{"query": "The Millennium sources — the papers behind the seven sticks", "count": 20, "results": [{"id": "card_spine_millennium_sources", "title": "The Millennium sources — the papers behind the seven sticks", "shelf": "spine", "surface": "secular", "snippet": "63 sources located for the seven Millennium sticks (Riemann, Birch and Swinnerton-Dyer, Navier-Stokes, Yang-Mills, P versus NP, Hodge, Poincare), one reference card each: the bibliographic record, DOI", "authority_tier": "reference", "source": "The Millennium sources — a spine of located records", "readable": false, "generated": false}, {"id": "card_theory_population_ecology", "title": "Population ecology (Lotka–Volterra, carrying capacity)", "shelf": "theories", "surface": "secular", "snippet": "Population ecology (Lotka–Volterra, carrying capacity) — an engine domain that can touch it: ecology. Calibration: seals — logistic and predator-prey models compute. Unlimited resources give exponenti", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_chart_euler_char", "title": "Topology and Euler's formula", "shelf": "codex", "surface": "secular", "snippet": "Topology and Euler's formula. A chart on the one map: this is the tick stick stick_topology_and_euler_s_formula, placed at the node it charts. Basis: the stick seals V - E + F = 2 for the Platonic sol", "authority_tier": "engine_derived", "source": "Narrow Highway - a chart: a tick stick placed on the one map", "readable": false, "generated": false}, {"id": "card_src_mill_karp_1972", "title": "R. M. Karp 1972 — Reducibility among combinatorial problems", "shelf": "millennium", "surface": "secular", "snippet": "R. M. Karp (1972). Reducibility among combinatorial problems. Complexity of Computer Computations (Plenum, 1972) 85–103. DOI 10.1007/978-1-4684-2001-2_9. Canonical: https://doi.org/10.1007/978-1-4684-", "authority_tier": "reference", "source": "R. M. Karp (1972), Complexity of Computer Computations (Plenum, 1972) 85–103", "readable": false, "generated": false}, {"id": "card_src_mill_hamilton_1982", "title": "R. S. Hamilton 1982 — Three-manifolds with positive Ricci curvature", "shelf": "millennium", "surface": "secular", "snippet": "R. S. Hamilton (1982). Three-manifolds with positive Ricci curvature. J. Differential Geom. 17 (1982) 255–306. DOI 10.4310/jdg/1214436922. Canonical: https://doi.org/10.4310/jdg/1214436922. Free copy:", "authority_tier": "reference", "source": "R. S. Hamilton (1982), J. Differential Geom. 17 (1982) 255–306", "readable": false, "generated": false}, {"id": "card_joint_renormalization_group", "title": "The renormalization group, and the continuum limit as the question", "shelf": "codex", "surface": "secular", "snippet": "Wilson's lattice (1974) and Forster, Nelson and Stephen's randomly stirred fluid (1977) run the same renormalization group: a coupling that changes with scale, a finite system whose continuum limit is", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_floor_chemistry", "title": "Chemistry — quantum mechanics applied, the periodic table", "shelf": "codex", "surface": "secular", "snippet": "The world of substances, standing on the physics region. Chemistry is the Schrodinger equation for electrons around nuclei, plus Pauli exclusion, plus electromagnetism; the periodic table falls out of", "authority_tier": "engine_derived", "source": "Narrow Highway — chemistry", "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_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_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_astronomy", "title": "Astronomy — orbits, distances, and the cosmos", "shelf": "codex", "surface": "secular", "snippet": "Orbits obey Kepler and Newton; distances climb the ladder (parallax, standard candles); the cosmos is governed by general relativity. The orbital arithmetic is already sealed on the astronomy stick; t", "authority_tier": "engine_derived", "source": "Narrow Highway — astro", "readable": false, "generated": false}, {"id": "card_floor_physical_chemistry", "title": "Physical chemistry — rate, equilibrium, acid-base, redox", "shelf": "codex", "surface": "secular", "snippet": "Deeper