{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SSQES7V3L3TU6DOOZHFPMY7K34","merge_version":"pith-open-graph-merge-v1","event_count":6,"valid_event_count":6,"invalid_event_count":0,"equivocation_count":1,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f4f63b90a5d6019420eea43815f39e24130fa0e10e9c1e2cb8c0b9cd02eca4fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T17:51:07Z","title_canon_sha256":"4e529a7eec3d4167c81da1bdd6aacabaa06736c274111f63ea4df093638f3cc4"},"schema_version":"1.0","source":{"id":"2607.08753","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2607.08753","created_at":"2026-07-10T01:19:59Z"},{"alias_kind":"arxiv_version","alias_value":"2607.08753v1","created_at":"2026-07-10T01:19:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2607.08753","created_at":"2026-07-10T01:19:59Z"},{"alias_kind":"pith_short_12","alias_value":"SSQES7V3L3TU","created_at":"2026-07-10T01:19:59Z"},{"alias_kind":"pith_short_16","alias_value":"SSQES7V3L3TU6DOO","created_at":"2026-07-10T01:19:59Z"},{"alias_kind":"pith_short_8","alias_value":"SSQES7V3","created_at":"2026-07-10T01:19:59Z"}],"graph_snapshots":[{"event_id":"sha256:c721a6cb5cc7b18699646479c156386665076b5b32344f3c7f150f55bb885d9c","target":"graph","created_at":"2026-07-10T01:19:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2607.08753/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Progress in mathematics often requires more than a certificate of truth: it requires proof structures that are transparent, checkable, and reusable. Automated systems can increasingly certify that a result is true; what they typically return, however, is a dense certificate rather than an interpretable, reusable proof structure.\n  Recent work on performance estimation problems has shown that performance bounds and complexity analyses of first-order optimization methods can be discovered by searching over a structured space of Lagrangian dual certificates. We cast the search for simpler proof s","authors_text":"Adrien Taylor, Aymeric Dieuleveut, Baptiste Goujaud, Daniel Berg Thomsen, Manu Upadhyaya","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T17:51:07Z","title":"Finding Simple Proofs for First-Order Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08753","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:4e1e64131d6a6d57cee3da017026a5e0c71b5246d2f46dbf6b11ae273f27b6ca","target":"record","created_at":"2026-07-10T01:19:59Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f4f63b90a5d6019420eea43815f39e24130fa0e10e9c1e2cb8c0b9cd02eca4fd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2026-07-09T17:51:07Z","title_canon_sha256":"4e529a7eec3d4167c81da1bdd6aacabaa06736c274111f63ea4df093638f3cc4"},"schema_version":"1.0","source":{"id":"2607.08753","kind":"arxiv","version":1}},"canonical_sha256":"94a0497ebb5ee74f0dcec9caf663eadf02ae5d22590fabed054888ab6f300627","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94a0497ebb5ee74f0dcec9caf663eadf02ae5d22590fabed054888ab6f300627","first_computed_at":"2026-07-10T01:19:59.322361Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-10T01:19:59.322361Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"smzTo0DYds8DTNLxTfBcdWFcIzOWSd7UTrI1T1Ty/El514ia6vGYOzGC6aMW022DVqBGc0lAlBJkIH0amEkdDA==","signature_status":"signed_v1","signed_at":"2026-07-10T01:19:59.322770Z","signed_message":"canonical_sha256_bytes"},"source_id":"2607.08753","source_kind":"arxiv","source_version":1}}},"equivocations":[{"signer_id":"pith.science","event_type":"integrity_finding","target":"integrity","event_ids":["sha256:13854f5e74cdc8c305476b2f66769072d9bf5d629da845d18f783a2caf28d5dd","sha256:17c8d70cc1f54b49a1a80dd3a9b66024f37bb88dcf51d00a725c5df3e51bbffc","sha256:1c150a68548c233bcc48b27ab665c4ecdcd863f73c6461b1d89d8ea62fd0a2ab","sha256:8b49a044e6ede6013d510258b817a44238d7b8c3c6f37da1daf29579c2994f78"]}],"invalid_events":[],"applied_event_ids":["sha256:4e1e64131d6a6d57cee3da017026a5e0c71b5246d2f46dbf6b11ae273f27b6ca","sha256:c721a6cb5cc7b18699646479c156386665076b5b32344f3c7f150f55bb885d9c"],"state_sha256":"ce415df53134c48b616c09b5ed6daf9b5bbc75004587dc3415016a760d7abd9a"}