{"query": "The Planck scale (ħ)", "count": 20, "results": [{"id": "card_instr_planck_scale", "title": "The Planck scale (ħ)", "shelf": "codex", "surface": "secular", "snippet": "The The Planck scale (ħ) verifier (src/concordance/verifiers/planck_scale.py). Builds on: The physical constants — one source, The scale base — the shared mechanism. Found from the code's own imports,", "authority_tier": "engine_derived", "source": "verifier: planck_scale", "readable": false, "generated": false}, {"id": "card_theory_quantum_gravity_problem", "title": "Spacetime & the quantum-gravity problem (where physics ends)", "shelf": "theories", "surface": "secular", "snippet": "Spacetime & the quantum-gravity problem (where physics ends) — an engine domain that can touch it: physics. Calibration: map-only — the Planck quantities compute, but there is no accepted theory here ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "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_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_041763374eca", "title": "Fokker–Planck & Liouville — probability flow in statistical mechanics", "shelf": "science", "surface": "secular", "snippet": "The stochastic instantiation of probability-as-fluid. Fokker–Planck sets the current\nJ = μρ − D∇ρ (drift + diffusion); its steady state is the Boltzmann distribution ρ ∝ e^(−U/kT),\nwhich makes the cur", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "readable": false, "generated": false}, {"id": "card_floor_the_instruments", "title": "The instruments — every verifier and validator, and where they join", "shelf": "codex", "surface": "secular", "snippet": "The engine's checking instruments on the one map: the 89 verifiers and the gate that validates them, joined by their real import graph (read from the code at seed time, so it cannot drift). A MEASURE ", "authority_tier": "engine_derived", "source": "Narrow Highway - the instruments on the one map (found from the import graph)", "readable": false, "generated": false}, {"id": "card_c_c1d4f07c75cd", "title": "Fokker–Planck & Liouville — probability flow ↔ Fluid probability dynamics — one continuity ", "shelf": "connections", "surface": null, "snippet": "The stochastic instantiation of probability-as-fluid. ... In Hamiltonian phase space, Liouville's theorem gives dρ/dt = 0 — the probability fluid is incompressible.  — a concord the card itself states", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_3cc9f3e8e74f", "title": "Fokker–Planck & Liouville instantiates Fluid probability dynamics", "shelf": "connections", "surface": null, "snippet": "Statistical mechanics is the stochastic instance of the probability-continuity equation.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-08", "readable": false, "generated": false}, {"id": "card_instr_physics", "title": "Physics", "shelf": "codex", "surface": "secular", "snippet": "The Physics verifier (src/concordance/verifiers/physics.py). Builds on: The gravitational scale (G), The Planck scale (ħ), The relativistic scale (c). Found from the code's own imports, never invented", "authority_tier": "engine_derived", "source": "verifier: physics", "readable": false, "generated": false}, {"id": "card_src_openstax_physics_critical_thinking_items_506c3152", "title": "Critical Thinking Items — Physics", "shelf": "physics", "surface": "secular", "snippet": "Critical Thinking Items\n\n21.1\n\nPlanck and Quantum Nature of Light\n\n10\n.\n\nHow is the frequency of a blackbody’s emission influenced by temperature?\n\nThe frequency is independent of temperature.\n\nThe fr", "authority_tier": "reference", "source": "OpenStax: Physics (CC-BY 4.0)", "readable": false, "generated": false}, {"id": "card_instr_photonics", "title": "Photonics", "shelf": "codex", "surface": "secular", "snippet": "The Photonics verifier (src/concordance/verifiers/photonics.py). Builds on: The fine-structure scale (α), The Planck scale (ħ). Found from the code's own imports, never invented; the module keeps the ", "authority_tier": "engine_derived", "source": "verifier: photonics", "readable": false, "generated": false}, {"id": "card_c_ec9bfe0734fd", "title": "Gibbs free energy — will a reaction go? ↔ Fokker–Planck & Liouville — probability flow", "shelf": "connections", "surface": null, "snippet": "This is the second law of thermodynamics doing chemistry, the same entropy arrow that pointed the Fokker–Planck fluid toward equilibrium.  — a concord the card itself states; mined + verified.", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_calc_fokker_planck", "title": "Fokker-Planck equation", "shelf": "calculations", "surface": "secular", "snippet": "Fokker-Planck equation — statistics. Formula: dp/dt = -d(mu p)/dx + D d2p/dx2. Canonical FORM: diffusion (du/dt = D * laplacian(u)) — the density of a drifting, diffusing particle — the diffusion equa", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_seal_8823da54887bde28af7202dc2470949af5d60a397705c6b9036b58926fa16059", "title": "Receipt 8823da54887b… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"physical_constants\",\n  \"dimensions\": [\n   \"conservation_balance\",\n   \"physical_substance\",\n   \"reasoning\"\n  ],\n  \"umbrella\": \"physics\"\n },\n \"gate_results", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_instr_quantum_computing", "title": "Quantum computing", "shelf": "codex", "surface": "secular", "snippet": "The Quantum computing verifier (src/concordance/verifiers/quantum_computing.py). Builds on: The Planck scale (ħ). Found from the code's own imports, never invented; the module keeps the logic, this ca", "authority_tier": "engine_derived", "source": "verifier: quantum_computing", "readable": false, "generated": false}, {"id": "card_c_583b49254af6", "title": "Fluid probability dynamics — one continuity  ↔ Optimal transport — the geometry of moving p", "shelf": "connections", "surface": null, "snippet": "geometry (optimal transport: distance = least kinetic energy to carry one distribution to another; Fokker–Planck is the gradient flow of free energy in Wasserstein space)  — a concord the card itself ", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_n_d59ca677ea24", "title": "Optimal transport — the geometry of moving probability", "shelf": "science", "surface": "secular", "snippet": "Benamou–Brenier: the distance between two distributions is the least kinetic energy of a\nfluid that carries one to the other, subject to the continuity equation. 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