{"query": "The Lagrangian — the Hamiltonian's dual, the path chosen", "count": 20, "results": [{"id": "card_floor_the_lagrangian", "title": "The Lagrangian — the Hamiltonian's dual, the path chosen", "shelf": "codex", "surface": "secular", "snippet": "L = T - V, and the action S = integral L dt. Its law is the principle of least action: of all paths, nature takes the one where the action is stationary. Four pillars rest on the floors already seeded", "authority_tier": "engine_derived", "source": "Narrow Highway — the Lagrangian", "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_thermo_statistical_mechanics", "title": "Statistical mechanics — many microstates, one macrostate", "shelf": "codex", "surface": "secular", "snippet": "The bridge from the reversible microscopic law to the irreversible macrostate: 10^23 particles, one temperature and one pressure. Boltzmann S = k_B ln W counts the microstates; the macrostate is what ", "authority_tier": "engine_derived", "source": "Narrow Highway — thermodynamics", "readable": false, "generated": false}, {"id": "card_ham_eigenbasis", "title": "The energy eigenbasis — the stationary states", "shelf": "codex", "surface": "secular", "snippet": "H psi = E psi: the eigenvectors are the stationary states, the eigenvalues the allowed energies (hydrogen's ground state 13.6057 eV, the 1/n^2 ladder - sealed on the stick). Diagonalizing H is exactly", "authority_tier": "engine_derived", "source": "Narrow Highway — the Hamiltonian", "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_theory_sabermetrics_sports_analytics", "title": "Sabermetrics / sports analytics (Pythagorean expectation, Elo)", "shelf": "theories", "surface": "secular", "snippet": "Sabermetrics / sports analytics (Pythagorean expectation, Elo) — an engine domain that can touch it: sports_analytics. Calibration: seals — expected win ratios and Elo updates compute. Bill James's Py", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_vsepr_theory", "title": "VSEPR theory (molecular geometry)", "shelf": "theories", "surface": "secular", "snippet": "VSEPR theory (molecular geometry) — an engine domain that can touch it: molecular_geometry. Calibration: seals — shapes and bond angles predict directly. Valence Shell Electron Pair Repulsion: electro", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_circulation_harvey", "title": "Circulation of the blood (Harvey's quantitative argument)", "shelf": "theories", "surface": "secular", "snippet": "Circulation of the blood (Harvey's quantitative argument) — an engine domain that can touch it: medicine. Calibration: seals — cardiac output and flow arithmetic compute. Blood circulates in a closed ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_structural_statics", "title": "Structural statics (load, moment, floor-area ratio)", "shelf": "theories", "surface": "secular", "snippet": "Structural statics (load, moment, floor-area ratio) — an engine domain that can touch it: architecture. Calibration: seals — reactions, moments and load paths compute. Nothing accelerates, so forces a", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_hess_s_law_thermochemistry", "title": "Hess's law / thermochemistry", "shelf": "theories", "surface": "secular", "snippet": "Hess's law / thermochemistry — an engine domain that can touch it: chemistry. Calibration: seals — enthalpy sums compute exactly. The total enthalpy change of a reaction is the same whatever route it ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_c3b2790c36e5", "title": "Psalm 25 — Psalm 25", "shelf": "codex", "surface": "witness", "snippet": "<<By David.>> To you, Yahweh, do I lift up my soul. My God, I have trusted in you. Don't let me be shamed. Don't let my enemies triumph over me. Yes, no one who waits for you shall be shamed. They sha", "authority_tier": "scripture", "source": "Psalm 25", "readable": false, "generated": false}, {"id": "card_theory_digital_analog", "title": "Digital versus analog (why discreteness survives copying)", "shelf": "theories", "surface": "secular", "snippet": "Digital versus analog (why discreteness survives copying) — an engine domain that can touch it: computer_science. Calibration: map-only — sampling rates and bit depth are ordinary arithmetic, and THIS", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_biological_nitrogen_fixation", "title": "Crop rotation & biological nitrogen fixation (the low-input path)", "shelf": "theories", "surface": "secular", "snippet": "Crop rotation & biological nitrogen fixation (the low-input path) — an engine domain that can touch it: agriculture. Calibration: map-only — rotation effects are empirical; nutrient budgets compute. L", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_numerical_analysis", "title": "Numerical analysis (why the computer's answer is not the answer)", "shelf": "theories", "surface": "secular", "snippet": "Numerical analysis (why the computer's answer is not the answer) — an engine domain that can touch it: computer_science. Calibration: map-only — error bounds and condition numbers are computable in pr", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_stoichiometry_the_mole_concept", "title": "Stoichiometry & the mole concept", "shelf": "theories", "surface": "secular", "snippet": "Stoichiometry & the mole concept — an engine domain that can touch it: chemistry. Calibration: seals — molar masses, yields and limiting reagents compute exactly. A mole is 6.022×10²³ particles, chose", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_differential_geometry", "title": "Differential geometry (curvature measured from inside)", "shelf": "theories", "surface": "secular", "snippet": "Differential geometry (curvature measured from inside) — an engine domain that can touch it: geometry. Calibration: map-only — specific curvature and geodesic computations verify; the framework is bro", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_n_5d24a8a62b0b", "title": "Psalm 116 — I Love the LORD", "shelf": "codex", "surface": "witness", "snippet": "I love Yahweh, because he listens to my voice, and my cries for mercy. Because he has turned his ear to me, therefore I will call on him as long as I live. The cords of death surrounded me, the pains ", "authority_tier": "scripture", "source": "Psalm 116", "readable": false, "generated": false}, {"id": "card_theory_quantization", "title": "Quantization (why nature comes in whole units)", "shelf": "theories", "surface": "secular", "snippet": "Quantization (why nature comes in whole units) — an engine domain that can touch it: physics. Calibration: seals — energy levels, photon energies and charge multiples compute exactly. Certain physical", "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_exercise_physiology", "title": "Exercise physiology (VO₂max, HR zones)", "shelf": "theories", "surface": "secular", "snippet": "Exercise physiology (VO₂max, HR zones) — an engine domain that can touch it: exercise_science. Calibration: seals — max HR estimates, zones and work rates compute. VO₂max is the maximum rate of oxygen", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_the_lagrangian"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}