{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:R6FS46IKOK5MPXTWIVFNQ3EZVR","short_pith_number":"pith:R6FS46IK","canonical_record":{"source":{"id":"1311.0132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-01T10:09:09Z","cross_cats_sorted":[],"title_canon_sha256":"2731d0ab811cfcb3ee574b560f8a005012545d695579d6de17d3aa8d79209621","abstract_canon_sha256":"6e3780fc7badaf0c169c80012f5c3862cceea86d1686876bf8b5b0583a6b2101"},"schema_version":"1.0"},"canonical_sha256":"8f8b2e790a72bac7de76454ad86c99ac6879b0b38615e15142e2ef11c74f7b8c","source":{"kind":"arxiv","id":"1311.0132","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0132","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0132v1","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0132","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"R6FS46IKOK5M","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R6FS46IKOK5MPXTW","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R6FS46IK","created_at":"2026-05-18T12:27:57Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:R6FS46IKOK5MPXTWIVFNQ3EZVR","target":"record","payload":{"canonical_record":{"source":{"id":"1311.0132","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-01T10:09:09Z","cross_cats_sorted":[],"title_canon_sha256":"2731d0ab811cfcb3ee574b560f8a005012545d695579d6de17d3aa8d79209621","abstract_canon_sha256":"6e3780fc7badaf0c169c80012f5c3862cceea86d1686876bf8b5b0583a6b2101"},"schema_version":"1.0"},"canonical_sha256":"8f8b2e790a72bac7de76454ad86c99ac6879b0b38615e15142e2ef11c74f7b8c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:15.463946Z","signature_b64":"yG5uTaTWg+Pv7ISYy8igJQYoF1Zwu6nzMSvB/9LSD/AOW4uW8v1VTtXrcwh3FQRoTFdVpB9sjD08z5Nsop8nCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f8b2e790a72bac7de76454ad86c99ac6879b0b38615e15142e2ef11c74f7b8c","last_reissued_at":"2026-05-18T03:08:15.463492Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:15.463492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.0132","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JgXm6jSg7ZlZwU1qMNyME1bsRj+BcIka5pqUIzXcyb93JvgG6+2UIXrt48zioY9wT+HfUsqU9eKTlBv9XVL+Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:46:28.483773Z"},"content_sha256":"22462626621972b263761c080ef6800d7c0c5d71cebccad91f8bf4e901dea343","schema_version":"1.0","event_id":"sha256:22462626621972b263761c080ef6800d7c0c5d71cebccad91f8bf4e901dea343"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:R6FS46IKOK5MPXTWIVFNQ3EZVR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Lagrangian tori near resonances of near-integrable Hamiltonian systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anatoly Neishtadt, Anton Medvedev, Dmitry Treschev","submitted_at":"2013-11-01T10:09:09Z","abstract_excerpt":"In this paper we study families of Lagrangian tori that appear in a neighborhood of a resonance of a near-integrable Hamiltonian system. Such families disappear in the \"integrable\" limit $\\varepsilon\\to 0$. Dynamics on these tori is oscillatory in the direction of the resonance phases and rotating with respect to the other (non-resonant) phases.\n  We also show that, if multiplicity of the resonance equals one, generically these tori occupy a set of large relative measure in the resonant domains in the sense that the relative measure of the remaining \"chaotic\" set is of order $\\sqrt\\varepsilon$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0132","kind":"arxiv","version":1},"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":"2026-05-18T03:08:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QR1YuEPKdyVwWZeh3Sqfgk1yfixzsr2BFamNZR4Xg/i+51tHzYmtl6DesAZ7clZZ8LL1Jsuxba4v0e05yMn8Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T20:46:28.484561Z"},"content_sha256":"3421fca5b5b465cac08dafcd4a299fa2a41c3d784d4837f1ca4e5502daa3fb21","schema_version":"1.0","event_id":"sha256:3421fca5b5b465cac08dafcd4a299fa2a41c3d784d4837f1ca4e5502daa3fb21"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6FS46IKOK5MPXTWIVFNQ3EZVR/bundle.json","state_url":"https://pith.science/pith/R6FS46IKOK5MPXTWIVFNQ3EZVR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