{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2008:UG7STBQWYDOTSERTCYMOIGZT4R","short_pith_number":"pith:UG7STBQW","canonical_record":{"source":{"id":"0807.0678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-07-04T04:19:40Z","cross_cats_sorted":[],"title_canon_sha256":"370e51ef6a88c4bad8bbf2c27efedbdbc25c094fe068993fb84792f2d37694fc","abstract_canon_sha256":"a2b1542e2f7b2ee8539eea9b1d957b99a50bd9aa1db8a5abdca7a4d10cb0e27d"},"schema_version":"1.0"},"canonical_sha256":"a1bf298616c0dd3912331618e41b33e443a3cb189d11ad97e748bb311f2aaff1","source":{"kind":"arxiv","id":"0807.0678","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.0678","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"0807.0678v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0678","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"UG7STBQWYDOT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UG7STBQWYDOTSERT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UG7STBQW","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2008:UG7STBQWYDOTSERTCYMOIGZT4R","target":"record","payload":{"canonical_record":{"source":{"id":"0807.0678","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-07-04T04:19:40Z","cross_cats_sorted":[],"title_canon_sha256":"370e51ef6a88c4bad8bbf2c27efedbdbc25c094fe068993fb84792f2d37694fc","abstract_canon_sha256":"a2b1542e2f7b2ee8539eea9b1d957b99a50bd9aa1db8a5abdca7a4d10cb0e27d"},"schema_version":"1.0"},"canonical_sha256":"a1bf298616c0dd3912331618e41b33e443a3cb189d11ad97e748bb311f2aaff1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:20:19.258039Z","signature_b64":"VpnzH6Fjw+J/fm/hyijj+1hd0QN9xt9txPV5OCoYPXYOyr5MTkHQhYVRNrmlH6ejnoj7AiX/pPlt3mYk5JZWBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1bf298616c0dd3912331618e41b33e443a3cb189d11ad97e748bb311f2aaff1","last_reissued_at":"2026-05-18T03:20:19.257281Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:20:19.257281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0807.0678","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":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DvHt9ZQTjxHyyCxqkZA6XSCG0DspQKWDRjgxUByhntd2W/wBoql3jvEY+zptOmB0piQsR9JQzxAmDfx89CsKBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:28:54.810891Z"},"content_sha256":"9100f1e95d1ac962ce21f3b72e2573602686ba5e2ae6bf5f089d5c3eea7f8108","schema_version":"1.0","event_id":"sha256:9100f1e95d1ac962ce21f3b72e2573602686ba5e2ae6bf5f089d5c3eea7f8108"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2008:UG7STBQWYDOTSERTCYMOIGZT4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.CD","authors_text":"Holger R. Dullin, James D. Meiss","submitted_at":"2008-07-04T04:19:40Z","abstract_excerpt":"We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and also is the general form of a quadratic three-dimensional map with a quadratic inverse. Much of the nontrivial dynamics of this map occurs when its two fixed points are saddle-foci with intersecting two-dimensional stable and unstable manifolds that bound a spherical ``vortex-bubble''. We show that this occurs near a saddle-center-Neimark-Sacker (SCNS) bifurcation that also creates, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0678","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":"2026-05-18T03:20:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hbmdGNoPVv1JS/6REm9mHcmPNvfIPSDrXaUC5Oj7/Z6vkdull6jYcNRTHqz0AX3+6QDx9RSEwy5SXhREVZzDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T09:28:54.811233Z"},"content_sha256":"5aae17baaa99e7ff17a60f4d9b956e806207a5703d380b85361175d05c496d7f","schema_version":"1.0","event_id":"sha256:5aae17baaa99e7ff17a60f4d9b956e806207a5703d380b85361175d05c496d7f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UG7STBQWYDOTSERTCYMOIGZT4R/bundle.json","state_url":"https://pith.science/pith/UG7STBQWYDOTSERTCYMOIGZT4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UG7STBQWYDOTSERTCYMOIGZT4R/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":"2026-06-01T09:28:54Z","links":{"resolver":"https://pith.science/pith/UG7STBQWYDOTSERTCYMOIGZT4R","bundle":"https://pith.science/pith/UG7STBQWYDOTSERTCYMOIGZT4R/bundle.json","state":"https://pith.science/pith/UG7STBQWYDOTSERTCYMOIGZT4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UG7STBQWYDOTSERTCYMOIGZT4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:UG7STBQWYDOTSERTCYMOIGZT4R","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":"a2b1542e2f7b2ee8539eea9b1d957b99a50bd9aa1db8a5abdca7a4d10cb0e27d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-07-04T04:19:40Z","title_canon_sha256":"370e51ef6a88c4bad8bbf2c27efedbdbc25c094fe068993fb84792f2d37694fc"},"schema_version":"1.0","source":{"id":"0807.0678","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0807.0678","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"arxiv_version","alias_value":"0807.0678v1","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.0678","created_at":"2026-05-18T03:20:19Z"},{"alias_kind":"pith_short_12","alias_value":"UG7STBQWYDOT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"UG7STBQWYDOTSERT","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"UG7STBQW","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:5aae17baaa99e7ff17a60f4d9b956e806207a5703d380b85361175d05c496d7f","target":"graph","created_at":"2026-05-18T03:20:19Z","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 study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point with a triple-one multiplier and also is the general form of a quadratic three-dimensional map with a quadratic inverse. Much of the nontrivial dynamics of this map occurs when its two fixed points are saddle-foci with intersecting two-dimensional stable and unstable manifolds that bound a spherical ``vortex-bubble''. We show that this occurs near a saddle-center-Neimark-Sacker (SCNS) bifurcation that also creates, ","authors_text":"Holger R. Dullin, James D. Meiss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-07-04T04:19:40Z","title":"Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.0678","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":"sha256:9100f1e95d1ac962ce21f3b72e2573602686ba5e2ae6bf5f089d5c3eea7f8108","target":"record","created_at":"2026-05-18T03:20:19Z","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":"a2b1542e2f7b2ee8539eea9b1d957b99a50bd9aa1db8a5abdca7a4d10cb0e27d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"nlin.CD","submitted_at":"2008-07-04T04:19:40Z","title_canon_sha256":"370e51ef6a88c4bad8bbf2c27efedbdbc25c094fe068993fb84792f2d37694fc"},"schema_version":"1.0","source":{"id":"0807.0678","kind":"arxiv","version":1}},"canonical_sha256":"a1bf298616c0dd3912331618e41b33e443a3cb189d11ad97e748bb311f2aaff1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a1bf298616c0dd3912331618e41b33e443a3cb189d11ad97e748bb311f2aaff1","first_computed_at":"2026-05-18T03:20:19.257281Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:20:19.257281Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VpnzH6Fjw+J/fm/hyijj+1hd0QN9xt9txPV5OCoYPXYOyr5MTkHQhYVRNrmlH6ejnoj7AiX/pPlt3mYk5JZWBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:20:19.258039Z","signed_message":"canonical_sha256_bytes"},"source_id":"0807.0678","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9100f1e95d1ac962ce21f3b72e2573602686ba5e2ae6bf5f089d5c3eea7f8108","sha256:5aae17baaa99e7ff17a60f4d9b956e806207a5703d380b85361175d05c496d7f"],"state_sha256":"3f6dbaf7b3b9c3870926a64f083e570e316b156ac0e435de1911f18713766871"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3Tx/bhF8vMK1tUWYA1VRCVhvAPwz4VV+1Sd2qp1A62hJsBKhAk1kRhNa6BapLKRRJaniMuNZLVrrhkUa8ZrpCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T09:28:54.813110Z","bundle_sha256":"3bec75c451059471e2ad298eeb8c22385c7671edcdae3ea6b67ace94c8f134a3"}}