{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d3d2ff1f9b077479794eabb786b03498a59e016b7487ee76a0ee9fbead03e99e","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["3aa3308ec11884f917f1766769579cd9607c5179cf7198157322768c02d06862","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"3558fac520b05762802b9c5e8da5fbc8770e772804fd79e49725f53e2f595ef5","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":["ai:gpt-5.5"],"external_id":"cm.sign-problem-numerics.dynamical-sign-problem","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Simulating how electrons evolve in time requires summing complex phases that cancel more and more as time grows, so the cost rises exponentially with simulated time. For a single magnetic impurity, new methods reduced this to polynomial cost; whether this is possible for whole lattices is open.","posed_since":"","precise":"Real-time diagrammatic and path-integral Monte Carlo for nonequilibrium Green's functions have variance growing as $\\exp(c t)$. Inchworm Monte Carlo (Cohen et al. 2015) and related methods reach polynomial scaling in t for Anderson impurity models. Determine whether a classical algorithm computes local real-time correlators of the infinite 2D Hubbard model at $U/t \\sim 4$, starting from a thermal state at $T \\sim t$, up to time $t_{\\max}$ with error $\\epsilon$ at cost polynomial in $t_{\\mathrm{max}}$ and $1/\\epsilon$, or prove that this is hard (e.g. by a complexity reduction). An answer is an algorithm with proven scaling or a hardness proof.","problem_ref":"3aa3308ec11884f917f1766769579cd9607c5179cf7198157322768c02d06862","references":"","settled_by":"An algorithm with a proven polynomial cost bound verified against exact results, or a complexity-theoretic reduction showing such an algorithm would imply an unlikely collapse.","status_note":"Polynomial-cost methods exist for quantum impurity models since 2015; no such method is known for lattices.","title":"Polynomial-cost real-time simulation of interacting fermion