{"query": "Noether's theorem — symmetry is the source of conservation", "count": 20, "results": [{"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_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_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_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_floor_thermodynamics", "title": "Thermodynamics — the arrow and the one end", "shelf": "codex", "surface": "secular", "snippet": "The four laws. The first law is energy conservation (Noether's energy, now counting heat and work). The second law - entropy never decreases - is the one place physics is not time-reversible: the arro", "authority_tier": "engine_derived", "source": "Narrow Highway — thermodynamics", "readable": false, "generated": false}, {"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_noether_time_gives_energy", "title": "Time-translation symmetry gives energy — the Hamiltonian", "shelf": "codex", "surface": "secular", "snippet": "The laws do not change in time; Noether turns that one symmetry into conservation of energy - and energy is exactly the Hamiltonian. So the Lagrangian's symmetry produces the Hamiltonian's conserved q", "authority_tier": "engine_derived", "source": "Narrow Highway — Noether's theorem", "readable": false, "generated": false}, {"id": "card_noether_gauge_gives_charge", "title": "Gauge symmetry gives charge — the Standard Model's currents", "shelf": "codex", "surface": "secular", "snippet": "The phase (gauge) symmetry of the wavefunction gives conservation of electric charge; the Standard Model's gauge symmetries give its conserved currents. The forces themselves are read off the symmetri", "authority_tier": "engine_derived", "source": "Narrow Highway — Noether's theorem", "readable": false, "generated": false}, {"id": "card_spine_noethers_theorem", "title": "Noether's theorem — a spine", "shelf": "spine", "surface": "secular", "snippet": "The pillars of Noether's theorem.", "authority_tier": "engine_derived", "source": "Narrow Highway — Noether's theorem", "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_chem_conservation", "title": "Conservation — atoms and mass balance", "shelf": "codex", "surface": "secular", "snippet": "Atoms are conserved in every reaction, so every equation balances (2 H2 + O2 -> 2 H2O, sealed) and mass is conserved (water's molar mass, 18.016 g/mol, sealed). Chemistry's first law, and Noether's co", "authority_tier": "engine_derived", "source": "Narrow Highway — chemistry", "readable": false, "generated": false}, {"id": "card_c_3705098a23ca", "title": "Easton: Nergal-sharezer references Euphrates", "shelf": "connections", "surface": null, "snippet": "Mentions Euphrates (place) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a place.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_src_lex_h6578", "title": "H6578 — פְּרָת (pe.rat): Euphrates", "shelf": "lexicon", "surface": "secular", "snippet": "פְּרָת (pe.rat), Strong's H6578: Euphrates. § Euphrates = \"fruitfulness\" the largest and longest river of western Asia; rises from two chief sources in the Armenian mountains and flows into the Persia", "authority_tier": "reference", "source": "STEPBible TBESH/TBESG — Extended Strong's lexicon (CC-BY, Tyndale House)", "readable": false, "generated": false}, {"id": "card_src_word_euphrates", "title": "euphrates", "shelf": "dictionary", "surface": "secular", "snippet": "euphrates: (noun) a river in southwestern Asia; flows into the Persian Gulf; was important in the development of several great civilizations in ancient Mesopotamia — syn: Euphrates River", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_euphrates_river", "title": "euphrates river", "shelf": "dictionary", "surface": "secular", "snippet": "euphrates river: (noun) a river in southwestern Asia; flows into the Persian Gulf; was important in the development of several great civilizations in ancient Mesopotamia — syn: Euphrates", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_c_615e59c2bc00", "title": "Genesis 15 references Euphrates", "shelf": "connections", "surface": null, "snippet": "Mentions Euphrates (place) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a place.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_c_7d789f71fb0b", "title": "Genesis 2 references Euphrates", "shelf": "connections", "surface": null, "snippet": "Mentions Euphrates (place) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a place.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_c_085348f109fa", "title": "Easton: Helam references Euphrates", "shelf": "connections", "surface": null, "snippet": "Mentions Euphrates (place) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a place.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "readable": false, "generated": false}, {"id": "card_c_0a05ed66c25d", "title": "Easton: Cush references Euphrates", "shelf": "connections", "surface": null, "snippet": "Mentions Euphrates (place) — the name appears in the card text; the entry is Easton's Bible Dictionary (public domain), which classifies it as a place.", "authority_tier": "engine_derived", "source": "Name mention (Easton's Bible Dictionary, PD)", "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_floor_noethers_theorem"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}