{"query": "The energy eigenbasis — the stationary states", "count": 20, "results": [{"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_theory_quantum_information___entanglement__von_neumann_entr", "title": "Quantum information & entanglement (von Neumann entropy)", "shelf": "theories", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) — an engine domain that can touch it: information_theory. Calibration: seals. S = -Tr(ρ log ρ), the entropy of a density matrix, which reduces ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_linear_algebra", "title": "Linear algebra (vector spaces, eigenvalues)", "shelf": "theories", "surface": "secular", "snippet": "Linear algebra (vector spaces, eigenvalues) — an engine domain that can touch it: linear_algebra. Calibration: seals. Vectors, the linear maps between them, and matrices as those maps written down. Th", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_quantum_information___entanglement__von_neumann_entr__shannon_information_theory", "title": "Bridge: Quantum information & entanglement (von Neumann entropy)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Quantum information & entanglement (von Neumann entropy) and Shannon information theory (entropy, channel capacity) are the same form in different domains. von Neumann entropy S = -Tr(rho log rho) red", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_n_84ee70059175", "title": "The map's axes are its spectral modes (the Fourier lens)", "shelf": "concepts", "surface": "secular", "snippet": "Fourier's move — decompose a whole into the few fundamental modes that generate it — generalized off the regular cycle (where the FFT lives) to the map: the EIGENMODES of the dimension correlation mat", "authority_tier": "matt", "source": "Operator's seed (Matt) — honest grade: plausible", "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_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_solve_change_domain", "title": "Change of domain — solve in the eigenbasis, map back (the exact flip)", "shelf": "codex", "surface": "secular", "snippet": "Put the problem in the space where it diagonalizes (its eigenbasis, the frequency basis), solve it as independent scalars, map back — exact when the basis is known and cheap (Fourier, diagonalization;", "authority_tier": "engine_derived", "source": "Narrow Highway — a step of the solve path", "readable": false, "generated": false}, {"id": "card_instr_spectral", "title": "Change of domain - the eigenbasis flip", "shelf": "codex", "surface": "secular", "snippet": "The Change of domain - the eigenbasis flip verifier (src/concordance/verifiers/spectral.py). On the one map it instruments: card_question_p_vs_np. Found from the code's own imports, never invented; th", "authority_tier": "engine_derived", "source": "verifier: spectral", "readable": false, "generated": false}, {"id": "card_seal_ce54b737f9e5970db997377874e365f3939641b12e598886b8b4f197b83d3295", "title": "Receipt ce54b737f9e5… — sealed: record", "shelf": "seals", "surface": "secular", "snippet": "{\n \"anchors\": [],\n \"axis_coords\": {\n  \"axis\": \"mathematics\",\n  \"dimensions\": [\n   \"reasoning\"\n  ]\n },\n \"gate_results\": [\n  {\n   \"details\": {\n    \"broken_at\": null,\n    \"confirmed_steps\": 1,\n    \"error", "authority_tier": "engine_derived", "source": "Narrow Highway engine — sealed record", "readable": false, "generated": false}, {"id": "card_floor_the_solve_path", "title": "The solve path — two jaws that close on the answer", "shelf": "codex", "surface": "secular", "snippet": "How the engine solves a hard problem when no rule finds the exact answer (the barriers). Two jaws: EXCLUDE from outside (the barriers, the moat — cut the dead branches) and CONVERGE from inside (ancho", "authority_tier": "engine_derived", "source": "Narrow Highway — the solve path (operator seed)", "readable": false, "generated": false}, {"id": "card_doctrine_reservoir_manifold", "title": "The reservoir and the manifold — value is in the routing layer, not the engine", "shelf": "doctrine", "surface": "secular", "snippet": "\"The most valuable asset in an energy system is not the fuel or the engine. It is the reservoir that stores a gradient and the manifold that routes that gradient to useful work.