{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:4QUNYF3VZFQQRJYNWLZH3F5OXA","short_pith_number":"pith:4QUNYF3V","schema_version":"1.0","canonical_sha256":"e428dc1775c96108a70db2f27d97aeb83ad28a683fa5a04750d92f8097a59777","source":{"kind":"arxiv","id":"2606.28298","version":1},"attestation_state":"computed","paper":{"title":"Stationary point complexity via minimal supersymmetry breaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Jaron Kent-Dobias","submitted_at":"2026-06-26T17:41:03Z","abstract_excerpt":"The statistics of stationary points are a powerful way to understand mean-field random landscapes, and the Kac--Rice formula is a general way to compute them. A longstanding technical barrier to these calculations is the presence of the absolute value of the determinant of the Hessian. Neglecting the absolute value produces an elegant 2-index supersymmetric representation of the problem, but is often incorrect. We develop an expanded 4-index supersymmetric representation of the complexity problem which incorporates the absolute value naturally via spontaneous supersymmetry breaking along a par"},"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":"2606.28298","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.dis-nn","submitted_at":"2026-06-26T17:41:03Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"6a039b9225e8284a46aaf96047760f99380ba701f6e3bec2c92940fb07e3eb59","abstract_canon_sha256":"fb13e6158fd858b8546fabd40d9225d6c67e6454358dd33ebf543b57071e6682"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-29T01:15:12.367547Z","signature_b64":"M2wfHVVN0+xeHxQfXVrHE/RgTIH0oOu0HeKiKSal+202s8qTTHS+4WnjJanSeXQ6EW610jPFXN8k07Fly4X7AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e428dc1775c96108a70db2f27d97aeb83ad28a683fa5a04750d92f8097a59777","last_reissued_at":"2026-06-29T01:15:12.367155Z","signature_status":"signed_v1","first_computed_at":"2026-06-29T01:15:12.367155Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Stationary point complexity via minimal supersymmetry breaking","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"cond-mat.dis-nn","authors_text":"Jaron Kent-Dobias","submitted_at":"2026-06-26T17:41:03Z","abstract_excerpt":"The statistics of stationary points are a powerful way to understand mean-field random landscapes, and the Kac--Rice formula is a general way to compute them. A longstanding technical barrier to these calculations is the presence of the absolute value of the determinant of the Hessian. Neglecting the absolute value produces an elegant 2-index supersymmetric representation of the problem, but is often incorrect. We develop an expanded 4-index supersymmetric representation of the complexity problem which incorporates the absolute value naturally via spontaneous supersymmetry breaking along a par"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28298","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/2606.28298/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":"2606.28298","created_at":"2026-06-29T01:15:12.367219+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.28298v1","created_at":"2026-06-29T01:15:12.367219+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.28298","created_at":"2026-06-29T01:15:12.367219+00:00"},{"alias_kind":"pith_short_12","alias_value":"4QUNYF3VZFQQ","created_at":"2026-06-29T01:15:12.367219+00:00"},{"alias_kind":"pith_short_16","alias_value":"4QUNYF3VZFQQRJYN","created_at":"2026-06-29T01:15:12.367219+00:00"},{"alias_kind":"pith_short_8","alias_value":"4QUNYF3V","created_at":"2026-06-29T01:15:12.367219+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/4QUNYF3VZFQQRJYNWLZH3F5OXA","json":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA.json","graph_json":"https://pith.science/api/pith-number/4QUNYF3VZFQQRJYNWLZH3F5OXA/graph.json","events_json":"https://pith.science/api/pith-number/4QUNYF3VZFQQRJYNWLZH3F5OXA/events.json","paper":"https://pith.science/paper/4QUNYF3V"},"agent_actions":{"view_html":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA","download_json":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA.json","view_paper":"https://pith.science/paper/4QUNYF3V","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.28298&json=true","fetch_graph":"https://pith.science/api/pith-number/4QUNYF3VZFQQRJYNWLZH3F5OXA/graph.json","fetch_events":"https://pith.science/api/pith-number/4QUNYF3VZFQQRJYNWLZH3F5OXA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/action/storage_attestation","attest_author":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/action/author_attestation","sign_citation":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/action/citation_signature","submit_replication":"https://pith.science/pith/4QUNYF3VZFQQRJYNWLZH3F5OXA/action/replication_record"}},"created_at":"2026-06-29T01:15:12.367219+00:00","updated_at":"2026-06-29T01:15:12.367219+00:00"}