{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:SIQ5JUKAOS2P6TLMCZIDGVOE3M","short_pith_number":"pith:SIQ5JUKA","canonical_record":{"source":{"id":"0801.3568","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-01-23T15:28:20Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"e1c6582422e9206d805770abd4ba3c9dd0d24eee0cef7a00821ff660f9c53088","abstract_canon_sha256":"7050db2fb0e509bccfbd49ada188b439eb2115d11b3062dcef018daf3be4a972"},"schema_version":"1.0"},"canonical_sha256":"9221d4d14074b4ff4d6c16503355c4db23e0e4a96aee3508fd95d112ae704a5c","source":{"kind":"arxiv","id":"0801.3568","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.3568","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"0801.3568v2","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3568","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"SIQ5JUKAOS2P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SIQ5JUKAOS2P6TLM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SIQ5JUKA","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:SIQ5JUKAOS2P6TLMCZIDGVOE3M","target":"record","payload":{"canonical_record":{"source":{"id":"0801.3568","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-01-23T15:28:20Z","cross_cats_sorted":["math-ph","math.MP","math.SG"],"title_canon_sha256":"e1c6582422e9206d805770abd4ba3c9dd0d24eee0cef7a00821ff660f9c53088","abstract_canon_sha256":"7050db2fb0e509bccfbd49ada188b439eb2115d11b3062dcef018daf3be4a972"},"schema_version":"1.0"},"canonical_sha256":"9221d4d14074b4ff4d6c16503355c4db23e0e4a96aee3508fd95d112ae704a5c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:33:48.733237Z","signature_b64":"1Yqf8MEWkLOuinACsrcV993Z+H3wNYtA1Oqql5jlw0tf2TreQIeoFr/sEGPL/MinNw37BRBb4yZVMIjciHsfDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9221d4d14074b4ff4d6c16503355c4db23e0e4a96aee3508fd95d112ae704a5c","last_reissued_at":"2026-05-18T04:33:48.732644Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:33:48.732644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0801.3568","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"eFlSj1G7RkQKfWl8A55ZMhjxt5V4gr4LDgzG5wiNC4er46w8iACBPYDujLNK5PUvP8tYe7n0+4CeEzjwB7bqAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:23:56.826353Z"},"content_sha256":"7b8cc5d38a4ea6a9933aa183404e40f636011b795bfc4fc6591da06103bbc1df","schema_version":"1.0","event_id":"sha256:7b8cc5d38a4ea6a9933aa183404e40f636011b795bfc4fc6591da06103bbc1df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:SIQ5JUKAOS2P6TLMCZIDGVOE3M","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.SG"],"primary_cat":"math.DS","authors_text":"Albert Fathi, Alessandro Giuliani, Alfonso Sorrentino","submitted_at":"2008-01-23T15:28:20Z","abstract_excerpt":"Given a smooth compact Riemannian manifold $M$ and a Hamiltonian $H$ on the cotangent space $T^*M$, strictly convex and superlinear in the momentum variables, we prove uniqueness of certain ergodic invariant Lagrangian graphs within a given homology or cohomology class. In particular, in the context of quasi-integrable Hamiltonian systems, our result implies global uniqueness of Lagrangian KAM tori with rotation vector $\\rho$. This result extends generically to the $C^0$-closure of KAM tori."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3568","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T04:33:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kfGavSBohMPdeowchcKjQ+SxgSx0tqF7Xez9gvikhYMGmjIL67+gfRu5a5QZHnfeWawSwpdGT0MrdfQHi9Z+AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T23:23:56.826709Z"},"content_sha256":"377ecff8f590fdd0900f36375ca16057b3592db92ff55039c69c6c2d9abc144e","schema_version":"1.0","event_id":"sha256:377ecff8f590fdd0900f36375ca16057b3592db92ff55039c69c6c2d9abc144e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SIQ5JUKAOS2P6TLMCZIDGVOE3M/bundle.json","state_url":"https://pith.science/pith/SIQ5JUKAOS2P6TLMCZIDGVOE3M/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SIQ5JUKAOS2P6TLMCZIDGVOE3M/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