_mappable", "title": "Almanac: Reality is mappable: the same verified structure recurs across every domain", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  Across this whole moat -- physics, computer science, music, genetics -- the engine kept finding the SAME structures wearing different clothes, and this grand capstone confirms it by drawin", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_bridge_theory_hermeneutics__the_theory_of_interpretation__bayes_theorem", "title": "Bridge: Hermeneutics (the theory of interpretation)  ↔  Bayes' theorem", "shelf": "bridges", "surface": "secular", "snippet": "Hermeneutics (the theory of interpretation) and Bayes' theorem are the same form in different domains. the hermeneutical circle IS iterative conditioning: pre-understanding is a prior, the text is evi", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_dual_trigonometric__periodic", "title": "Duality: trigonometric  ↔  periodic  (circle vs oscillation)", "shelf": "bridges", "surface": "secular", "snippet": "A deep bridge between two forms — circle vs oscillation. sine and cosine are the projection of uniform circular motion; the trigonometric relations and periodic oscillation are the circle seen two way", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_builder_johannes_kepler", "title": "Johannes Kepler", "shelf": "builders", "surface": "secular", "snippet": "Johannes Kepler (1571–1630 AD) — science. The gift: the three laws of planetary motion — he broke the 2000-year spell of the circle and found the ellipse, uniting physics and astronomy. Where it fell ", "authority_tier": "reference", "source": "The builders of the Floor — credited with love, calibrated to the plumb-line", "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_bridge_theory_algebraic_geometry__euclidean_geometry_the_parallel_postulate", "title": "Bridge: Algebraic geometry (solution sets as shapes)  ↔  Euclidean geometry & the parallel postulate", "shelf": "bridges", "surface": "secular", "snippet": "Algebraic geometry (solution sets as shapes) and Euclidean geometry & the parallel postulate are the same form in different domains. Descartes put coordinates on the plane in 1637 and made equation an", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_domchk_geometry_claimed_circle_area", "title": "Geometry: circle area", "shelf": "geometry", "surface": "secular", "snippet": "A worked check in geometry: circle area.\n\nGIVEN\n  circle_radius = 5\n  pyth_a = 3\n  pyth_b = 4\n  pyth_c = 5\n  tri_a = 3\n  tri_b = 4\n  tri_c = 5\n\nCLAIMED\n  claimed_circle_area = 78.5398\n\nTHE ENGINE'S VE", "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_domchk_geometry_claimed_circle_circumference", "title": "Geometry: circle circumference", "shelf": "geometry", "surface": "secular", "snippet": "A worked check in geometry: circle circumference.\n\nGIVEN\n  circle_radius = 5\n  pyth_a = 3\n  pyth_b = 4\n  pyth_c = 5\n  tri_a = 3\n  tri_b = 4\n  tri_c = 5\n\nCLAIMED\n  claimed_circle_circumference = 31.415", "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_survival_save_seed", "title": "Saving your own seed", "shelf": "survival", "surface": "secular", "snippet": "Seed you save closes the circle and costs nothing. Save only from OPEN-POLLINATED (heirloom) plants — hybrids ('F1') won't come true. Let the best, healthiest plants fully ripen; scoop and dry the see", "authority_tier": "reference", "source": "USDA Farmers' Bulletins (public domain)", "readable": false, "generated": false}, {"id": "card_n_05f7744be9ca", "title": "Martyrdom of Polycarp XV", "shelf": "patristics", "surface": "witness", "snippet": "When he had pronounced this _amen_, and so finished his prayer, those who were appointed for the purpose kindled the fire. And as the flame blazed forth in great fury, we, to whom it was given to witn", "authority_tier": "father", "source": "Martyrdom of Polycarp (trans. Roberts-Donaldson, 1885)", "readable": false, "generated": false}, {"id": "card_span_012e3175af88", "title": "COUNCIL-FIRE CIRCLE", "shelf": "sources", "surface": "secular", "snippet": "In every large permanent camp I establish a proper \nTouncil-fire Circle or Council Camp. The uses and \n\n\nCampercraft or the Summer Camp 183 \n\n\nbenefits of these will be seen more and more, as camp \ngo", "authority_tier": "primary_pd", "source": "The Book of Woodcraft and Indian Lore", "readable": true, "generated": false}, {"id": "card_span_0959f04f8186", "title": "CARPENTRY AND JOINERY", "shelf": "practical", "surface": "secular", "snippet": "CARPENTRY   AND    JOINERY. \n\n\nround  as  indicated  by  the  dotted  lines,  care \nbeing  taken  that  it  is  always  in  contact  with \nthe  nails  at  c  and  d,  and  a  true  segment  of  a \ncir", "authority_tier": "primary_pd", "source": "Cassell's carpentry and joinery", "readable": true, "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_works_haversine"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}