lattices","topic_ref":null},"content_withheld":"false","files":[],"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"57edeb3035979307c0c3b141afe26b93e5d0242e45833d2b8346f8262cc18507","schema":"pubphys.attested/1"},"id_token":null,"id_token_withheld":"false","envelope":{"attested_hash":"624318360454cb3b5370f42e0524396b21a43d840e43cec3d82b5580fdcc675e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ZkZCMq-v0jn5jv4v4EdCVBUqD-4Cz_wmaTJACWJWl3mUsqssYVZmDubbRwaveHawQhYJ7gsVTWghtFdnkmqsCA"},"schema":"pubphys.envelope/1"},"ots":{"attested":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIYkMYNgRUyztTcPQuBSQ5ayGkPYQOQ87D2CtVgP3MZ17wIGKWKmm16rqJGgOvtGnxf8D-Pda2gRpjBylKIl6EDy6xCPAg5-sGk_CBMbIjb9nf726hkau6vOPBlRLmL-mJShdGhUAI8CDtTJRTvbF8tPzqHYxhod9FyT8bGAgCHLd-2rLUAgdGEgjxILvrUh91T-6JcrzGl13kvGxgjpiSSMAgxa_ngZuXuKIECPEgSBCY6nk9meSCpsIgqugtgUS928s-u_enlO65LhBbZwgI8CDSTi3UbP9XXsgIMxDLkvmBMs90bVBKmRvZEYKuvTOdywjwIOBhAE_usQZ2nBBNY4wzw4-dYOTzn3zDoB6qJnk6bujrCPAgNWsj73C-FdBKnM-YIq56Rzi4rZw0zXjVnprUdC52gz4I8SBcP9hQb3hxUiLf8dFx-DuqZHA2xkmG-c_qCFt8QfQHCAjwIOv_x0B6HyZ6WMHKeIf_d_EUIvwPGdZeVY-hXN3RLDM5CPEgHd9u6OIGCvUV12A1B1xdiOprSJ-4w0cqwfe7CzVX5HsI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"],"envelope":["AE9wZW5UaW1lc3RhbXBzAABQcm9vZgC_ieLohOiSlAEIUURQLR4out00t4kCFdU_DD7mjl4BfErwvECASjHANWnwIFFKv0ZBApw5mTjbpfMkrR2RiQfEMfkj1c6z3EszI3D8CPAgYHf1bc4DIFNvlvpWHRqANmJFEW-uTMPDBEuXSK7IrzwI8SDnhJnMDIu39c31Blk4Ip-jWObJExfuiw8dvyaWzo-2-QjwIFNciBlW4fVPBRwjZY7lkQhA2QUaBTBsFrdNU2NPrvpBCPAgFRpzxmfeAohfkiAPlD3_mqCX1UAjWeJJpBX20XLYkf8I8SA2Gqw6uEz1JGVClpngXfIbA7O-VJRz-QR7EaJFhlzYDQjwILRHKIw6kWwderhYJaG85inV3mmnLkU_qFqH8lkj_LlZCPAgPjYOETLLdPZ3KisQfRmeRF8geFLOzyylnb3d7Q66gUQI8CCFjG9pSMiq3eVzHAmZsjRKj0iAZic3nIa3eyIChZggbAjwIOv_x0B6HyZ6WMHKeIf_d_EUIvwPGdZeVY-hXN3RLDM5CPEgHd9u6OIGCvUV12A1B1xdiOprSJ-4w0cqwfe7CzVX5HsI8CDQo_sIWZiWXaTGRSQBLmU-lHJKskYKqsjO1r02DhB8LAj_8Ajn9YmozHwo9QjwEJ46aM9ZDv3TdtqV3ZbRsNgI8SBOF8pILGf1kodr5MKmQs6Cd93joraGn3g6UPt_-kewPwjwIOG-gmM7bd_eR4AiDMNfluS3xvr7vicLR-sCBr5qtG2cCPAgrVNFrCoeQcCxhlmnE0BzHgR8HQpZAlfqzDDFzfWb8GUI8QRq0WWT8AjZJ2cF_c7k8ACD3-MNLvkMjiwraHR0cHM6Ly9ib2IuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZ_AI9ZMS1zxd7IEI8BDd00WgJZ0RncsC1Fyai_4aCPEgvxMFrnu7F05IW5INiraQ3OVEYMjNx6JfBxw1Q4jPLi4I8QRq0WWS8Ag2zxPAtI5JsP8Ag9_jDS75DI4uLWh0dHBzOi8vYWxpY2UuYnRjLmNhbGVuZGFyLm9wZW50aW1lc3RhbXBzLm9yZwjxIHAnv4KFFf4uiYEFJvLxiMxSyz8VowJP4roTfDD9h7bICPAgj5tgvbNF7mxSP4jGGE66ezUFRLnI4g1VTkvuV4VtCPAI8CCxlc1HuKORuHgn7DYIYcDhc4oo99OkTWBEvddBypoa7AjwIFcjjaF8kDNDYCZGaNISlRjvX-I7in-QNwsr4JYQbFJvCPAgnl0k4gs7LuY5i1umiHO-J7My3uBThLJUWQoY9LdVSrQI8SA6-Ft11_K_GqMNWYhkVsVqCFvXSYbp4S8JoLsLBnUzvgjxIBC8_mAE7JBP35