{"query": "Computation - interference and complexity", "count": 20, "results": [{"id": "card_qc_computation", "title": "Computation - interference and complexity", "shelf": "codex", "surface": "secular", "snippet": "The speedup is making wrong answers interfere away (Grover sqrt-N, sealed; Shor); still computation, class BQP.", "authority_tier": "engine_derived", "source": "Narrow Highway — qc", "readable": false, "generated": false}, {"id": "card_theory_emergence", "title": "Emergence & self-organization (more is different)", "shelf": "theories", "surface": "secular", "snippet": "Emergence & self-organization (more is different) — an engine domain that can touch it: physics. Calibration: map-only — a structural claim about levels, not a computation. A system has properties non", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_computational_complexity__p__np__reductions", "title": "Computational complexity (P, NP, reductions)", "shelf": "theories", "surface": "secular", "snippet": "Computational complexity (P, NP, reductions) — an engine domain that can touch it: computer_science. Calibration: map-only — P vs NP is open, and this card says so. Not whether a problem can be solved", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_theory_kolmogorov_complexity", "title": "Algorithmic information (Kolmogorov complexity)", "shelf": "theories", "surface": "secular", "snippet": "Algorithmic information (Kolmogorov complexity) — an engine domain that can touch it: computer_science. Calibration: map-only — out of scope for sealing — foundational, empirical or interpretive (RESO", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (lone-domain seeding)", "readable": false, "generated": false}, {"id": "card_theory_combinatorial_enumeration", "title": "Combinatorial enumeration (permutations, combinations, binomial)", "shelf": "theories", "surface": "secular", "snippet": "Combinatorial enumeration (permutations, combinations, binomial) — an engine domain that can touch it: combinatorics. Calibration: seals. Counting arrangements without listing them. Permutations when ", "authority_tier": "reference", "source": "The Theory Assay — calibrated, not judged (docs/THEORY_CATALOG.md)", "readable": false, "generated": false}, {"id": "card_bridge_theory_kolmogorov_complexity__church_turing_thesis_computability", "title": "Bridge: Algorithmic information (Kolmogorov complexity)  ↔  Church–Turing thesis / computability", "shelf": "bridges", "surface": "secular", "snippet": "Algorithmic information (Kolmogorov complexity) and Church–Turing thesis / computability are the same form in different domains. its uncomputability is a Turing-halting result in disguise", "authority_tier": "reference", "source": "The Bridges — cross-domain isomorphisms", "readable": false, "generated": false}, {"id": "card_joint_weil_conjectures", "title": "The Weil conjectures (Deligne 1974): the Riemann hypothesis over finite fields, a theorem", "shelf": "codex", "surface": "secular", "snippet": "The Weil conjectures are the analogue of the Riemann hypothesis for the zeta functions of varieties over FINITE FIELDS, and they are a theorem (Deligne 1974): every eigenvalue of Frobenius on the i-th", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_mulmuley_2011", "title": "K. D. Mulmuley 2011 — On P vs. NP and geometric complexity theory", "shelf": "millennium", "surface": "secular", "snippet": "K. D. Mulmuley (2011). On P vs. NP and geometric complexity theory. J. ACM 58 (2011) 5:1–26. DOI 10.1145/1944345.1944346. arXiv: 0908.1936. Canonical: https://doi.org/10.1145/1944345.1944346. Free cop", "authority_tier": "reference", "source": "K. D. Mulmuley (2011), J. ACM 58 (2011) 5:1–26", "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_works_nested_control", "title": "The nested control-systems rule: meet a failure at its own layer", "shelf": "the-works", "surface": "secular", "snippet": "From Matt's Nested Control-Systems Framework: regulation is a stack of layers, and the layers do not compete — they nest. Two validity rules follow, and the engine checks them. First, a failure at a h", "authority_tier": "verified", "source": "The Works — worked & sealed", "readable": false, "generated": false}, {"id": "card_src_mill_mulmuley_sohoni_2001", "title": "K. D. Mulmuley 2001 — Geometric complexity theory I: an approach to the P vs. NP and related problems", "shelf": "millennium", "surface": "secular", "snippet": "K. D. Mulmuley, M. Sohoni (2001). Geometric complexity theory I: an approach to the P vs. NP and related problems. SIAM J. Comput. 