\"\n\nSource → Gradient → ", "authority_tier": "author", "source": "Universal Gradient Manifold — A Heat-Source-Agnostic Energy Operating System — Matt Harris", "readable": false, "generated": false}, {"id": "card_src_fed_nasa_techdoc_19980226989", "title": "Satellite Networks: Architectures, Applications, and Technologies", "shelf": "science", "surface": "secular", "snippet": "Satellite Networks: Architectures, Applications, and Technologies. A United States federal publication, public domain (17 USC 105). The full text (503,365 bytes) is held on the ark; waybill sha256 c94", "authority_tier": "reference", "source": "NASA technical documents (PD, 17 USC 105)", "readable": true, "generated": false}, {"id": "card_arch_096dc73d20379265", "title": "Technologie und Terminologie der Gewerbe und Künste bei Griechen und Römern", "shelf": "trades", "surface": "secular", "snippet": "Technologie und Terminologie der Gewerbe und Künste bei Griechen und Römern — a public-domain work on industrial arts, published 1912. Held in the ark; the full text is the TORTOISE — fetched on deman", "authority_tier": "reference", "source": "Internet Archive — technologieundte00blmn (public domain)", "readable": true, "generated": false}, {"id": "card_src_book_56330", "title": "Handbuch der chemischen Technologie Achte Auflage — Johannes Rudolf Wagner", "shelf": "gutenberg", "surface": "secular", "snippet": "Handbuch der chemischen Technologie Achte Auflage, by Johannes Rudolf Wagner (in de). Subjects: Chemistry, Technical; Chemical industry. Read the full text (public domain): https://www.gutenberg.org/e", "authority_tier": "reference", "source": "Project Gutenberg (public domain)", "readable": true, "generated": false}, {"id": "card_src_pd_technologieundte00blmn", "title": "Technologie und Terminologie der Gewerbe und Künste bei Griechen und Römern", "shelf": "practical", "surface": "secular", "snippet": "Technologie und Terminologie der Gewerbe und Künste bei Griechen und Römern (1912). A book returned to the public domain — public domain by copyright expiry (published 1912, pre-1929). The full text (", "authority_tier": "reference", "source": "public domain (copyright expired)", "readable": true, "generated": false}, {"id": "card_src_fed_nasa_techdoc_19930021260", "title": "Goddard Conference on Mass Storage Systems and Technologies, Volume 1", "shelf": "science", "surface": "secular", "snippet": "Goddard Conference on Mass Storage Systems and Technologies, Volume 1. A United States federal publication, public domain (17 USC 105). The full text (685,746 bytes) is held on the ark; waybill sha256", "authority_tier": "reference", "source": "NASA technical documents (PD, 17 USC 105)", "readable": true, "generated": false}, {"id": "card_src_fed_nasa_techdoc_19870013020", "title": "Shuttle ground operations efficiencies/technologies study. Volume 4: Preliminary Issues Database (PIDB) catalog", "shelf": "science", "surface": "secular", "snippet": "Shuttle ground operations efficiencies/technologies study. Volume 4: Preliminary Issues Database (PIDB) catalog. A United States federal publication, public domain (17 USC 105). The full text (1,299,8", "authority_tier": "reference", "source": "NASA technical documents (PD, 17 USC 105)", "readable": true, "generated": false}, {"id": "card_src_fed_nasa_techdoc_19910072589", "title": "Shuttle ground operations efficiencies/technologies study, phase 3. Volume 3: Simplified launch system operational criteria", "shelf": "science", "surface": "secular", "snippet": "Shuttle ground operations efficiencies/technologies study, phase 3. Volume 3: Simplified launch system operational criteria. A United States federal publication, public domain (17 USC 105). The full t", "authority_tier": "reference", "source": "NASA technical documents (PD, 17 USC 105)", "readable": true, "generated": false}, {"id": "card_src_etym_technology", "title": "technology", "shelf": "etymology", "surface": "secular", "snippet": "technology: etymology (Webster 1913) — n.: [Gr. -logy; cf. Gr. technologie.]. From Webster's Revised Unabridged Dictionary (1913), public domain.", "authority_tier": "reference", "source": "Webster's Revised Unabridged Dictionary (1913), Project Gutenberg eBook #29765 — public domain", "readable": true, "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_ham_eigenbasis"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}