{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2002:X6XEWGE7HGYDU4UEMUSNUGI5Z4","short_pith_number":"pith:X6XEWGE7","canonical_record":{"source":{"id":"math-ph/0212079","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-12-01T00:00:00Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ba43e41e1505862a77ca862132188c0f04030a75d3bc0d12e5689453a59ded73","abstract_canon_sha256":"3f26b99bed48ee2da434d9de4846be24938f9858f178bcc7495a15542e16aa8f"},"schema_version":"1.0"},"canonical_sha256":"bfae4b189f39b03a72846524da191dcf13d673b970b5cc17ceee686c18cba521","source":{"kind":"arxiv","id":"math-ph/0212079","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0212079","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0212079v1","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0212079","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"pith_short_12","alias_value":"X6XEWGE7HGYD","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"pith_short_16","alias_value":"X6XEWGE7HGYDU4UE","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"pith_short_8","alias_value":"X6XEWGE7","created_at":"2026-07-04T14:33:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2002:X6XEWGE7HGYDU4UEMUSNUGI5Z4","target":"record","payload":{"canonical_record":{"source":{"id":"math-ph/0212079","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math-ph","submitted_at":"2002-12-01T00:00:00Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"ba43e41e1505862a77ca862132188c0f04030a75d3bc0d12e5689453a59ded73","abstract_canon_sha256":"3f26b99bed48ee2da434d9de4846be24938f9858f178bcc7495a15542e16aa8f"},"schema_version":"1.0"},"canonical_sha256":"bfae4b189f39b03a72846524da191dcf13d673b970b5cc17ceee686c18cba521","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:33:46.216019Z","signature_b64":"ei+IRwofvgLrkDGqnaAU7br6LicSX5IkOpJWkRjlUI3Xt9vXmOCEQweWkOgv3KW48jQCjYGTse6a7ceJMuHeDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bfae4b189f39b03a72846524da191dcf13d673b970b5cc17ceee686c18cba521","last_reissued_at":"2026-07-04T14:33:46.215641Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:33:46.215641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math-ph/0212079","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":"2026-07-04T14:33:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a+3L3ZDlQspUK9tnmHnHrojsGoae7K+8+gQ9RAlo4ctUN6vecb9VmzPQI6di/KIepvQYYUgTwvvHMcFjXM8MBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:52:41.479814Z"},"content_sha256":"41ec9433465b4e00302b11e3a22cee3b0396ba83c422971fa67d27f5f7413fc9","schema_version":"1.0","event_id":"sha256:41ec9433465b4e00302b11e3a22cee3b0396ba83c422971fa67d27f5f7413fc9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2002:X6XEWGE7HGYDU4UEMUSNUGI5Z4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Knotted solitons","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ludvig D. Faddeev","submitted_at":"2002-12-01T00:00:00Z","abstract_excerpt":"The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf invariant. Some applications in realistic physical systems are indicated."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0212079","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0212079/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:33:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nx1ySxGKkB3GFHvYR0VW/Rwv4UBGgsmougqPFsHmdlvtYQb3aPYxRgwAgodbQh16wCTa3FsmGXKx9HcFPkgeAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T15:52:41.480686Z"},"content_sha256":"f4ff8abb4ed76b18367c5e75401119ce13565d1dd4369a0cd6042254b04ee3e1","schema_version":"1.0","event_id":"sha256:f4ff8abb4ed76b18367c5e75401119ce13565d1dd4369a0cd6042254b04ee3e1"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X6XEWGE7HGYDU4UEMUSNUGI5Z4/bundle.json","state_url":"https://pith.science/pith/X6XEWGE7HGYDU4UEMUSNUGI5Z4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X6XEWGE7HGYDU4UEMUSNUGI5Z4/