T23:23:56Z","links":{"resolver":"https://pith.science/pith/SIQ5JUKAOS2P6TLMCZIDGVOE3M","bundle":"https://pith.science/pith/SIQ5JUKAOS2P6TLMCZIDGVOE3M/bundle.json","state":"https://pith.science/pith/SIQ5JUKAOS2P6TLMCZIDGVOE3M/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SIQ5JUKAOS2P6TLMCZIDGVOE3M/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:SIQ5JUKAOS2P6TLMCZIDGVOE3M","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":"7050db2fb0e509bccfbd49ada188b439eb2115d11b3062dcef018daf3be4a972","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-01-23T15:28:20Z","title_canon_sha256":"e1c6582422e9206d805770abd4ba3c9dd0d24eee0cef7a00821ff660f9c53088"},"schema_version":"1.0","source":{"id":"0801.3568","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0801.3568","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"arxiv_version","alias_value":"0801.3568v2","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0801.3568","created_at":"2026-05-18T04:33:48Z"},{"alias_kind":"pith_short_12","alias_value":"SIQ5JUKAOS2P","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"SIQ5JUKAOS2P6TLM","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"SIQ5JUKA","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:377ecff8f590fdd0900f36375ca16057b3592db92ff55039c69c6c2d9abc144e","target":"graph","created_at":"2026-05-18T04:33:48Z","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":"Given a smooth compact Riemannian manifold $M$ and a Hamiltonian $H$ on the cotangent space $T^*M$, strictly convex and superlinear in the momentum variables, we prove uniqueness of certain ergodic invariant Lagrangian graphs within a given homology or cohomology class. In particular, in the context of quasi-integrable Hamiltonian systems, our result implies global uniqueness of Lagrangian KAM tori with rotation vector $\\rho$. This result extends generically to the $C^0$-closure of KAM tori.","authors_text":"Albert Fathi, Alessandro Giuliani, Alfonso Sorrentino","cross_cats":["math-ph","math.MP","math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-01-23T15:28:20Z","title":"Uniqueness of Invariant Lagrangian Graphs in a Homology or a Cohomology Class"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.3568","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":"sha256:7b8cc5d38a4ea6a9933aa183404e40f636011b795bfc4fc6591da06103bbc1df","target":"record","created_at":"2026-05-18T04:33:48Z","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":"7050db2fb0e509bccfbd49ada188b439eb2115d11b3062dcef018daf3be4a972","cross_cats_sorted":["math-ph","math.MP","math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-01-23T15:28:20Z","title_canon_sha256":"e1c6582422e9206d805770abd4ba3c9dd0d24eee0cef7a00821ff660f9c53088"},"schema_version":"1.0","source":{"id":"0801.3568","kind":"arxiv","version":2}},"canonical_sha256":"9221d4d14074b4ff4d6c16503355c4db23e0e4a96aee3508fd95d112ae704a5c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9221d4d14074b4ff4d6c16503355c4db23e0e4a96aee3508fd95d112ae704a5c","first_computed_at":"2026-05-18T04:33:48.732644Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:33:48.732644Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1Yqf8MEWkLOuinACsrcV993Z+H3wNYtA1Oqql5jlw0tf2TreQIeoFr/sEGPL/MinNw37BRBb4yZVMIjciHsfDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:33:48.733237Z","signed_message":"canonical_sha256_bytes"},"source_id":"0801.3568","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b8cc5d38a4ea6a9933aa183404e40f636011b795bfc4fc6591da06103bbc1df","sha256:377ecff8f590fdd0900f36375ca16057b3592db92ff55039c69c6c2d9abc144e"],"state_sha256":"4641f18f048e61b26b742f0df6965da6a8d7396dd19731b770381f8ef4ec245e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QxUXHLutOLYPO4tKVLC0YWrqUb/KUPltYnZII+iK31UO2iE8O9iaJoE5lMS1RxXdJbPLu5mmsJgrTj2Nsr1aAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T23:23:56.828674Z","bundle_sha256":"7e37fed0b901dc70787d6d9c3d49e88de460f70755eec32e4bb2eda0272efa0f"}}