{"query": "Change of domain — solve in the eigenbasis, map back (the ex", "count": 12, "results": [{"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_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_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_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_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_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_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_src_port_tcp_90_dnsix", "title": "Port 90/tcp — dnsix", "shelf": "networking", "surface": "secular", "snippet": "Port 90/tcp is assigned to dnsix: DNSIX Securit Attribute Token Map.", "authority_tier": "reference", "source": "IANA Service Name and Port Number Registry (public domain)", "readable": false, "generated": false}, {"id": "card_src_port_udp_90_dnsix", "title": "Port 90/udp — dnsix", "shelf": "networking", "surface": "secular", "snippet": "Port 90/udp is assigned to dnsix: DNSIX Securit Attribute Token Map.", "authority_tier": "reference", "source": "IANA Service Name and Port Number Registry (public domain)", "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_theory_quantum_information___entanglement__von_neumann_entr"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}