{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1999:Q54HKMNIMGTFL3YYD6X7M5HU2T","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":"941310806ad5a95cb790edd9ec615c66728353aff338f118b9e239e0aaedb822","cross_cats_sorted":["math.DS","nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1999-06-23T09:19:22Z","title_canon_sha256":"63e68a6a3e6ea1e19d8fed9d2a3a8a8e5462d7286e8fad822229f864e9d56b7e"},"schema_version":"1.0","source":{"id":"chao-dyn/9906036","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"chao-dyn/9906036","created_at":"2026-05-18T01:07:24Z"},{"alias_kind":"arxiv_version","alias_value":"chao-dyn/9906036v2","created_at":"2026-05-18T01:07:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.chao-dyn/9906036","created_at":"2026-05-18T01:07:24Z"},{"alias_kind":"pith_short_12","alias_value":"Q54HKMNIMGTF","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_16","alias_value":"Q54HKMNIMGTFL3YY","created_at":"2026-05-18T12:25:49Z"},{"alias_kind":"pith_short_8","alias_value":"Q54HKMNI","created_at":"2026-05-18T12:25:49Z"}],"graph_snapshots":[{"event_id":"sha256:37dd873e044272962530fc52dbeb78d86c44193f04919783f89d81af4b04063b","target":"graph","created_at":"2026-05-18T01:07:24Z","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 establish a connection between the Aubry-Mather theory of invariant sets of a 1D dynamical system described by a Lagrangian with potential periodic in space and time, on the one hand, and idempotent spectral theory of the Bellman operator of the corresponding optimization problem, on the other hand. This connection is applied to obtain a uniqueness result for an eigenfunction of the Bellman operator in the case of irrational rotation number.","authors_text":"Andrei Sobolevskii","cross_cats":["math.DS","nlin.CD"],"headline":"","license":"","primary_cat":"chao-dyn","submitted_at":"1999-06-23T09:19:22Z","title":"Aubry-Mather theory and idempotent eigenfunctions of the Bellman operator"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"chao-dyn/9906036","kind":"arxiv","version":2},"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":"sha256:668a237680a8a181220bc2ad2eb330f5732a090651b4649d6d68a80325768dfe","target":"record","created_at":"2026-05-18T01:07:24Z","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":"941310806ad5a95cb790edd9ec615c66728353aff338f118b9e239e0aaedb822","cross_cats_sorted":["math.DS","nlin.CD"],"license":"","primary_cat":"chao-dyn","submitted_at":"1999-06-23T09:19:22Z","title_canon_sha256":"63e68a6a3e6ea1e19d8fed9d2a3a8a8e5462d7286e8fad822229f864e9d56b7e"},"schema_version":"1.0","source":{"id":"chao-dyn/9906036","kind":"arxiv","version":2}},"canonical_sha256":"87787531a861a655ef181faff674f4d4d4329d7a570fd12a18c55785b0c14e8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"87787531a861a655ef181faff674f4d4d4329d7a570fd12a18c55785b0c14e8c","first_computed_at":"2026-05-18T01:07:24.479448Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:07:24.479448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IzKpDTQWXlXVYTFNGwfLHB15VN8RGcb87Ju7sLtwcdx57bfB7lRTqXv9HhLLpHUCNToX5PZNFLbxb5gboifrAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:07:24.480006Z","signed_message":"canonical_sha256_bytes"},"source_id":"chao-dyn/9906036","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:668a237680a8a181220bc2ad2eb330f5732a090651b4649d6d68a80325768dfe","sha256:37dd873e044272962530fc52dbeb78d86c44193f04919783f89d81af4b04063b"],"state_sha256":"7b6254edb362d727fea84d297e6513d2db18b7fcfeb184a2e8009298bab985ad"}