{"query": "The first law — energy is conserved", "count": 20, "results": [{"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}, {"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_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_law_of_conservation_of_mass", "title": "Law of conservation of mass (Lavoisier)", "shelf": "theories", "surface": "secular", "snippet": "Law of conservation of mass (Lavoisier) — an engine domain that can touch it: chemistry. Calibration: seals — balanced equations verify exactly. Mass is neither created nor destroyed in a chemical rea", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_ohm_s_law_circuit_theory", "title": "Ohm's law & circuit theory (Kirchhoff)", "shelf": "theories", "surface": "secular", "snippet": "Ohm's law & circuit theory (Kirchhoff) — an engine domain that can touch it: electrical. Calibration: seals — voltages, currents and power all compute directly. V = IR, plus Kirchhoff's two rules: cur", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_8530c72a2201", "title": "Fluid probability dynamics — one continuity equation across physics, geometry, and ML", "shelf": "science", "surface": "secular", "snippet": "One equation wears many clothes. Probability is a conserved fluid: the continuity equation\ndρ/dt + ∇·J = 0 (current J = ρv) says density is never created or destroyed — it only flows. The\nsame skeleto", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "readable": false, "generated": false}, {"id": "card_n_ae08bd563c6e", "title": "Balancing equations — nothing is created or destroyed", "shelf": "science", "surface": "secular", "snippet": "Lavoisier's law: matter is conserved, so a chemical equation must have equal atoms on\nboth sides. The engine balances in-domain — given CH4 + O2 -> CO2 + H2O it returns the true\ncoefficients CH4 + 2 O", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "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_gene_ef_tu", "title": "elongation factor (EF-Tu / EF-1alpha) — a universal gene (a homolog across the domains)", "shelf": "codex", "surface": "secular", "snippet": "elongation factor (EF-Tu / EF-1alpha): delivers each aminoacyl-tRNA to the ribosome during translation. Found in Bacteria, Archaea, Eukaryota - a homologous gene descended from a single ancestral gene", "authority_tier": "reference", "source": "molecular phylogenetics; universal homologs of LUCA", "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_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_chart_hermitian_operators", "title": "Hermitian operators — real eigenvalues, the observables", "shelf": "codex", "surface": "secular", "snippet": "A chart on the one map: the tick stick stick_hermitian_operators_real_eigenvalues_the_observables, placed on the quantum-mechanics floor. A Hermitian operator A = A-dagger has real eigenvalues (so obs", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_src_openstax_physics_multiple_choice_ed30c748", "title": "Multiple Choice — Physics", "shelf": "physics", "surface": "secular", "snippet": "Multiple Choice\n\n12.1\n\nZeroth Law of Thermodynamics: Thermal Equilibrium\n\n30\n.\n\nWhat thermodynamic principle forms the basis for our ability to measure temperature?\n\nthe zeroth law\n\nthe first law\n\nthe", "authority_tier": "reference", "source": "OpenStax: Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_calc_energy_balance", "title": "First law (energy balance)", "shelf": "calculations", "surface": "secular", "snippet": "First law (energy balance) — thermodynamics. Formula: dU = Q - W. Canonical FORM: conservation (in = out + change_in_store) — energy is conserved — the same ledger, for heat and work. Same form, diffe", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "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_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_src_openstax_university_physics_volume_1_introduction_647dc0b6", "title": "Introduction — University Physics Volume 1", "shelf": "physics", "surface": "secular", "snippet": "Figure\n9.1\n\nThe concepts of impulse, momentum, and center of mass are crucial for a major-league baseball player to successfully get a hit. If he misjudges these quantities, he might break his bat ins", "authority_tier": "reference", "source": "OpenStax: University Physics Volume 1 (CC-BY 4.0)", "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}], "house": {"door": "FIND", "kind": "cards", "trail": "results", "seal": null, "next_step": {"do": "open the top card", "door": "FIND", "tool": "card_get", "params": {"id": "card_thermo_first_law"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}