{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GV47EVUKCOPZAFBLTNF52HTXVG","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":"393d2b097e1cfd96c6b4cdc71b4789860cf5df5dd987d540ed515ada941b6c82","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T19:37:17Z","title_canon_sha256":"5f55ae28cffcab899b1911dd486ed62a6cc0e84e1ea0cf9cf96ec08390424fa5"},"schema_version":"1.0","source":{"id":"1104.3849","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.3849","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"arxiv_version","alias_value":"1104.3849v1","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.3849","created_at":"2026-05-18T04:23:55Z"},{"alias_kind":"pith_short_12","alias_value":"GV47EVUKCOPZ","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GV47EVUKCOPZAFBL","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GV47EVUK","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:a77443b7f4454997c8ac879939827b135af9546d8e8c9fb10275b2ab1788184b","target":"graph","created_at":"2026-05-18T04:23:55Z","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 consider Aubry-Mather theory for a subclass of class A spacetimes, i.e. compact vicious spacetimes with globally hyperbolic Abelian cover. In this subclass, called class A_1, we obtain improved results on timelike maximizers and Lipschitz continuity of the time separation of the Abelian cover on the i.g. optimal subsets.","authors_text":"Stefan Suhr","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T19:37:17Z","title":"Aubry-Mather theory and Lipschitz continuity of the time separation"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3849","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:e9625895256cfb8a3adeb93d1301ef7ff6e8097e11c6952c3f79c30d5a79ecca","target":"record","created_at":"2026-05-18T04:23:55Z","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":"393d2b097e1cfd96c6b4cdc71b4789860cf5df5dd987d540ed515ada941b6c82","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-04-19T19:37:17Z","title_canon_sha256":"5f55ae28cffcab899b1911dd486ed62a6cc0e84e1ea0cf9cf96ec08390424fa5"},"schema_version":"1.0","source":{"id":"1104.3849","kind":"arxiv","version":1}},"canonical_sha256":"3579f2568a139f90142b9b4bdd1e77a98a51f95dc596b94109a26317f017a579","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3579f2568a139f90142b9b4bdd1e77a98a51f95dc596b94109a26317f017a579","first_computed_at":"2026-05-18T04:23:55.599340Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:23:55.599340Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JL3piBpjIQ6jbomZe7hLYGVPKSFZSQGpOwIwyc3kmgftcIOwDUSDzfQvj3KCukDgR7IDk+0QuoQdj6anc7vyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:23:55.599785Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.3849","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9625895256cfb8a3adeb93d1301ef7ff6e8097e11c6952c3f79c30d5a79ecca","sha256:a77443b7f4454997c8ac879939827b135af9546d8e8c9fb10275b2ab1788184b"],"state_sha256":"0ee2c77130833cee834a816e86a6dbd5dcb39ebe675515fc29cc4cf74da0287a"}