6FS46IKOK5MPXTWIVFNQ3EZVR/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":"2026-05-31T20:46:28Z","links":{"resolver":"https://pith.science/pith/R6FS46IKOK5MPXTWIVFNQ3EZVR","bundle":"https://pith.science/pith/R6FS46IKOK5MPXTWIVFNQ3EZVR/bundle.json","state":"https://pith.science/pith/R6FS46IKOK5MPXTWIVFNQ3EZVR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6FS46IKOK5MPXTWIVFNQ3EZVR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:R6FS46IKOK5MPXTWIVFNQ3EZVR","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":"6e3780fc7badaf0c169c80012f5c3862cceea86d1686876bf8b5b0583a6b2101","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-01T10:09:09Z","title_canon_sha256":"2731d0ab811cfcb3ee574b560f8a005012545d695579d6de17d3aa8d79209621"},"schema_version":"1.0","source":{"id":"1311.0132","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.0132","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"arxiv_version","alias_value":"1311.0132v1","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.0132","created_at":"2026-05-18T03:08:15Z"},{"alias_kind":"pith_short_12","alias_value":"R6FS46IKOK5M","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_16","alias_value":"R6FS46IKOK5MPXTW","created_at":"2026-05-18T12:27:57Z"},{"alias_kind":"pith_short_8","alias_value":"R6FS46IK","created_at":"2026-05-18T12:27:57Z"}],"graph_snapshots":[{"event_id":"sha256:3421fca5b5b465cac08dafcd4a299fa2a41c3d784d4837f1ca4e5502daa3fb21","target":"graph","created_at":"2026-05-18T03:08:15Z","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 paper we study families of Lagrangian tori that appear in a neighborhood of a resonance of a near-integrable Hamiltonian system. Such families disappear in the \"integrable\" limit $\\varepsilon\\to 0$. Dynamics on these tori is oscillatory in the direction of the resonance phases and rotating with respect to the other (non-resonant) phases.\n  We also show that, if multiplicity of the resonance equals one, generically these tori occupy a set of large relative measure in the resonant domains in the sense that the relative measure of the remaining \"chaotic\" set is of order $\\sqrt\\varepsilon$","authors_text":"Anatoly Neishtadt, Anton Medvedev, Dmitry Treschev","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-01T10:09:09Z","title":"Lagrangian tori near resonances of near-integrable Hamiltonian systems"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.0132","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":"sha256:22462626621972b263761c080ef6800d7c0c5d71cebccad91f8bf4e901dea343","target":"record","created_at":"2026-05-18T03:08:15Z","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":"6e3780fc7badaf0c169c80012f5c3862cceea86d1686876bf8b5b0583a6b2101","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-01T10:09:09Z","title_canon_sha256":"2731d0ab811cfcb3ee574b560f8a005012545d695579d6de17d3aa8d79209621"},"schema_version":"1.0","source":{"id":"1311.0132","kind":"arxiv","version":1}},"canonical_sha256":"8f8b2e790a72bac7de76454ad86c99ac6879b0b38615e15142e2ef11c74f7b8c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f8b2e790a72bac7de76454ad86c99ac6879b0b38615e15142e2ef11c74f7b8c","first_computed_at":"2026-05-18T03:08:15.463492Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:15.463492Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yG5uTaTWg+Pv7ISYy8igJQYoF1Zwu6nzMSvB/9LSD/AOW4uW8v1VTtXrcwh3FQRoTFdVpB9sjD08z5Nsop8nCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:15.463946Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.0132","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:22462626621972b263761c080ef6800d7c0c5d71cebccad91f8bf4e901dea343","sha256:3421fca5b5b465cac08dafcd4a299fa2a41c3d784d4837f1ca4e5502daa3fb21"],"state_sha256":"3126e49a225a5c712930c3ec2a876dd78eb6c3de608c672a2aa7dae4552e88d7"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DBvARFnwopaId3iXc9d7CiERIrCxRD9C4Xcq+FB+lpWa5/LUf4SVIWhSOEmHXQ/xRDr+KgNSghrgY4DUrBKUCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T20:46:28.488645Z","bundle_sha256":"08714b6e47a38a3affb27de8f69d36b79d130f7067632e699855c6face0337c5"}}