{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:X4RLWDK4UZHLDRMTCFCSQVSYOF","short_pith_number":"pith:X4RLWDK4","schema_version":"1.0","canonical_sha256":"bf22bb0d5ca64eb1c5931145285658714f99a7b8a0ecd40c06211ff4985a120c","source":{"kind":"arxiv","id":"1609.04368","version":4},"attestation_state":"computed","paper":{"title":"On the energy landscape of the mixed even $p$-spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Gilad Lerman, Madeline Handschy, Wei-Kuo Chen","submitted_at":"2016-09-14T18:01:35Z","abstract_excerpt":"We investigate the energy landscape of the mixed even $p$-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level. Furthermore, their magnetizations and overlaps are concentrated around some fixed constants. In particular, at the level of maximal energy, we prove that the Hamiltonian exhibits exponentially many orthogonal peaks. This improves the results of Chatterjee and Ding-Eldan-Zhai, w"},"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":"1609.04368","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-09-14T18:01:35Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"0e98f24b437f5d93773900b00e1e5fa6133f947667cd2ff6c3c98382328d6199","abstract_canon_sha256":"a8a078daa27434e9e89ce7a5bf771c4074b477651bb5f1ebe2116b3c1e7b52fb"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:30.741778Z","signature_b64":"vhYtsf4qUEHSHUbAl8nNqDs7jdUdx7w8yJyMayuGA6aQNcEI+CQ5aR6G7QzpLzjEgX6MyHi5nkrCHgypwXkkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf22bb0d5ca64eb1c5931145285658714f99a7b8a0ecd40c06211ff4985a120c","last_reissued_at":"2026-05-18T00:01:30.741140Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:30.741140Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the energy landscape of the mixed even $p$-spin model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Gilad Lerman, Madeline Handschy, Wei-Kuo Chen","submitted_at":"2016-09-14T18:01:35Z","abstract_excerpt":"We investigate the energy landscape of the mixed even $p$-spin model with Ising spin configurations. We show that for any given energy level between zero and the maximal energy, with overwhelming probability there exist exponentially many distinct spin configurations such that their energies stay near this energy level. Furthermore, their magnetizations and overlaps are concentrated around some fixed constants. In particular, at the level of maximal energy, we prove that the Hamiltonian exhibits exponentially many orthogonal peaks. This improves the results of Chatterjee and Ding-Eldan-Zhai, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.04368","kind":"arxiv","version":4},"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":"1609.04368","created_at":"2026-05-18T00:01:30.741226+00:00"},{"alias_kind":"arxiv_version","alias_value":"1609.04368v4","created_at":"2026-05-18T00:01:30.741226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1609.04368","created_at":"2026-05-18T00:01:30.741226+00:00"},{"alias_kind":"pith_short_12","alias_value":"X4RLWDK4UZHL","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_16","alias_value":"X4RLWDK4UZHLDRMT","created_at":"2026-05-18T12:30:51.357362+00:00"},{"alias_kind":"pith_short_8","alias_value":"X4RLWDK4","created_at":"2026-05-18T12:30:51.357362+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/X4RLWDK4UZHLDRMTCFCSQVSYOF","json":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF.json","graph_json":"https://pith.science/api/pith-number/X4RLWDK4UZHLDRMTCFCSQVSYOF/graph.json","events_json":"https://pith.science/api/pith-number/X4RLWDK4UZHLDRMTCFCSQVSYOF/events.json","paper":"https://pith.science/paper/X4RLWDK4"},"agent_actions":{"view_html":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF","download_json":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF.json","view_paper":"https://pith.science/paper/X4RLWDK4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1609.04368&json=true","fetch_graph":"https://pith.science/api/pith-number/X4RLWDK4UZHLDRMTCFCSQVSYOF/graph.json","fetch_events":"https://pith.science/api/pith-number/X4RLWDK4UZHLDRMTCFCSQVSYOF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF/action/storage_attestation","attest_author":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF/action/author_attestation","sign_citation":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF/action/citation_signature","submit_replication":"https://pith.science/pith/X4RLWDK4UZHLDRMTCFCSQVSYOF/action/replication_record"}},"created_at":"2026-05-18T00:01:30.741226+00:00","updated_at":"2026-05-18T00:01:30.741226+00:00"}