{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:WSYCFQGV5LGKC4IQGNNHLAHNQY","short_pith_number":"pith:WSYCFQGV","canonical_record":{"source":{"id":"1311.7334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-28T14:38:47Z","cross_cats_sorted":[],"title_canon_sha256":"13c3b4c6d28744542bfe4d8a28c9dcd3edb3faf896d8ca0e773c9aa5e862f219","abstract_canon_sha256":"a5b386ca0749bf46a76dd416e5f8ef982a877f9117a60a652fb592f4d8798c3c"},"schema_version":"1.0"},"canonical_sha256":"b4b022c0d5eacca17110335a7580ed862ae5e96416844d9346f86216d5c88c1b","source":{"kind":"arxiv","id":"1311.7334","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7334","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7334v1","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7334","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"pith_short_12","alias_value":"WSYCFQGV5LGK","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WSYCFQGV5LGKC4IQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WSYCFQGV","created_at":"2026-05-18T12:28:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:WSYCFQGV5LGKC4IQGNNHLAHNQY","target":"record","payload":{"canonical_record":{"source":{"id":"1311.7334","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-28T14:38:47Z","cross_cats_sorted":[],"title_canon_sha256":"13c3b4c6d28744542bfe4d8a28c9dcd3edb3faf896d8ca0e773c9aa5e862f219","abstract_canon_sha256":"a5b386ca0749bf46a76dd416e5f8ef982a877f9117a60a652fb592f4d8798c3c"},"schema_version":"1.0"},"canonical_sha256":"b4b022c0d5eacca17110335a7580ed862ae5e96416844d9346f86216d5c88c1b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:28:15.070774Z","signature_b64":"/gM7iQe1893k0b7TLewXeegnjnURaLMQHR3JSyawqB7nh4ObCJsy4+hAT2cnzGaYZKAe+h+KDOEOkONnxiCUBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4b022c0d5eacca17110335a7580ed862ae5e96416844d9346f86216d5c88c1b","last_reissued_at":"2026-05-18T01:28:15.070087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:28:15.070087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1311.7334","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":"2026-05-18T01:28:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZQs/wOfO3XLMQHIa8Hg8pbqoPgX3sra45SlMM5NVl1xzcuDPl9znYVPaaf/EsC342HBbd/vjKD3lVTcZfcEOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:13:20.017293Z"},"content_sha256":"45fbcc79be060c9193a96284eb4fdabcf0e173e906b126ca2e37d805a5ae07d1","schema_version":"1.0","event_id":"sha256:45fbcc79be060c9193a96284eb4fdabcf0e173e906b126ca2e37d805a5ae07d1"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:WSYCFQGV5LGKC4IQGNNHLAHNQY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Around the stability of KAM-tori","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Bassam Fayad, Hakan Eliasson, Rapha\\\"el Krikorian","submitted_at":"2013-11-28T14:38:47Z","abstract_excerpt":"We show that an analytic invariant torus $\\cT_0$ with Diophantine frequency $\\o_0$ is never isolated due to the following alternative. If the Birkhoff normal form of the Hamiltonian at $\\cT_0$ satisfies a R\\\"ussmann transversality condition, the torus $\\cT_0$ is accumulated by KAM tori of positive total measure. If the Birkhoff normal form is degenerate, there exists a subvariety of dimension at least $d+1$ that is foliated by analytic invariant tori with frequency $\\o_0$.\n  For frequency vectors $\\o_0$ having a finite uniform Diophantine exponent (this includes a residual set of Liouville vec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7334","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":"2026-05-18T01:28:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jskDTY0+4QEiZ0zkx4OzyAOh4003q+x0FJiUcWW+62WLFVHrmCMbtZr9sQGe0BY9FoFZyLTKyZhF8+SL8CfjAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T10:13:20.017961Z"},"content_sha256":"39f43f886c55171446887dbda7cf6d6a9162e1d845ef9866cd227bb4eb48b7bd","schema_version":"1.0","event_id":"sha256:39f43f886c55171446887dbda7cf6d6a9162e1d845ef9866cd227bb4eb48b7bd"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WSYCFQGV5LGKC4IQGNNHLAHNQY/bundle.json","state_url":"https://pith.science/pith/WSYCFQGV5LGKC4IQGNNHLAHNQY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WSYCFQGV5LGKC4IQGNNHLAHNQY/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":"2026-06-09T10:13:20Z","links":{"resolver":"https://pith.science/pith/WSYCFQGV5LGKC4IQGNNHLAHNQY","bundle":"https://pith.science/pith/WSYCFQGV5LGKC4IQGNNHLAHNQY/bundle.json","state":"https://pith.science/pith/WSYCFQGV5LGKC4IQGNNHLAHNQY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WSYCFQGV5LGKC4IQGNNHLAHNQY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:WSYCFQGV5LGKC4IQGNNHLAHNQY","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":"a5b386ca0749bf46a76dd416e5f8ef982a877f9117a60a652fb592f4d8798c3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-28T14:38:47Z","title_canon_sha256":"13c3b4c6d28744542bfe4d8a28c9dcd3edb3faf896d8ca0e773c9aa5e862f219"},"schema_version":"1.0","source":{"id":"1311.7334","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1311.7334","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"arxiv_version","alias_value":"1311.7334v1","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1311.7334","created_at":"2026-05-18T01:28:15Z"},{"alias_kind":"pith_short_12","alias_value":"WSYCFQGV5LGK","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"WSYCFQGV5LGKC4IQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"WSYCFQGV","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:39f43f886c55171446887dbda7cf6d6a9162e1d845ef9866cd227bb4eb48b7bd","target":"graph","created_at":"2026-05-18T01:28:15Z","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":"We show that an analytic invariant torus $\\cT_0$ with Diophantine frequency $\\o_0$ is never isolated due to the following alternative. If the Birkhoff normal form of the Hamiltonian at $\\cT_0$ satisfies a R\\\"ussmann transversality condition, the torus $\\cT_0$ is accumulated by KAM tori of positive total measure. If the Birkhoff normal form is degenerate, there exists a subvariety of dimension at least $d+1$ that is foliated by analytic invariant tori with frequency $\\o_0$.\n  For frequency vectors $\\o_0$ having a finite uniform Diophantine exponent (this includes a residual set of Liouville vec","authors_text":"Bassam Fayad, Hakan Eliasson, Rapha\\\"el Krikorian","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-28T14:38:47Z","title":"Around the stability of KAM-tori"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7334","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":"sha256:45fbcc79be060c9193a96284eb4fdabcf0e173e906b126ca2e37d805a5ae07d1","target":"record","created_at":"2026-05-18T01:28:15Z","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":"a5b386ca0749bf46a76dd416e5f8ef982a877f9117a60a652fb592f4d8798c3c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-11-28T14:38:47Z","title_canon_sha256":"13c3b4c6d28744542bfe4d8a28c9dcd3edb3faf896d8ca0e773c9aa5e862f219"},"schema_version":"1.0","source":{"id":"1311.7334","kind":"arxiv","version":1}},"canonical_sha256":"b4b022c0d5eacca17110335a7580ed862ae5e96416844d9346f86216d5c88c1b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4b022c0d5eacca17110335a7580ed862ae5e96416844d9346f86216d5c88c1b","first_computed_at":"2026-05-18T01:28:15.070087Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:28:15.070087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/gM7iQe1893k0b7TLewXeegnjnURaLMQHR3JSyawqB7nh4ObCJsy4+hAT2cnzGaYZKAe+h+KDOEOkONnxiCUBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:28:15.070774Z","signed_message":"canonical_sha256_bytes"},"source_id":"1311.7334","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:45fbcc79be060c9193a96284eb4fdabcf0e173e906b126ca2e37d805a5ae07d1","sha256:39f43f886c55171446887dbda7cf6d6a9162e1d845ef9866cd227bb4eb48b7bd"],"state_sha256":"17a92dd99835e4169cc18ed16b5a39e5b007961bdc18667961a19bb161ecc6a3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RWPTX4AudwysYhr6XV7EzJj1O+/xx4+3d5PvzevtIgmpSppXXsaZqgq+Msmxqg+7/Vlo7OtZDJMLf4hAslzGCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T10:13:20.021299Z","bundle_sha256":"d861094d07cb8f75893402b52e861505279278ecccbe3cb2ff94d7de28112f7f"}}