{"query": "The lattice sign problem is NP-hard", "count": 20, "results": [{"id": "card_joint_sign_problem", "title": "The lattice sign problem is NP-hard", "shelf": "codex", "surface": "secular", "snippet": "Troyer and Wiese (2005): the fermion sign problem of quantum Monte Carlo - the obstacle to simulating lattice gauge theory at finite density - is NP-hard. A proof that P = NP would remove it; its hard", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor, a joint found in the literature (operator seed)", "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_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_millennium", "title": "The Millennium floor - seven open questions, and where they connect", "shelf": "codex", "surface": "secular", "snippet": "The seven Millennium Prize Problems on the one map of reality. The FLOOR is what is proven or observed: the joints where two of the questions meet at one established thing - the GUE statistics shared ", "authority_tier": "engine_derived", "source": "Narrow Highway - the Millennium floor (operator seed)", "readable": false, "generated": false}, {"id": "card_src_mill_deligne_1974", "title": "P. Deligne 1974 — La conjecture de Weil. I", "shelf": "millennium", "surface": "secular", "snippet": "P. Deligne (1974). La conjecture de Weil. I. Publ. Math. IHÉS 43 (1974) 273–307. DOI 10.1007/BF02684373. Canonical: https://doi.org/10.1007/BF02684373. Free copy: http://www.numdam.org/item/PMIHES_197", "authority_tier": "reference", "source": "P. Deligne (1974), Publ. Math. IHÉS 43 (1974) 273–307", "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_troyer_wiese_2005", "title": "M. Troyer 2005 — Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations", "shelf": "millennium", "surface": "secular", "snippet": "M. Troyer, U.-J. Wiese (2005). Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys. Rev. Lett. 94 (2005) 170201. DOI 10.1103/PhysRevLett.94.170201. ", "authority_tier": "reference", "source": "M. Troyer, U.-J. Wiese (2005), Phys. Rev. Lett. 94 (2005) 170201", "readable": false, "generated": false}, {"id": "card_src_mill_aaronson_2016", "title": "S. Aaronson 2016 — P =? NP", "shelf": "millennium", "surface": "secular", "snippet": "S. Aaronson (2016). P =? NP. Open Problems in Mathematics (Springer, 2016) 1–122. DOI 10.1007/978-3-319-32162-2_1. Canonical: https://doi.org/10.1007/978-3-319-32162-2_1. Free copy: https://www.scotta", "authority_tier": "reference", "source": "S. Aaronson (2016), Open Problems in Mathematics (Springer, 2016) 1–122", "readable": false, "generated": false}, {"id": "card_question_p_vs_np", "title": "P versus NP", "shelf": "millennium", "surface": "secular", "snippet": "P versus NP. Is every problem whose solution can be checked in polynomial time also solvable in polynomial time? Its chart is the tick stick stick_p_versus_np: what is sealed, what is cited and what s", "authority_tier": "reference", "source": "Clay Mathematics Institute, the Millennium Prize Problems (2000)", "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_src_nuclide_np_219", "title": "Np-219 — np-219", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-219: 93 protons, 126 neutrons, mass number A=219. Half-life 0.00015 s. Primary decay: A 1%. Atomic mass 219.031602 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_220", "title": "Np-220 — np-220", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-220: 93 protons, 127 neutrons, mass number A=220. Half-life 2.5e-05 s. Primary decay: A 1%. Atomic mass 220.032716 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_222", "title": "Np-222 — np-222", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-222: 93 protons, 129 neutrons, mass number A=222. Half-life 3.8e-07 s. Primary decay: A 1%. Atomic mass 222.033575 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_223", "title": "Np-223 — np-223", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-223: 93 protons, 130 neutrons, mass number A=223. Half-life 2.2e-06 s. Primary decay: A 1%. Atomic mass 223.032913 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_224", "title": "Np-224 — np-224", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-224: 93 protons, 131 neutrons, mass number A=224. Half-life 3.8e-05 s. Primary decay: A 1%. Atomic mass 224.034388 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_225", "title": "Np-225 — np-225", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-225: 93 protons, 132 neutrons, mass number A=225. Half-life 0.0036 s. Primary decay: A 1%. Atomic mass 225.033943 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_226", "title": "Np-226 — np-226", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-226: 93 protons, 133 neutrons, mass number A=226. Half-life 0.035 s. Primary decay: A 1%. Atomic mass 226.035230 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_227", "title": "Np-227 — np-227", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-227: 93 protons, 134 neutrons, mass number A=227. Half-life 0.51 s. Primary decay: A 1%. Atomic mass 227.034975 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (public domain)", "readable": false, "generated": false}, {"id": "card_src_nuclide_np_237", "title": "Np-237 — np-237", "shelf": "nuclear_physics", "surface": "secular", "snippet": "Nuclide Np-237: 93 protons, 144 neutrons, mass number A=237. Half-life 67658049289525.3 s. Primary decay: A 1%. Atomic mass 237.048172 u.", "authority_tier": "reference", "source": "NNDC / AME nuclide data (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_joint_sign_problem"}}, "ends": "a verdict or a card · the trail · a seal · one next step"}}