{"query": "Capacity - Shannon's ceiling", "count": 15, "results": [{"id": "card_net_capacity", "title": "Capacity - Shannon's ceiling", "shelf": "codex", "surface": "secular", "snippet": "A channel carries at most C = B log2(1+S/N) bits/s (Shannon); no code beats it. Packets and error-correction live under it.", "authority_tier": "engine_derived", "source": "Narrow Highway — net", "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_boolean_algebra_propositional_logic", "title": "Boolean algebra / propositional logic", "shelf": "theories", "surface": "secular", "snippet": "Boolean algebra / propositional logic — an engine domain that can touch it: formal_logic. Calibration: seals. Two values and three operations — AND, OR, NOT — with laws of their own (De Morgan's, dist", "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_bridge_theory_shannon_information_theory__second_law_of_thermodynamics", "title": "Bridge: Shannon information theory (entropy, channel capacity)  ↔  Second law of thermodynamics (entropy)", "shelf": "bridges", "surface": "secular", "snippet": "Shannon information theory (entropy, channel capacity) and Second law of thermodynamics (entropy) are the same form in different domains. Shannon's H = -sum p log p and Boltzmann's S = k log W are the", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_landauer__shannon_information_theory", "title": "Bridge: Landauer's principle (erasing information costs heat)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Landauer's principle (erasing information costs heat) and Shannon information theory (entropy, channel capacity) are the same form in different domains. THIS CLOSES THE INFORMATION-THERMODYNAMICS BRID", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_bridge_theory_statistical_mechanics__shannon_information_theory", "title": "Bridge: Statistical mechanics (Boltzmann — why the second law is a counting argument)  ↔  Shannon information theory (entropy, channel capacity)", "shelf": "bridges", "surface": "secular", "snippet": "Statistical mechanics (Boltzmann — why the second law is a counting argument) and Shannon information theory (entropy, channel capacity) are the same form in different domains. Boltzmann's log W and S", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_floor_p_vs_np", "title": "The P versus NP chain - from the machine and the circuit to the three barriers", "shelf": "codex", "surface": "secular", "snippet": "Two trees. Computability: Turing's machine (1936), time as a resource (Hartmanis-Stearns 1965), feasible as polynomial in the input's length (Cobham 1965, Edmonds 1965). Circuits: Shannon's count of g", "authority_tier": "engine_derived", "source": "Narrow Highway - a chain on the one map (operator seed)", "readable": false, "generated": false}, {"id": "card_src_pron_shannon_s", "title": "shannon's", "shelf": "pronunciation", "surface": "secular", "snippet": "shannon's: pronounced (ARPABET) SH AE1 N AH0 N Z. From the CMU Pronouncing Dictionary — the standard machine-readable pronunciations of North American English.", "authority_tier": "reference", "source": "CMU Pronouncing Dictionary (cmudict) — BSD-2-Clause, Carnegie Mellon", "readable": false, "generated": false}, {"id": "card_c_305b16a890ad", "title": "Pheromones — the molecule is the message ↔ The radio spectrum — one law from the cavity", "shelf": "connections", "surface": null, "snippet": "Radio waves (EM), DNA (genetic), morphemes (linguistic), neurotransmitters (neural), and the sealed receipt of this very engine (cryptographic) are all the same abstraction — Shannon's channel.  — a c", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_c_9a732b4ecc5d", "title": "Pheromones — the molecule is the message ↔ The genome as information — and the algebra ", "shelf": "connections", "surface": null, "snippet": "Radio waves (EM), DNA (genetic), morphemes (linguistic), neurotransmitters (neural), and the sealed receipt of this very engine (cryptographic) are all the same abstraction — Shannon's channel.  — a c", "authority_tier": "engine_derived", "source": "Concordance miner — 2026-07-11", "readable": false, "generated": false}, {"id": "card_bridge_master_entropy_log", "title": "Master equation: S = -k * sum(p_i log p_i)", "shelf": "bridges", "surface": "secular", "snippet": "disorder and information are one quantity — Boltzmann's S and Shannon's H are the same sum. ONE equation, 4 domains, connected by a change of variable: information_theory [k = 1/ln2 (bits), p = symbol", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_c_2e19e9b96f7d", "title": "A signal's information is a logarithm", "shelf": "connections", "surface": null, "snippet": "log2 of the distinguishable blends — Shannon's bits, the same log scale.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_79236eb0162f", "title": "A word's information is a logarithm", "shelf": "connections", "surface": null, "snippet": "log2(120) ~ 6.9 bits per word — Shannon's measure, the same log scale.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "readable": false, "generated": false}, {"id": "card_c_0706824b5f9f", "title": "Information IS a logarithm", "shelf": "connections", "surface": null, "snippet": "2 bits per DNA base = log2(4), sealed in the genome card — Shannon's measure is a log.", "authority_tier": "engine_derived", "source": "Concordance assay — 2026-07-09", "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_net_capacity"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}