{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:ZJSKJA3H3ZNP6QTS7JBLNG3JTG","short_pith_number":"pith:ZJSKJA3H","schema_version":"1.0","canonical_sha256":"ca64a48367de5aff4272fa42b69b6999a32b88c9c7e4b4a292a8c74235137205","source":{"kind":"arxiv","id":"1812.10897","version":2},"attestation_state":"computed","paper":{"title":"Optimization of the Sherrington-Kirkpatrick Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.OC"],"primary_cat":"math.PR","authors_text":"Andrea Montanari","submitted_at":"2018-12-28T05:47:36Z","abstract_excerpt":"Let ${\\boldsymbol A}\\in{\\mathbb R}^{n\\times n}$ be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing $\\langle{\\boldsymbol \\sigma},{\\boldsymbol A}{\\boldsymbol \\sigma}\\rangle$ over binary vectors ${\\boldsymbol \\sigma}\\in\\{+1,-1\\}^n$. In the language of statistical physics, this amounts to finding the ground state of the Sherrington-Kirkpatrick model of spin glasses. The asymptotic value of this optimization problem was characterized by Parisi via a celebrated variational principle, subsequently proved"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1812.10897","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-12-28T05:47:36Z","cross_cats_sorted":["cond-mat.stat-mech","math.OC"],"title_canon_sha256":"5742b2a150f59fb8c54fb9b4a3fb74c5a56c403834c1c1e5881a36f25abafead","abstract_canon_sha256":"9aed79b613aa4d830ef3caec4ffa8d4ce3c38190d555345d6ce1b8e07e2f1229"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:22.006681Z","signature_b64":"4Wri9aw3Pyq8bNr6hHnbFwbJYZ7mu72ETRVcJ/RDImqv94zmdbvnuL+0H2A0AJl+G13FKkOjQxtT+vFwO/FXCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ca64a48367de5aff4272fa42b69b6999a32b88c9c7e4b4a292a8c74235137205","last_reissued_at":"2026-05-17T23:49:22.005658Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:22.005658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimization of the Sherrington-Kirkpatrick Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","math.OC"],"primary_cat":"math.PR","authors_text":"Andrea Montanari","submitted_at":"2018-12-28T05:47:36Z","abstract_excerpt":"Let ${\\boldsymbol A}\\in{\\mathbb R}^{n\\times n}$ be a symmetric random matrix with independent and identically distributed Gaussian entries above the diagonal. We consider the problem of maximizing $\\langle{\\boldsymbol \\sigma},{\\boldsymbol A}{\\boldsymbol \\sigma}\\rangle$ over binary vectors ${\\boldsymbol \\sigma}\\in\\{+1,-1\\}^n$. In the language of statistical physics, this amounts to finding the ground state of the Sherrington-Kirkpatrick model of spin glasses. The asymptotic value of this optimization problem was characterized by Parisi via a celebrated variational principle, subsequently proved"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1812.10897","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1812.10897","created_at":"2026-05-17T23:49:22.005764+00:00"},{"alias_kind":"arxiv_version","alias_value":"1812.10897v2","created_at":"2026-05-17T23:49:22.005764+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1812.10897","created_at":"2026-05-17T23:49:22.005764+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZJSKJA3H3ZNP","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZJSKJA3H3ZNP6QTS","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZJSKJA3H","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":2,"internal_anchor_count":2,"sample":[{"citing_arxiv_id":"2605.23377","citing_title":"SAFE ma-QAOA: Surrogate-Assisted and Fine-Tuning Enhanced Multi-Angle QAOA with Parameter Distillation","ref_index":62,"is_internal_anchor":true},{"citing_arxiv_id":"2505.07929","citing_title":"Spin-Boson Mapping of the Quantum Approximate Optimization Algorithm","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG","json":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG.json","graph_json":"https://pith.science/api/pith-number/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/graph.json","events_json":"https://pith.science/api/pith-number/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/events.json","paper":"https://pith.science/paper/ZJSKJA3H"},"agent_actions":{"view_html":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG","download_json":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG.json","view_paper":"https://pith.science/paper/ZJSKJA3H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1812.10897&json=true","fetch_graph":"https://pith.science/api/pith-number/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/graph.json","fetch_events":"https://pith.science/api/pith-number/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/action/storage_attestation","attest_author":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/action/author_attestation","sign_citation":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/action/citation_signature","submit_replication":"https://pith.science/pith/ZJSKJA3H3ZNP6QTS7JBLNG3JTG/action/replication_record"}},"created_at":"2026-05-17T23:49:22.005764+00:00","updated_at":"2026-05-17T23:49:22.005764+00:00"}