{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:JV45WBM3YTHZRLVXQIQLPGIYAL","short_pith_number":"pith:JV45WBM3","canonical_record":{"source":{"id":"1205.6143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-28T15:35:16Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ba09e61b109d51277571fc384e409d3d649be36ae9da6dc4831eb332fa18ff7b","abstract_canon_sha256":"ebebf406c72a65fb59586cebacf281342931bd07d5a0488322b4bb82478ef27a"},"schema_version":"1.0"},"canonical_sha256":"4d79db059bc4cf98aeb78220b7991802d12ca0bbce22937fcc79e9885f7c8ba7","source":{"kind":"arxiv","id":"1205.6143","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6143","created_at":"2026-05-18T03:36:26Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6143v1","created_at":"2026-05-18T03:36:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6143","created_at":"2026-05-18T03:36:26Z"},{"alias_kind":"pith_short_12","alias_value":"JV45WBM3YTHZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JV45WBM3YTHZRLVX","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JV45WBM3","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:JV45WBM3YTHZRLVXQIQLPGIYAL","target":"record","payload":{"canonical_record":{"source":{"id":"1205.6143","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-28T15:35:16Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"ba09e61b109d51277571fc384e409d3d649be36ae9da6dc4831eb332fa18ff7b","abstract_canon_sha256":"ebebf406c72a65fb59586cebacf281342931bd07d5a0488322b4bb82478ef27a"},"schema_version":"1.0"},"canonical_sha256":"4d79db059bc4cf98aeb78220b7991802d12ca0bbce22937fcc79e9885f7c8ba7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:36:26.861242Z","signature_b64":"BZV9DB13Q3Ujb/BXDbbgdyV4X/DkteEMZtVgNavHC3jGYXxiDfxzEVQ2hYaUfgo1dbcB7m9A4Df/6M53ZG0PAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4d79db059bc4cf98aeb78220b7991802d12ca0bbce22937fcc79e9885f7c8ba7","last_reissued_at":"2026-05-18T03:36:26.860847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:36:26.860847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1205.6143","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":"2026-05-18T03:36:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"v4AvaBLhWFOy86xNir0UcPxYxqONgFgWasCyK+bZWd09o6hIEI7FyQVXTWI8Jc7VNDC+eVINfmZZIno0lA5BAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:30:53.646283Z"},"content_sha256":"565f47464cfdcbc790dd4961245454989012895d1fb94b777d1875be305a2b89","schema_version":"1.0","event_id":"sha256:565f47464cfdcbc790dd4961245454989012895d1fb94b777d1875be305a2b89"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:JV45WBM3YTHZRLVXQIQLPGIYAL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"nlin.CD","authors_text":"Adam M. Fox, James D. Meiss","submitted_at":"2012-05-28T15:35:16Z","abstract_excerpt":"Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable, volume-preserving maps with one action and $d$ angles. For the area-preserving case, Greene's residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. We study a three-dimensional, rev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6143","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":"2026-05-18T03:36:26Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QTTIFl4vepS7m4khpYu2XoAe38yFNeIOFkMfjCoUnEg42dSbBm86wZUnFeJ0OyG4wEZ9wZcFJS3sDHE+/bN9BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:30:53.646980Z"},"content_sha256":"f4c1d88b81e521d519d7438a8b1531e9483e354676a7b8a61517cdcd483b18e5","schema_version":"1.0","event_id":"sha256:f4c1d88b81e521d519d7438a8b1531e9483e354676a7b8a61517cdcd483b18e5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JV45WBM3YTHZRLVXQIQLPGIYAL/bundle.json","state_url":"https://pith.science/pith/JV45WBM3YTHZRLVXQIQLPGIYAL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JV45WBM3YTHZRLVXQIQLPGIYAL/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":"2026-06-06T20:30:53Z","links":{"resolver":"https://pith.science/pith/JV45WBM3YTHZRLVXQIQLPGIYAL","bundle":"https://pith.science/pith/JV45WBM3YTHZRLVXQIQLPGIYAL/bundle.json","state":"https://pith.science/pith/JV45WBM3YTHZRLVXQIQLPGIYAL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JV45WBM3YTHZRLVXQIQLPGIYAL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:JV45WBM3YTHZRLVXQIQLPGIYAL","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":"ebebf406c72a65fb59586cebacf281342931bd07d5a0488322b4bb82478ef27a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-28T15:35:16Z","title_canon_sha256":"ba09e61b109d51277571fc384e409d3d649be36ae9da6dc4831eb332fa18ff7b"},"schema_version":"1.0","source":{"id":"1205.6143","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.6143","created_at":"2026-05-18T03:36:26Z"},{"alias_kind":"arxiv_version","alias_value":"1205.6143v1","created_at":"2026-05-18T03:36:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.6143","created_at":"2026-05-18T03:36:26Z"},{"alias_kind":"pith_short_12","alias_value":"JV45WBM3YTHZ","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"JV45WBM3YTHZRLVX","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"JV45WBM3","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:f4c1d88b81e521d519d7438a8b1531e9483e354676a7b8a61517cdcd483b18e5","target":"graph","created_at":"2026-05-18T03:36:26Z","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":"Invariant tori play a fundamental role in the dynamics of symplectic and volume-preserving maps. Codimension-one tori are particularly important as they form barriers to transport. Such tori foliate the phase space of integrable, volume-preserving maps with one action and $d$ angles. For the area-preserving case, Greene's residue criterion is often used to predict the destruction of tori from the properties of nearby periodic orbits. Even though KAM theory applies to the three-dimensional case, the robustness of tori in such systems is still poorly understood. We study a three-dimensional, rev","authors_text":"Adam M. Fox, James D. Meiss","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-28T15:35:16Z","title":"Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.6143","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":"sha256:565f47464cfdcbc790dd4961245454989012895d1fb94b777d1875be305a2b89","target":"record","created_at":"2026-05-18T03:36:26Z","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":"ebebf406c72a65fb59586cebacf281342931bd07d5a0488322b4bb82478ef27a","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2012-05-28T15:35:16Z","title_canon_sha256":"ba09e61b109d51277571fc384e409d3d649be36ae9da6dc4831eb332fa18ff7b"},"schema_version":"1.0","source":{"id":"1205.6143","kind":"arxiv","version":1}},"canonical_sha256":"4d79db059bc4cf98aeb78220b7991802d12ca0bbce22937fcc79e9885f7c8ba7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4d79db059bc4cf98aeb78220b7991802d12ca0bbce22937fcc79e9885f7c8ba7","first_computed_at":"2026-05-18T03:36:26.860847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:26.860847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BZV9DB13Q3Ujb/BXDbbgdyV4X/DkteEMZtVgNavHC3jGYXxiDfxzEVQ2hYaUfgo1dbcB7m9A4Df/6M53ZG0PAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:26.861242Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.6143","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:565f47464cfdcbc790dd4961245454989012895d1fb94b777d1875be305a2b89","sha256:f4c1d88b81e521d519d7438a8b1531e9483e354676a7b8a61517cdcd483b18e5"],"state_sha256":"76d9134e9d9c6eaa47e81ca7f6d476c1e2b9770365be9204f112e90e747dc6d9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KKY/uLFIpNtpOR6EhxjrUbtRSt3+R5onFeYZ8I0/CrzTx8ab+gdztrrG4u3VB/a1doBxCE/3B/m4TnYFJOkiAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:30:53.649649Z","bundle_sha256":"d0ebde4af040dfbc09b2abc560edf1cfa41640514ece0d8a199147b821d9fad1"}}