{"query": "The conserved invariant — energy, the same end through the f", "count": 20, "results": [{"id": "card_theory_topology", "title": "Topology (what survives stretching)", "shelf": "theories", "surface": "secular", "snippet": "Topology (what survives stretching) — an engine domain that can touch it: mathematics. Calibration: map-only — specific invariants compute; the classification results are proofs, not computations. Geo", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_group_theory", "title": "Group theory & symmetry (the mathematics of what stays the same)", "shelf": "theories", "surface": "secular", "snippet": "Group theory & symmetry (the mathematics of what stays the same) — an engine domain that can touch it: mathematics. Calibration: seals — group orders, subgroup structure and symmetry counts compute. A", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_spectral_geometry", "title": "Spectral geometry (can one hear the shape of a drum?)", "shelf": "theories", "surface": "secular", "snippet": "Spectral geometry (can one hear the shape of a drum?) — an engine domain that can touch it: mathematics. Calibration: partial — specific relations verify; the theory as a whole is not a sealable compu", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "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_special_relativity", "title": "Special relativity", "shelf": "theories", "surface": "secular", "snippet": "Special relativity — an engine domain that can touch it: physics. Calibration: partial — Lorentz and E = mc² relations verify; the postulates are map-only. Two postulates (Einstein, 1905): the laws of", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_maxwell_s_equations_classical_electromagnetism", "title": "Maxwell's equations / classical electromagnetism", "shelf": "theories", "surface": "secular", "snippet": "Maxwell's equations / classical electromagnetism — an engine domain that can touch it: electrical. Calibration: partial — circuit and field relations verify; the full field theory is map-only. Four eq", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_linear_algebra", "title": "Linear algebra (vector spaces, eigenvalues)", "shelf": "theories", "surface": "secular", "snippet": "Linear algebra (vector spaces, eigenvalues) — an engine domain that can touch it: linear_algebra. Calibration: seals. Vectors, the linear maps between them, and matrices as those maps written down. Th", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_renormalization_group", "title": "The renormalization group (physics across scales)", "shelf": "theories", "surface": "secular", "snippet": "The renormalization group (physics across scales) — an engine domain that can touch it: physics. Calibration: partial — specific relations verify; the theory as a whole is not a sealable computation. ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_floor_the_hamiltonian", "title": "The Hamiltonian — the law of the flow", "shelf": "codex", "surface": "secular", "snippet": "The energy operator and the generator of time evolution: it governs how the many potentials develop between the one source and the one end. Four pillars rest on the floors already seeded - the generat", "authority_tier": "engine_derived", "source": "Narrow Highway — the Hamiltonian", "readable": false, "generated": false}, {"id": "card_question_bsd", "title": "The Birch and Swinnerton-Dyer conjecture", "shelf": "millennium", "surface": "secular", "snippet": "The Birch and Swinnerton-Dyer conjecture. The rank of the group of rational points of an elliptic curve over Q equals the order of vanishing of its L-function at s = 1, and the leading coefficient is ", "authority_tier": "reference", "source": "Clay Mathematics Institute, the Millennium Prize Problems (2000)", "readable": false, "generated": false}, {"id": "card_src_mill_cremona_ecdata", "title": "J. E. Cremona 1997 — ecdata — elliptic curves over Q (the allbsd files: conductor, isogeny class, number, a-invariants, rank, |T|, prod c_p, real period Omega, L^(r)(E,1)/r!, regul", "shelf": "millennium", "surface": "secular", "snippet": "J. E. Cremona (1997-2026). ecdata — elliptic curves over Q (the allbsd files: conductor, isogeny class, number, a-invariants, rank, |T|, prod c_p, real period Omega, L^(r)(E,1)/r!, regulator, |Sha|). ", "authority_tier": "reference", "source": "J. E. Cremona (1997-2026), github.com/JohnCremona/ecdata (conductor <= 500000)", "readable": false, "generated": false}, {"id": "card_chart_euler_char", "title": "Topology and Euler's formula", "shelf": "codex", "surface": "secular", "snippet": "Topology and Euler's formula. A chart on the one map: this is the tick stick stick_topology_and_euler_s_formula, placed at the node it charts. Basis: the stick seals V - E + F = 2 for the Platonic sol", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_floor_noethers_theorem", "title": "Noether's theorem — symmetry is the source of conservation", "shelf": "codex", "surface": "secular", "snippet": "For every continuous symmetry of the action there is a conserved quantity (Emmy Noether, 1918). The seam between the Lagrangian and the Hamiltonian: the Lagrangian's time-symmetry PRODUCES the Hamilto", "authority_tier": "engine_derived", "source": "Narrow Highway — Noether's theorem", "readable": false, "generated": false}, {"id": "card_alm_connection_watson_crick_is_reversible_code", "title": "Almanac: Watson-Crick complementarity is a reversible code: each strand backs up the other", "shelf": "almanac", "surface": "secular", "snippet": "SITUATION\n  DNA is a double strand for a deep reason: each strand is the exact complement of the other, so the molecule carries its own backup. genetics confirmed the base-pairing -- the complement of", "authority_tier": "reference", "source": "The Almanac — verified-only practical wisdom (sealed)", "readable": false, "generated": false}, {"id": "card_floor_relativity", "title": "Relativity — many frames, one invariant", "shelf": "codex", "surface": "secular", "snippet": "Special relativity: the laws and the speed of light are the same in every inertial frame; observers disagree on time and length but agree on the invariant interval - many frames, one invariant truth. ", "authority_tier": "engine_derived", "source": "Narrow Highway — relativity", "readable": false, "generated": false}, {"id": "card_ham_noether", "title": "The conserved invariant — energy, the same end through the flow", "shelf": "codex", "surface": "secular", "snippet": "By Noether's theorem, time-translation symmetry gives one conserved quantity: the Hamiltonian, the energy. It is the invariant along every path the system can take. 'Many possibilities but the story e", "authority_tier": "engine_derived", "source": "Narrow Highway — the Hamiltonian", "readable": false, "generated": false}, {"id": "card_noether_the_invariant", "title": "The invariant — the same end carried through every path", "shelf": "codex", "surface": "secular", "snippet": "The conserved quantity is the invariant: the same at the end as at the beginning, carried unchanged through every path the system can take. 'Many possibilities but the story ends the same' as a theore", "authority_tier": "engine_derived", "source": "Narrow Highway — Noether's theorem", "readable": false, "generated": false}, {"id": "card_rel_special", "title": "Special relativity — many frames, one invariant", "shelf": "codex", "surface": "secular", "snippet": "The laws and the speed of light are the same in every inertial frame; observers disagree on time and length but agree on c and on the invariant interval s^2 = (ct)^2 - x^2. A clock at 0.6c runs slow b", "authority_tier": "engine_derived", "source": "Narrow Highway — relativity", "readable": false, "generated": false}, {"id": "card_src_book_9933", "title": "A Treatise on the Theory of Invariants — Oliver E. (Oliver Edmunds) Glenn", "shelf": "gutenberg", "surface": "secular", "snippet": "A Treatise on the Theory of Invariants, by Oliver E. (Oliver Edmunds) Glenn. Subjects: Invariants. Read the full text (public domain): https://www.gutenberg.org/ebooks/9933", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_thermo_first_law", "title": "The first law — energy is conserved", "shelf": "codex", "surface": "secular", "snippet": "dU = dQ - dW: energy is conserved, counted now as heat and work. This is exactly the conserved energy Noether derives from time-translation symmetry - the same invariant, bookkept for a thermal system", "authority_tier": "engine_derived", "source": "Narrow Highway — thermodynamics", "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_topology"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}