{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:K2FWAG4UUYKEDOOYO4AYOB45P4","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0c9d3aa4ffbaca2851da082aa5eac373cd88e9f6bcc1c129f66a21de8d9cd87e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-01T07:32:34Z","title_canon_sha256":"9a9a8c67552da59b46d483a30ad9a010298f9811149196d9edfcf74362c27fe2"},"schema_version":"1.0","source":{"id":"1307.0287","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.0287","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"arxiv_version","alias_value":"1307.0287v1","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.0287","created_at":"2026-05-18T03:19:33Z"},{"alias_kind":"pith_short_12","alias_value":"K2FWAG4UUYKE","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_16","alias_value":"K2FWAG4UUYKEDOOY","created_at":"2026-05-18T12:27:49Z"},{"alias_kind":"pith_short_8","alias_value":"K2FWAG4U","created_at":"2026-05-18T12:27:49Z"}],"graph_snapshots":[{"event_id":"sha256:4685ce9a42bb7187c39d9747d8a490ab97d0c5534afd8a5d22d9265eef9d8841","target":"graph","created_at":"2026-05-18T03:19:33Z","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"},"paper":{"abstract_excerpt":"In this work we prove the existence of Fathi's weak KAM solutions for periodic Lagrangians and give a construction of all of them.","authors_text":"Gonzalo Contreras, Hector Sanchez-Morgado, Renato Iturriaga","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-01T07:32:34Z","title":"Weak solutions of the Hamilton-Jacobi equation for time periodic lagrangians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.0287","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":"sha256:79335621e16aa2bb77d55e41d91cbf15dab961d2eee543baadc812dc05c14077","target":"record","created_at":"2026-05-18T03:19:33Z","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":"0c9d3aa4ffbaca2851da082aa5eac373cd88e9f6bcc1c129f66a21de8d9cd87e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-01T07:32:34Z","title_canon_sha256":"9a9a8c67552da59b46d483a30ad9a010298f9811149196d9edfcf74362c27fe2"},"schema_version":"1.0","source":{"id":"1307.0287","kind":"arxiv","version":1}},"canonical_sha256":"568b601b94a61441b9d8770187079d7f38957b22777d47b288b9e1d38fc95d68","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"568b601b94a61441b9d8770187079d7f38957b22777d47b288b9e1d38fc95d68","first_computed_at":"2026-05-18T03:19:33.745746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:19:33.745746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vvQ0ShvkcJkx9bx44J8w6ibmxAXXbcKTFta2e38I6s4W3yMQmgxbwRx8imk5Ncv5vwLhLuMyrJcbyMiB0DO/DA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:19:33.746259Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.0287","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79335621e16aa2bb77d55e41d91cbf15dab961d2eee543baadc812dc05c14077","sha256:4685ce9a42bb7187c39d9747d8a490ab97d0c5534afd8a5d22d9265eef9d8841"],"state_sha256":"9147d01508afdc35975a34e3175cdf28d542f720a9009b1269e1b7d543545409"}