SNxDBcG7joLJwURpMxdV2vSO64_jEOCPEge04Coj1xSi7CE8UwqiBGNhPyZ5QdD_YZwn-heSdObU4I8SBgdDSgr3VUx1j8m_pK7-OzMwwFgXeLy43ujffCv-hf5AjwIMl-PnAt4xjoBEVU4-nkyN0NKRa9AvX4kEMfllFyIJS9CPFZAQAAAAHz4rV-uwQFg02bVnEMUFgpIdGKjM4tWuID1kTVnrjisAAAAAAA_v___wJURAIAAAAAABYAFBFys2oc0-U-bYrC3VulGLzND5fbAAAAAAAAAAAiaiDwBHLTDgAICPEgMJIBYi46xOIuFDwzJ9nOx14ngW5HbglUf65ORpkoIYcICPAgHgGWEGCDHWgscwT92NOoJ7s-ezbPkyiWr2RnYZDC_dwICPAgtffMyyLu-MscJsDc0dzwGspwSrrmvVAnMNgsgWhHClgICPAgMUl1OfBDUwhp5VZjHwVA0nuz1F5HZTUJCHAnM1L1F3MICPAgStK7UWpnrUueV5EaE7uE0y6BLMp6EANmrbhrTqEBZu8ICPAg5LVW7IHtUL5mNOvPx1hOTfLMmqlQ7t9EFW-KDtrISIQICPAgABgXZ6upFU8qiDQKFtQFpqkjKwl0PsxM4JUjVLlDKbkICPAgEwb96FiOhjlbwI8GFZQ4a5GXwxs4bUdqVOMKrtBWV30ICPEgqBg-wp0c8CAPV9k6J7wIa9_GtQfpWmhpE1zqFZyi2pQICPAg2pZLTVPGJbriiz0UhMytYDVYAXOgQnWDcrMOewK9O8cICPEgxm3QwzbvT4siJzubQGnST67bWv-exYwSPP1KDi7CaUwICPEgm6udUudfjUaM0gUFTylKGDMypj7ptMTG0zmxd_T5yTcICPAgMpOInkjFCVp1pOZhfZnyPAl8hdWGmHzQcrGLgLwSKLgICAAFiJYNc9cZAQPzpjs"]},"log":{"leaf_index":"3026","tree_size":"3804","proof":["8f09f6c72a7100f35d318be03eaf59c1a36ec996c16f11125d392a57b0886909","ea481c1b27b992b1573f60fe274bab4caeeb2f6e948e8da2a3fd72e4b00c8dab","5e99af2b90e342e864e88d59c17b577487c059e3cf38cfcc8ce85b7b2961dcc2","636ae2029bb66676d8cdfaabc5a2812d0104d58778e232634531c57debcd0d71","3c2e3d6e50295d75f3bd94a2dad00a42736ec4ce9810bc71b3703e93e987d5f8","4144ec28590f19e0fc54750765647a0ad1a4721ff1d1d388d77adcb6308cc31a","4d342745f225337b5e11d27fcecea80f1e780419083c24bd0ca3f37687fe6b16","b54387979d97d9abde30a291e115dc6733875d3a816ad7f767bc7b5a22c80a0c","56960156727d0f461a1b3857ab83f18526eaef848c820c927094afc1f989d56c","b0b232078d071c92816af6274529aef23a2ea1f41246694fec32d768cfa09dc8","325287f5a43e4f3ad4072ec4bd53d43c50c1393021a056122e9cb0fad83b868f","3c578dccc15502c5f3efe228cadc99fee76ab536ed01f66b14d316fdcc157429"],"checkpoint":"pubphys.com/log/v1\n3804\nAK6t4qgu96+M9wScTrIlsJ10d/zhKVEtYguyM3aeJvo=\n\n— pubphys.com/log/v1 JFPwIPP8EtoxgcsQg7V7CwIdL4UKPqJtpv+eB8sFNJjyQHIdyA1VabmBsPyLqq2bLxJPn57rA6fQi8y0QDDjRXHvlQg=\n","promise":"pubphys.com/log/v1 promise\n389cfaa0dc62a8169de74725981439629d84aefd19055833dd7d3749d9c425f4\n3026\n2026-10-15T23:43:57Z\n2026-10-16T01:43:57Z\n\n— pubphys.com/log/v1 JFPwIP0p8upA1fLhg1wveMXVhlHk+8sCwfGptEpAz8smRBuZj1r8CJ8lCAQBO54cvpn/+uQ5gWL8sT/hqf1QrGnRXAE=\n"},"orcid_key_evidence":[],"attesting":null}