{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:PPCS4ICPQBA73QGQK5TILXSJNZ","short_pith_number":"pith:PPCS4ICP","schema_version":"1.0","canonical_sha256":"7bc52e204f8041fdc0d0576685de496e77d57b5f30bc9ff911e8814255c3aeeb","source":{"kind":"arxiv","id":"2103.12654","version":2},"attestation_state":"computed","paper":{"title":"Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Damien Barbier, Daniel A. Stariolo, Leticia F. Cugliandolo, Pedro H. de Freitas Pimenta","submitted_at":"2021-03-23T16:17:18Z","abstract_excerpt":"We revisit the gradient descent dynamics of the spherical Sherrington-Kirkpatrick ($p=2$) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the relaxation takes place in three time regimes: a first algebraic one controlled by the decay of the eigenvalue distribution of the random exchange interaction matrix at its edge in the infinite size limit; a faster algebraic one determined by the distribution of the gap between the two extreme eigenvalues; and a final exponential one determined by the minimal gap sampled in the disorder average. We also "},"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":"2103.12654","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2021-03-23T16:17:18Z","cross_cats_sorted":[],"title_canon_sha256":"096f92a5e885f6c5cc884ca2964db9b5c4dacf6e5b7a3c417ada5eba3d3b2b11","abstract_canon_sha256":"b17903c0687ed2863bb7f934c4d143dc79eb68add7bdfbba9f835a9c282bdb75"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:04:22.483951Z","signature_b64":"U8MRYcsgW1Lew7EPhDtOpnbZ1hHLuFBvHbFiZ+NtMUiRgusTyzq0etumk51V8POfimzDmzDQSta0JhxsTtTEDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7bc52e204f8041fdc0d0576685de496e77d57b5f30bc9ff911e8814255c3aeeb","last_reissued_at":"2026-07-05T03:04:22.483554Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:04:22.483554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Finite size effects and loss of self-averageness in the relaxational dynamics of the spherical Sherrington-Kirkpatrick model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cond-mat.stat-mech","authors_text":"Damien Barbier, Daniel A. Stariolo, Leticia F. Cugliandolo, Pedro H. de Freitas Pimenta","submitted_at":"2021-03-23T16:17:18Z","abstract_excerpt":"We revisit the gradient descent dynamics of the spherical Sherrington-Kirkpatrick ($p=2$) model with finite number of degrees of freedom. For fully random initial conditions we confirm that the relaxation takes place in three time regimes: a first algebraic one controlled by the decay of the eigenvalue distribution of the random exchange interaction matrix at its edge in the infinite size limit; a faster algebraic one determined by the distribution of the gap between the two extreme eigenvalues; and a final exponential one determined by the minimal gap sampled in the disorder average. We also "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2103.12654","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2103.12654/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":"2103.12654","created_at":"2026-07-05T03:04:22.483617+00:00"},{"alias_kind":"arxiv_version","alias_value":"2103.12654v2","created_at":"2026-07-05T03:04:22.483617+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2103.12654","created_at":"2026-07-05T03:04:22.483617+00:00"},{"alias_kind":"pith_short_12","alias_value":"PPCS4ICPQBA7","created_at":"2026-07-05T03:04:22.483617+00:00"},{"alias_kind":"pith_short_16","alias_value":"PPCS4ICPQBA73QGQ","created_at":"2026-07-05T03:04:22.483617+00:00"},{"alias_kind":"pith_short_8","alias_value":"PPCS4ICP","created_at":"2026-07-05T03:04:22.483617+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ","json":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ.json","graph_json":"https://pith.science/api/pith-number/PPCS4ICPQBA73QGQK5TILXSJNZ/graph.json","events_json":"https://pith.science/api/pith-number/PPCS4ICPQBA73QGQK5TILXSJNZ/events.json","paper":"https://pith.science/paper/PPCS4ICP"},"agent_actions":{"view_html":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ","download_json":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ.json","view_paper":"https://pith.science/paper/PPCS4ICP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2103.12654&json=true","fetch_graph":"https://pith.science/api/pith-number/PPCS4ICPQBA73QGQK5TILXSJNZ/graph.json","fetch_events":"https://pith.science/api/pith-number/PPCS4ICPQBA73QGQK5TILXSJNZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ/action/storage_attestation","attest_author":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ/action/author_attestation","sign_citation":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ/action/citation_signature","submit_replication":"https://pith.science/pith/PPCS4ICPQBA73QGQK5TILXSJNZ/action/replication_record"}},"created_at":"2026-07-05T03:04:22.483617+00:00","updated_at":"2026-07-05T03:04:22.483617+00:00"}