{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:YTPY3TFJPVH24MXO3XG7AERTAX","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":"fafb2ccc6839c34fab48daffb84f282f10695bef01f959be9680f4d804cd44bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-03T12:27:02Z","title_canon_sha256":"bf50508345285c88e089e8696672bb875886cd52755a8c5f8e7153aa266ac044"},"schema_version":"1.0","source":{"id":"0812.0705","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.0705","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"arxiv_version","alias_value":"0812.0705v1","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.0705","created_at":"2026-05-18T04:40:45Z"},{"alias_kind":"pith_short_12","alias_value":"YTPY3TFJPVH2","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"YTPY3TFJPVH24MXO","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"YTPY3TFJ","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:d3206a1419e6242bf9005aca0e0e37b1e16e151160bb30d8d63f71488b64b204","target":"graph","created_at":"2026-05-18T04:40:45Z","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":"We prove necessary optimality conditions for problems of the calculus of variations on time scales with a Lagrangian depending on the free end-point.","authors_text":"Agnieszka B. Malinowska, Delfim F. M. Torres","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-03T12:27:02Z","title":"Natural Boundary Conditions in the Calculus of Variations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.0705","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":"sha256:05cf2d62dc2873d287033dde4cc4150b2e928e8126548a0523385a3dcfebed02","target":"record","created_at":"2026-05-18T04:40:45Z","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":"fafb2ccc6839c34fab48daffb84f282f10695bef01f959be9680f4d804cd44bc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2008-12-03T12:27:02Z","title_canon_sha256":"bf50508345285c88e089e8696672bb875886cd52755a8c5f8e7153aa266ac044"},"schema_version":"1.0","source":{"id":"0812.0705","kind":"arxiv","version":1}},"canonical_sha256":"c4df8dcca97d4fae32eeddcdf0123305e03e481ff49eec1493752620572222c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c4df8dcca97d4fae32eeddcdf0123305e03e481ff49eec1493752620572222c3","first_computed_at":"2026-05-18T04:40:45.442227Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:40:45.442227Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mjZuvF1uwq9vbQs3Ptn8V18td95iUPDFaZRqPdJsdufHhG2m7D3khaDocyM3jh5Vz7DlmSU/c8lt74ItBuiNBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:40:45.442851Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.0705","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:05cf2d62dc2873d287033dde4cc4150b2e928e8126548a0523385a3dcfebed02","sha256:d3206a1419e6242bf9005aca0e0e37b1e16e151160bb30d8d63f71488b64b204"],"state_sha256":"cbb84a83c52c0384dae85cf5ec98c10f0a85437ede3f1b8fb82bc7677d3e4c8b"}