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":"2026-08-09T15:52:41Z","links":{"resolver":"https://pith.science/pith/X6XEWGE7HGYDU4UEMUSNUGI5Z4","bundle":"https://pith.science/pith/X6XEWGE7HGYDU4UEMUSNUGI5Z4/bundle.json","state":"https://pith.science/pith/X6XEWGE7HGYDU4UEMUSNUGI5Z4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X6XEWGE7HGYDU4UEMUSNUGI5Z4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:X6XEWGE7HGYDU4UEMUSNUGI5Z4","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":"3f26b99bed48ee2da434d9de4846be24938f9858f178bcc7495a15542e16aa8f","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-12-01T00:00:00Z","title_canon_sha256":"ba43e41e1505862a77ca862132188c0f04030a75d3bc0d12e5689453a59ded73"},"schema_version":"1.0","source":{"id":"math-ph/0212079","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math-ph/0212079","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"arxiv_version","alias_value":"math-ph/0212079v1","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math-ph/0212079","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"pith_short_12","alias_value":"X6XEWGE7HGYD","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"pith_short_16","alias_value":"X6XEWGE7HGYDU4UE","created_at":"2026-07-04T14:33:46Z"},{"alias_kind":"pith_short_8","alias_value":"X6XEWGE7","created_at":"2026-07-04T14:33:46Z"}],"graph_snapshots":[{"event_id":"sha256:f4ff8abb4ed76b18367c5e75401119ce13565d1dd4369a0cd6042254b04ee3e1","target":"graph","created_at":"2026-07-04T14:33:46Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math-ph/0212079/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The dynamical model on 3+1 dimensional spacetime admitting soliton solutions is discussed. The proposal soliton is localized in the vicinity of a closed contour, which could be linked and/or knotted. The topological charge is Hopf invariant. Some applications in realistic physical systems are indicated.","authors_text":"Ludvig D. Faddeev","cross_cats":["math.MP"],"headline":"","license":"","primary_cat":"math-ph","submitted_at":"2002-12-01T00:00:00Z","title":"Knotted solitons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0212079","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":"sha256:41ec9433465b4e00302b11e3a22cee3b0396ba83c422971fa67d27f5f7413fc9","target":"record","created_at":"2026-07-04T14:33:46Z","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":"3f26b99bed48ee2da434d9de4846be24938f9858f178bcc7495a15542e16aa8f","cross_cats_sorted":["math.MP"],"license":"","primary_cat":"math-ph","submitted_at":"2002-12-01T00:00:00Z","title_canon_sha256":"ba43e41e1505862a77ca862132188c0f04030a75d3bc0d12e5689453a59ded73"},"schema_version":"1.0","source":{"id":"math-ph/0212079","kind":"arxiv","version":1}},"canonical_sha256":"bfae4b189f39b03a72846524da191dcf13d673b970b5cc17ceee686c18cba521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bfae4b189f39b03a72846524da191dcf13d673b970b5cc17ceee686c18cba521","first_computed_at":"2026-07-04T14:33:46.215641Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:33:46.215641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ei+IRwofvgLrkDGqnaAU7br6LicSX5IkOpJWkRjlUI3Xt9vXmOCEQweWkOgv3KW48jQCjYGTse6a7ceJMuHeDA==","signature_status":"signed_v1","signed_at":"2026-07-04T14:33:46.216019Z","signed_message":"canonical_sha256_bytes"},"source_id":"math-ph/0212079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:41ec9433465b4e00302b11e3a22cee3b0396ba83c422971fa67d27f5f7413fc9","sha256:f4ff8abb4ed76b18367c5e75401119ce13565d1dd4369a0cd6042254b04ee3e1"],"state_sha256":"ffda6edaa60e439ff3bcb3f5deee8f8c161bd9c5d4ce911a886fe2f98661cec8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IeUs6Mh1zOeZk5FRu9eLLFTsoNAEh00DzHnBH32W4U6IXOx9YL9qZFezaLy5B978TzKMLqISCd8binhj4aRGBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T15:52:41.487466Z","bundle_sha256":"f9e0338ef4ab99a41cf59d47809b25b10fef82ac07cca2909fd30cff7f11c809"}}