in chemistry: the laws that make it predictive. Kinetics (how fast), equilibrium (the balance point, Delta G = -RT ln K), acid-base (pKa + pKb = 14), and electrochemistry (the cell potential). ", "authority_tier": "engine_derived", "source": "Narrow Highway — physical chemistry", "readable": false, "generated": false}, {"id": "card_floor_game_theory", "title": "Game theory — equilibrium, dilemmas, and strategy", "shelf": "codex", "surface": "secular", "snippet": "The mathematics of strategic choice. A Nash equilibrium is a fixed point where no one gains by deviating alone; the prisoner's dilemma shows rational players reaching a worse outcome than cooperation;", "authority_tier": "engine_derived", "source": "Narrow Highway — game theory", "readable": false, "generated": false}, {"id": "card_floor_biology", "title": "Biology — life is self-replicating chemistry", "shelf": "codex", "surface": "secular", "snippet": "The next rung of the emergence ladder: physics -> chemistry -> life. A cell is chemistry organized to copy itself and run on free energy; DNA spells proteins in a triplet code (64 codons), and evoluti", "authority_tier": "engine_derived", "source": "Narrow Highway — biology", "readable": false, "generated": false}, {"id": "card_floor_music", "title": "Music — interval, tuning, and the harmonic series", "shelf": "codex", "surface": "secular", "snippet": "Music is number made audible: the consonant intervals are small whole-number frequency ratios (octave 2:1, fifth 3:2, fourth 4:3), and a scale is a tuning that divides the octave — equal temperament b", "authority_tier": "engine_derived", "source": "Narrow Highway — music", "readable": false, "generated": false}, {"id": "card_floor_computer_science", "title": "Computer science — bits, logic, and what can be computed", "shelf": "codex", "surface": "secular", "snippet": "Information is bits (a byte is 2^8 = 256 values); logic gates build from the 16 Boolean functions of two inputs; good algorithms beat bad ones (merge sort's n log n against n^2); and computability and", "authority_tier": "engine_derived", "source": "Narrow Highway — computer science", "readable": false, "generated": false}, {"id": "card_floor_the_mind", "title": "The mind — matter aware of itself", "shelf": "codex", "surface": "secular", "snippet": "The top rung of the emergence ladder: physics -> chemistry -> life -> mind. The neuron signals by electrochemistry (a Nernst voltage), the brain computes (networks, information), and it is metabolical", "authority_tier": "engine_derived", "source": "Narrow Highway — the mind", "readable": false, "generated": false}, {"id": "card_floor_maxwells_equations", "title": "Maxwell's equations — the first unification", "shelf": "codex", "surface": "secular", "snippet": "Electricity, magnetism and light are one electromagnetic field, and its waves travel at the speed of light (c = 1/sqrt(mu0 eps0), sealed on stick_maxwell_s_equations_and_superconductivity). The archet", "authority_tier": "engine_derived", "source": "Narrow Highway — Maxwell's equations", "readable": false, "generated": false}, {"id": "card_floor_quantum_mechanics", "title": "Quantum mechanics — the quantum and its limits", "shelf": "codex", "surface": "secular", "snippet": "Not a floor beside the others - the framework they inhabit. Superposition and the Born rule are on the capstone, the Schrodinger equation on the Hamiltonian, the path integral on the Lagrangian. This ", "authority_tier": "engine_derived", "source": "Narrow Highway — quantum mechanics", "readable": false, "generated": false}, {"id": "card_floor_oceanography", "title": "Oceanography — the salt sea in motion", "shelf": "codex", "surface": "secular", "snippet": "Pressure rises with depth; seawater is 3.5 percent salt; density differences drive the thermohaline conveyor. Three pillars rest on earth science (the basins), chemistry (dissolved salts) and thermody", "authority_tier": "engine_derived", "source": "Narrow Highway — oceanography", "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_spine_millennium_sources"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}