{"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", "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)", "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)", "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)", "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)", "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)", "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)", "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)", "generated": false}, {"id": "card_src_word_osculating_circle", "title": "osculating circle", "shelf": "dictionary", "surface": "secular", "snippet": "osculating circle: (noun) the circle that touches a curve (on the concave side) and whose radius is the radius of curvature — syn: circle of curvature", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_circle_of_curvature", "title": "circle of curvature", "shelf": "dictionary", "surface": "secular", "snippet": "circle of curvature: (noun) the circle that touches a curve (on the concave side) and whose radius is the radius of curvature — syn: osculating circle", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_book_65787", "title": "Bess of Hardwick and Her Circle — Maud Stepney Rawson", "shelf": "gutenberg", "surface": "secular", "snippet": "Bess of Hardwick and Her Circle, by Maud Stepney Rawson. Subjects: Nobility -- Great Britain -- Biography; Great Britain -- History -- Elizabeth, 1558-1603 -- Biography; Shrewsbury, Elizabeth Hardwick", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_word_vertical_circle", "title": "vertical circle", "shelf": "dictionary", "surface": "secular", "snippet": "vertical circle: (noun) a great circle on the celestial sphere passing through the zenith and perpendicular to the horizon", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_great_circle", "title": "great circle", "shelf": "dictionary", "surface": "secular", "snippet": "great circle: (noun) a circular line on the surface of a sphere formed by intersecting it with a plane passing through the center", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_equinoctial_circle", "title": "equinoctial circle", "shelf": "dictionary", "surface": "secular", "snippet": "equinoctial circle: (noun) the great circle on the celestial sphere midway between the celestial poles — syn: celestial equator, equinoctial line, equinoctial", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_word_traffic_circle", "title": "traffic circle", "shelf": "dictionary", "surface": "secular", "snippet": "traffic circle: (noun) a road junction at which traffic streams circularly around a central island — syn: circle, rotary, roundabout", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "generated": false}, {"id": "card_src_book_48326", "title": "The Chautauquan, Vol. 03, February 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle. — Chautauqua Literary a", "shelf": "gutenberg", "surface": "secular", "snippet": "The Chautauquan, Vol. 03, February 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle., by Chautauqua Literary and Scientific Circ", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_52043", "title": "The Chautauquan, Vol. 04, November 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle. — Chautauqua Literary a", "shelf": "gutenberg", "surface": "secular", "snippet": "The Chautauquan, Vol. 04, November 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle., by Chautauqua Literary and Scientific Circ", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_48165", "title": "The Chautauquan, Vol. 03, January 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle — Chautauqua Literary and", "shelf": "gutenberg", "surface": "secular", "snippet": "The Chautauquan, Vol. 03, January 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle, by Chautauqua Literary and Scientific Circle", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_48166", "title": "The Chautauquan, Vol. 03, December 1882 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle — Chautauqua Literary an", "shelf": "gutenberg", "surface": "secular", "snippet": "The Chautauquan, Vol. 03, December 1882 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle, by Chautauqua Literary and Scientific Circl", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}, {"id": "card_src_book_48327", "title": "The Chautauquan, Vol. 03, March 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle. — Chautauqua Literary and ", "shelf": "gutenberg", "surface": "secular", "snippet": "The Chautauquan, Vol. 03, March 1883 A Monthly Magazine Devoted to the Promotion of True Culture. Organ of the Chautauqua Literary and Scientific Circle., by Chautauqua Literary and Scientific Circle.", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "generated": false}]}