{"query": "Every continuous symmetry a conservation law", "count": 20, "results": [{"id": "card_noether_symmetry_conservation", "title": "Every continuous symmetry a conservation law", "shelf": "codex", "surface": "secular", "snippet": "Noether (1918): for every continuous symmetry of the action there is a conserved quantity, and conversely. The deepest structural theorem in physics - it says WHY the conservation laws hold. It lives ", "authority_tier": "engine_derived", "source": "Narrow Highway — Noether's theorem", "readable": false, "generated": false}, {"id": "card_theory_conservation_of_energy", "title": "Conservation of energy (1st law of thermodynamics)", "shelf": "theories", "surface": "secular", "snippet": "Conservation of energy (1st law of thermodynamics) — an engine domain that can touch it: thermodynamics. Calibration: seals. Energy is neither created nor destroyed, only converted. ΔU = Q - W: the ch", "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_quasicrystals", "title": "Quasicrystals (forbidden symmetry in real matter)", "shelf": "theories", "surface": "secular", "snippet": "Matter that is ordered but not periodic. Dan Shechtman recorded an electron diffraction pattern from rapidly cooled Al-Mn on 8 April 1982 showing SHARP Bragg peaks with ten-fold symmetry — sharp peaks", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_aperiodic_tiling", "title": "Aperiodic tiling (Penrose, and the 2023 monotile)", "shelf": "theories", "surface": "secular", "snippet": "Two tile shapes plus local edge-matching rules that cover the plane completely and CANNOT repeat. Penrose (1974) gave two forms: P2, the kite and dart; P3, a thin rhombus (36°) and a fat one (72°). Th", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_superfluid_vacuum_theory", "title": "Superfluid vacuum theory (the vacuum as a quantum liquid)", "shelf": "theories", "surface": "secular", "snippet": "Superfluid vacuum theory (the vacuum as a quantum liquid) — an engine domain that can touch it: physics. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RES", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_noether_s_theorem__symmetry_and_conservation", "title": "Noether's theorem (symmetry and conservation)", "shelf": "theories", "surface": "secular", "snippet": "Noether's theorem (symmetry and conservation) — an engine domain that can touch it: physics. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RESONANCE); for", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_molecular_symmetry_point_groups", "title": "Molecular symmetry & point groups", "shelf": "theories", "surface": "secular", "snippet": "Molecular symmetry & point groups — an engine domain that can touch it: molecular_geometry. Calibration: seals — a deterministic verifier can CONFIRM or BREAK checkable claims drawn from it, and seal ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_conservation_of_linear_angular_momentum", "title": "Conservation of linear & angular momentum", "shelf": "theories", "surface": "secular", "snippet": "Conservation of linear & angular momentum — an engine domain that can touch it: physics. Calibration: seals. Total momentum before equals total momentum after, in any closed system. Linear: p = mv. An", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_quasicrystals__aperiodic_tiling", "title": "Bridge: Quasicrystals (forbidden symmetry in real matter)  ↔  Aperiodic tiling (Penrose, and the 2023 monotile)", "shelf": "bridges", "surface": "secular", "snippet": "Quasicrystals (forbidden symmetry in real matter) and Aperiodic tiling (Penrose, and the 2023 monotile) are the same form in different domains. a quasicrystal IS an aperiodic tiling realised in matter", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_category_theory__group_theory", "title": "Bridge: Category theory (the mathematics of structure-preserving maps)  ↔  Group theory & symmetry (the mathematics of what stays the same)", "shelf": "bridges", "surface": "secular", "snippet": "Category theory (the mathematics of structure-preserving maps) and Group theory & symmetry (the mathematics of what stays the same) are the same form in different domains. a group IS a category with o", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_c_130ff92ca772", "title": "Supersymmetry — pairing as the map's arrange ↔ The periodic table — the map of the elements", "shelf": "connections", "surface": null, "snippet": "the symmetry then PREDICTS the missing partner — a broken pair is a gap that tells us what to look for, the way SUSY predicts a superpartner.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_n_0be5414e0c37", "title": "Supersymmetry — pairing as the map's arrangement", "shelf": "concepts", "surface": "secular", "snippet": "Arrange the map so each axis/node has a dual; the symmetry then PREDICTS the missing partner — a broken pair is a gap that tells us what to look for, the way SUSY predicts a superpartner.\n\nHONEST STAT", "authority_tier": "matt", "source": "Operator's seed (Matt) — honest grade: resonance", "readable": false, "generated": false}, {"id": "card_builder_peter_higgs", "title": "Peter Higgs", "shelf": "builders", "surface": "secular", "snippet": "Peter Higgs (1929-2024 AD) - physics. the mechanism (1964) by which gauge bosons acquire mass through spontaneous symmetry breaking - the Higgs field (A builder of the Floor of Discovery, credited wit", "authority_tier": "reference", "source": "The builders of the Floor - credited with love, calibrated to the plumb-line", "readable": false, "generated": false}, {"id": "card_rel_poincare", "title": "Poincaré symmetry — the group that feeds Noether", "shelf": "codex", "surface": "secular", "snippet": "The symmetry group of relativity - boosts, rotations and translations - is a continuous symmetry, so by Noether it gives the conserved energy, momentum, angular momentum and the stress-energy tensor. ", "authority_tier": "engine_derived", "source": "Narrow Highway — relativity", "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_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_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_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_src_word_mirror_symmetry", "title": "mirror symmetry", "shelf": "dictionary", "surface": "secular", "snippet": "mirror symmetry: (noun) (physics) parity is conserved in a universe in which the laws of physics are the same in a right-handed system of coordinates as in a left-handed system — syn: parity, conserva", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "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_noether_symmetry_conservation"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}