31 (2001) 496–526. DOI 10.1137/S009753970038715X. Canonical: https://", "authority_tier": "reference", "source": "K. D. Mulmuley, M. Sohoni (2001), SIAM J. Comput. 31 (2001) 496–526", "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_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_pd_92ba08abf80f", "title": "Directions for cooking by troops : in camp and hospital", "shelf": "practical", "surface": "secular", "snippet": "Directions for cooking by troops : in camp and hospital (1861)\n\nA public-domain source: Internet Archive — https://archive.org/details/directionsforcoo00nigh. Carry the torch of Foxfire — practical kn", "authority_tier": "primary_pd", "source": "Internet Archive (1861)", "readable": true, "generated": false}, {"id": "card_chain_aaronson_wigderson_2009", "title": "Aaronson 2009 — Algebrization: a new barrier in complexity theory", "shelf": "codex", "surface": "secular", "snippet": "S. Aaronson, A. Wigderson (2009). Algebrization: a new barrier in complexity theory. ACM Trans. Comput. Theory 1 (2009) 2:1–54. DOI 10.1145/1490270.1490272. Canonical: https://doi.org/10.1145/1490270.", "authority_tier": "reference", "source": "S. Aaronson, A. Wigderson (2009), ACM Trans. Comput. Theory 1 (2009) 2:1–54", "readable": false, "generated": false}, {"id": "card_cs_computability", "title": "Computability and complexity — Turing to P vs NP", "shelf": "codex", "surface": "secular", "snippet": "A Turing machine defines what is computable; the universal machine runs any program (the engine, the laptop, the brain's computation). Some problems are undecidable (the halting problem); among the de", "authority_tier": "engine_derived", "source": "Narrow Highway — computer science", "readable": false, "generated": false}, {"id": "card_calc_v_verify_space_complexity", "title": "Space complexity", "shelf": "calculations", "surface": "secular", "snippet": "Space complexity — computer_science. Formula: S(n) ~ n^k. Canonical FORM: power_law (y = a * x^k) — engine verifier verify_space_complexity — the deterministic check the concordance runs. Same form, d", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_calc_v_verify_runtime_complexity", "title": "Runtime complexity", "shelf": "calculations", "surface": "secular", "snippet": "Runtime complexity — computer_science. Formula: T(n) ~ n^k (log-log fit). Canonical FORM: power_law (y = a * x^k) — engine verifier verify_runtime_complexity — the deterministic check the concordance ", "authority_tier": "reference", "source": "The Calculation Map — every calculation, mapped by form", "readable": false, "generated": false}, {"id": "card_src_etym_complexity", "title": "complexity", "shelf": "etymology", "surface": "secular", "snippet": "complexity: etymology (Webster 1913) — n.: [Cf. F. complexité.]. 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}, {"id": "card_src_mill_fghk_2016", "title": "M. G. Find 2016 — A better-than-3n lower bound for the circuit complexity of an explicit function", "shelf": "millennium", "surface": "secular", "snippet": "M. G. Find, A. Golovnev, E. A. Hirsch, A. S. Kulikov (2016). A better-than-3n lower bound for the circuit complexity of an explicit function. Proc. 57th IEEE FOCS (2016) 89–98; ECCC TR15-166 (2015, re", "authority_tier": "reference", "source": "M. G. Find, A. Golovnev, E. A. Hirsch, A. S. Kulikov (2016), Proc. 57th IEEE FOCS (2016) 89–98; ECCC TR15-166 (2015, revised 2022 as 'Improving 3n circuit complexity lower bounds')", "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_qc_computation"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}