{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2020:NJZH3EKTQGAY6PIOEDZY3U56I2","short_pith_number":"pith:NJZH3EKT","schema_version":"1.0","canonical_sha256":"6a727d915381818f3d0e20f38dd3be4693d3f48767b598df85f326f383b81b8e","source":{"kind":"arxiv","id":"2001.00904","version":1},"attestation_state":"computed","paper":{"title":"Optimization of Mean-field Spin Glasses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.OC"],"primary_cat":"math.PR","authors_text":"Ahmed El Alaoui, Andrea Montanari, Mark Sellke","submitted_at":"2020-01-03T17:39:35Z","abstract_excerpt":"Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper we consider the case of Ising mixed $p$-spin models, namely Hamiltonians $H_N:\\Sigma_N\\to {\\mathbb R}$ on the Hamming hypercube $\\Sigma_N = \\{\\pm 1\\}^N$, which are defined by the property that $\\{H_N({\\boldsymbol \\sigma})\\}_{{\\boldsymbol \\sigma}\\in \\Sigma_N}$ is a centered Gaussian process with covariance ${\\mathbb E}\\{H_N({\\boldsymbol \\sigma}_1)H_N({\\boldsymbol \\sigma}_2)\\}$ depending only on the scalar product $\\langle {\\boldsymbol \\sigma}_1,{\\boldsymbol \\sigma}_2\\"},"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":"2001.00904","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-01-03T17:39:35Z","cross_cats_sorted":["cond-mat.dis-nn","math.OC"],"title_canon_sha256":"a6fb79008144dd7a55bee31c9e4277e2ecb5713c4bffe9a7af6a47c05cbd464d","abstract_canon_sha256":"2b449be5b1f591af132339a1201d5aa4a2059ddfbb9ceb46ab78bc45baff54c0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:29:33.443874Z","signature_b64":"LpRYHLqDQASG0ESwcU/ZAIbfQTpgzBjXqqtrOJ0dnzykb0Od8dGn5KRbjD3c5lbNlWdEyE2FuJhLjcB5TKdLDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a727d915381818f3d0e20f38dd3be4693d3f48767b598df85f326f383b81b8e","last_reissued_at":"2026-07-05T00:29:33.443428Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:29:33.443428Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimization of Mean-field Spin Glasses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.dis-nn","math.OC"],"primary_cat":"math.PR","authors_text":"Ahmed El Alaoui, Andrea Montanari, Mark Sellke","submitted_at":"2020-01-03T17:39:35Z","abstract_excerpt":"Mean-field spin glasses are families of random energy functions (Hamiltonians) on high-dimensional product spaces. In this paper we consider the case of Ising mixed $p$-spin models, namely Hamiltonians $H_N:\\Sigma_N\\to {\\mathbb R}$ on the Hamming hypercube $\\Sigma_N = \\{\\pm 1\\}^N$, which are defined by the property that $\\{H_N({\\boldsymbol \\sigma})\\}_{{\\boldsymbol \\sigma}\\in \\Sigma_N}$ is a centered Gaussian process with covariance ${\\mathbb E}\\{H_N({\\boldsymbol \\sigma}_1)H_N({\\boldsymbol \\sigma}_2)\\}$ depending only on the scalar product $\\langle {\\boldsymbol \\sigma}_1,{\\boldsymbol \\sigma}_2\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2001.00904","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2001.00904/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2001.00904","created_at":"2026-07-05T00:29:33.443487+00:00"},{"alias_kind":"arxiv_version","alias_value":"2001.00904v1","created_at":"2026-07-05T00:29:33.443487+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2001.00904","created_at":"2026-07-05T00:29:33.443487+00:00"},{"alias_kind":"pith_short_12","alias_value":"NJZH3EKTQGAY","created_at":"2026-07-05T00:29:33.443487+00:00"},{"alias_kind":"pith_short_16","alias_value":"NJZH3EKTQGAY6PIO","created_at":"2026-07-05T00:29:33.443487+00:00"},{"alias_kind":"pith_short_8","alias_value":"NJZH3EKT","created_at":"2026-07-05T00:29:33.443487+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":3,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2607.08160","citing_title":"Weak Poincar\\'e Inequalities via Approximate Stochastic Localization: Application to Sampling the Sherrington-Kirkpatrick Model","ref_index":66,"is_internal_anchor":true},{"citing_arxiv_id":"2408.02360","citing_title":"Potential Hessian Ascent: The Sherrington-Kirkpatrick Model","ref_index":10,"is_internal_anchor":false},{"citing_arxiv_id":"2505.07929","citing_title":"Spin-Boson Mapping of the Quantum Approximate Optimization Algorithm","ref_index":6,"is_internal_anchor":false}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2","json":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2.json","graph_json":"https://pith.science/api/pith-number/NJZH3EKTQGAY6PIOEDZY3U56I2/graph.json","events_json":"https://pith.science/api/pith-number/NJZH3EKTQGAY6PIOEDZY3U56I2/events.json","paper":"https://pith.science/paper/NJZH3EKT"},"agent_actions":{"view_html":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2","download_json":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2.json","view_paper":"https://pith.science/paper/NJZH3EKT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2001.00904&json=true","fetch_graph":"https://pith.science/api/pith-number/NJZH3EKTQGAY6PIOEDZY3U56I2/graph.json","fetch_events":"https://pith.science/api/pith-number/NJZH3EKTQGAY6PIOEDZY3U56I2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2/action/storage_attestation","attest_author":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2/action/author_attestation","sign_citation":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2/action/citation_signature","submit_replication":"https://pith.science/pith/NJZH3EKTQGAY6PIOEDZY3U56I2/action/replication_record"}},"created_at":"2026-07-05T00:29:33.443487+00:00","updated_at":"2026-07-05T00:29:33.443487+00:00"}