{"query": "U(1) gauge symmetry → conservation of charge", "count": 20, "results": [{"id": "card_maxwell_gauge_charge", "title": "U(1) gauge symmetry → conservation of charge", "shelf": "codex", "surface": "secular", "snippet": "Electromagnetism is the U(1) gauge theory, and by Noether its symmetry gives conservation of electric charge - the continuity equation d(rho)/dt + div J = 0 is built into Maxwell's equations. The symm", "authority_tier": "engine_derived", "source": "Narrow Highway — Maxwell's equations", "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_noncommutative_geometry", "title": "Noncommutative geometry & the spectral triple (Connes)", "shelf": "theories", "surface": "secular", "snippet": "Noncommutative geometry & the spectral triple (Connes) — an engine domain that can touch it: mathematics. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RE", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_n_7898952343a9", "title": "Reading the body's dashboard — HRV, pupil, sleep, gut as a within-person slope", "shelf": "science", "surface": "secular", "snippet": "The framework reads four gauges as the body's dashboard: HRV/RSA (vagal brake), pupillometry (LC-NE\nproxy), sleep metrics (allostatic recovery), and GI signals (interoceptive load). The red-team's\nwar", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-10", "readable": false, "generated": false}, {"id": "card_floor_yang_mills", "title": "The Yang-Mills chain - from the gauge field and the axioms to the mass gap", "shelf": "codex", "surface": "secular", "snippet": "Two trees. The gauge field: Maxwell, Weyl's gauge principle (1929), Yang and Mills' non-abelian field (1954). The axioms: Wightman's (1956) and Osterwalder-Schrader's Euclidean ones (1973) - what it m", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_joint_gue_statistics", "title": "Zeta zeros and the lattice Dirac operator share GUE statistics", "shelf": "codex", "surface": "secular", "snippet": "The nearest-neighbour spacings of the zeros of zeta follow the Gaussian Unitary Ensemble of random matrix theory (Montgomery's pair correlation, 1973; Odlyzko's computation, 1987), and so does the low", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "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_builder_chen_ning_yang", "title": "Chen Ning Yang", "shelf": "builders", "surface": "secular", "snippet": "Chen Ning Yang (1922-2024 AD) - physics. non-abelian gauge theory with Mills (1954), and with Lee the prediction of parity violation (1956) - the trunk of the Standard Model (A builder of the Floor of", "authority_tier": "reference", "source": "The builders of the Floor - credited with love, calibrated to the plumb-line", "readable": false, "generated": false}, {"id": "card_power_wiring_fuses", "title": "Wire thick, fuse close — the safety that prevents fires", "shelf": "energy", "surface": "secular", "snippet": "Low-voltage DC carries BIG amps, so undersized wire overheats and starts fires. Use wire thick enough for the current and the run length (thicker for more amps and longer runs), keep connections tight", "authority_tier": "reference", "source": "U.S. Department of Energy / NREL consumer energy guidance (public domain)", "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_power_charge_controller", "title": "The charge controller — protect the battery", "shelf": "energy", "surface": "secular", "snippet": "Never wire a solar panel straight to a battery — a CHARGE CONTROLLER sits between them and regulates the charge so the panel can't overcharge and destroy the battery. Two kinds: PWM is cheap and fine ", "authority_tier": "reference", "source": "U.S. Department of Energy / NREL consumer energy guidance (public domain)", "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_chart_standard_model_content", "title": "The Standard Model — gauge forces and quarks", "shelf": "codex", "surface": "secular", "snippet": "A chart on the one map: the tick stick stick_the_standard_model_gauge_forces_and_quarks, placed on the Standard-Model floor. It seals the quark charges (the proton's +1 from +2/3, +2/3, -1/3) and the ", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_src_word_gas_gauge", "title": "gas gauge", "shelf": "dictionary", "surface": "secular", "snippet": "gas gauge: (noun) gauge that indicates the amount of gasoline left in the gasoline tank of a vehicle — syn: gasoline gauge, gasoline gage, gas gage, petrol gauge, petrol gage", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_gasoline_gauge", "title": "gasoline gauge", "shelf": "dictionary", "surface": "secular", "snippet": "gasoline gauge: (noun) gauge that indicates the amount of gasoline left in the gasoline tank of a vehicle — syn: gasoline gage, gas gauge, gas gage, petrol gauge, petrol gage", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_word_petrol_gauge", "title": "petrol gauge", "shelf": "dictionary", "surface": "secular", "snippet": "petrol gauge: (noun) gauge that indicates the amount of gasoline left in the gasoline tank of a vehicle — syn: gasoline gauge, gasoline gage, gas gauge, gas gage, petrol gage", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_src_etym_gauge", "title": "gauge", "shelf": "etymology", "surface": "secular", "snippet": "gauge: etymology (Webster 1913) — v. t.: [OF. gaugier, F. jauger, cf. OF. gauge gauge, measuring rod, F. jauge; of uncertain origin; perh. fr. an assumed L. qualificare to determine the qualities of a", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "generated": false}, {"id": "card_src_word_rain_gauge", "title": "rain gauge", "shelf": "dictionary", "surface": "secular", "snippet": "rain gauge: (noun) gauge consisting of an instrument to measure the quantity of precipitation — syn: rain gage, pluviometer, udometer", "authority_tier": "reference", "source": "WordNet 3.0, Princeton University (WordNet License)", "readable": false, "generated": false}, {"id": "card_chain_yang_mills_1954", "title": "Yang 1954 — Conservation of isotopic spin and isotopic gauge invariance", "shelf": "codex", "surface": "secular", "snippet": "C. N. Yang, R. L. Mills (1954). Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev. 96 (1954) 191–195. DOI 10.1103/PhysRev.96.191. Canonical: https://doi.org/10.1103/PhysRev.96.191", "authority_tier": "reference", "source": "C. N. Yang, R. L. Mills (1954), Phys. Rev. 96 (1954) 191–195", "readable": false, "generated": false}, {"id": "card_src_word_water_gauge", "title": "water gauge", "shelf": "dictionary", "surface": "secular", "snippet": "water gauge: (noun) gauge for indicating the level of water in e.g. a tank or boiler or reservoir — syn: water gage, water glass", "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_maxwell_gauge_charge"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}