{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:ZH2LBRUYS7CV2FWX6U2I4MUCST","short_pith_number":"pith:ZH2LBRUY","canonical_record":{"source":{"id":"hep-th/0411090","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-11-08T18:25:08Z","cross_cats_sorted":[],"title_canon_sha256":"c0e40431d667dd5a54196f423e7648a825dcb35bf64c1babe260450fa8b7e6c4","abstract_canon_sha256":"53ef4af617a36253d6a9f5e2a2586edd26cf61873851f001c7a3fff6b1404caa"},"schema_version":"1.0"},"canonical_sha256":"c9f4b0c69897c55d16d7f5348e328294da18ab5b3f26aab0c08779e9883f3319","source":{"kind":"arxiv","id":"hep-th/0411090","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0411090","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0411090v1","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0411090","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZH2LBRUYS7CV","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"ZH2LBRUYS7CV2FWX","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"ZH2LBRUY","created_at":"2026-07-04T14:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:ZH2LBRUYS7CV2FWX6U2I4MUCST","target":"record","payload":{"canonical_record":{"source":{"id":"hep-th/0411090","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"hep-th","submitted_at":"2004-11-08T18:25:08Z","cross_cats_sorted":[],"title_canon_sha256":"c0e40431d667dd5a54196f423e7648a825dcb35bf64c1babe260450fa8b7e6c4","abstract_canon_sha256":"53ef4af617a36253d6a9f5e2a2586edd26cf61873851f001c7a3fff6b1404caa"},"schema_version":"1.0"},"canonical_sha256":"c9f4b0c69897c55d16d7f5348e328294da18ab5b3f26aab0c08779e9883f3319","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:32:19.905828Z","signature_b64":"V3vpa3CxmgLDuRHg4VIiFIW/Yj7WraDTLlvCNskMgRsnuI8HJBLX8bXVyKS3fjRdxHlKZqjdJaQxI5D/XsRVAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9f4b0c69897c55d16d7f5348e328294da18ab5b3f26aab0c08779e9883f3319","last_reissued_at":"2026-07-04T14:32:19.905402Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:32:19.905402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"hep-th/0411090","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":"2026-07-04T14:32:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WflG4kljfYEitX9+IstBeJWYLvLFQlVUErV1Hid1FUv0qezQpyANKLfWNdz55gcE8WeygTaNPFwmiGeggy27CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T03:42:39.441204Z"},"content_sha256":"a8a70be0a5695aa8d59d17964fe2fc6136fc77b1aeb318c9747b38430202648b","schema_version":"1.0","event_id":"sha256:a8a70be0a5695aa8d59d17964fe2fc6136fc77b1aeb318c9747b38430202648b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:ZH2LBRUYS7CV2FWX6U2I4MUCST","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Bargmann-Wigner Equations in Spherical Space","license":"","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Canada), D.G.C. McKeon (Applied Mathematics, Ireland), London, National University of Ireland Galway, Ontario, T.N. Sherry (Mathematical Physics, University of Western Ontario","submitted_at":"2004-11-08T18:25:08Z","abstract_excerpt":"The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of parameters characterizing them. For spheres embedded in three, four and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second order models for two index antisymmetric tensor fields in any number of dimensions. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0411090","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/hep-th/0411090/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":"2026-07-04T14:32:19Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NIu++j9jHPUr3gzvfUVwglTecnw8bxTN5dT0EkttvLPIejgAT7G/KJ7RuqG0aXPd1sGDWK3nPJ7/X3L9i26YCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-06T03:42:39.441875Z"},"content_sha256":"5bfe0f48453c441322b90c84d9cad1263be19116979cd1ef5ac5eded9ac8a872","schema_version":"1.0","event_id":"sha256:5bfe0f48453c441322b90c84d9cad1263be19116979cd1ef5ac5eded9ac8a872"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZH2LBRUYS7CV2FWX6U2I4MUCST/bundle.json","state_url":"https://pith.science/pith/ZH2LBRUYS7CV2FWX6U2I4MUCST/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZH2LBRUYS7CV2FWX6U2I4MUCST/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":"2026-07-06T03:42:39Z","links":{"resolver":"https://pith.science/pith/ZH2LBRUYS7CV2FWX6U2I4MUCST","bundle":"https://pith.science/pith/ZH2LBRUYS7CV2FWX6U2I4MUCST/bundle.json","state":"https://pith.science/pith/ZH2LBRUYS7CV2FWX6U2I4MUCST/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZH2LBRUYS7CV2FWX6U2I4MUCST/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:ZH2LBRUYS7CV2FWX6U2I4MUCST","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":"53ef4af617a36253d6a9f5e2a2586edd26cf61873851f001c7a3fff6b1404caa","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2004-11-08T18:25:08Z","title_canon_sha256":"c0e40431d667dd5a54196f423e7648a825dcb35bf64c1babe260450fa8b7e6c4"},"schema_version":"1.0","source":{"id":"hep-th/0411090","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0411090","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0411090v1","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0411090","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"pith_short_12","alias_value":"ZH2LBRUYS7CV","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"ZH2LBRUYS7CV2FWX","created_at":"2026-07-04T14:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"ZH2LBRUY","created_at":"2026-07-04T14:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:5bfe0f48453c441322b90c84d9cad1263be19116979cd1ef5ac5eded9ac8a872","target":"graph","created_at":"2026-07-04T14:32:19Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/hep-th/0411090/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of parameters characterizing them. For spheres embedded in three, four and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second order models for two index antisymmetric tensor fields in any number of dimensions. Th","authors_text":"Canada), D.G.C. McKeon (Applied Mathematics, Ireland), London, National University of Ireland Galway, Ontario, T.N. Sherry (Mathematical Physics, University of Western Ontario","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2004-11-08T18:25:08Z","title":"The Bargmann-Wigner Equations in Spherical Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0411090","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:a8a70be0a5695aa8d59d17964fe2fc6136fc77b1aeb318c9747b38430202648b","target":"record","created_at":"2026-07-04T14:32:19Z","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":"53ef4af617a36253d6a9f5e2a2586edd26cf61873851f001c7a3fff6b1404caa","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2004-11-08T18:25:08Z","title_canon_sha256":"c0e40431d667dd5a54196f423e7648a825dcb35bf64c1babe260450fa8b7e6c4"},"schema_version":"1.0","source":{"id":"hep-th/0411090","kind":"arxiv","version":1}},"canonical_sha256":"c9f4b0c69897c55d16d7f5348e328294da18ab5b3f26aab0c08779e9883f3319","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c9f4b0c69897c55d16d7f5348e328294da18ab5b3f26aab0c08779e9883f3319","first_computed_at":"2026-07-04T14:32:19.905402Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:32:19.905402Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"V3vpa3CxmgLDuRHg4VIiFIW/Yj7WraDTLlvCNskMgRsnuI8HJBLX8bXVyKS3fjRdxHlKZqjdJaQxI5D/XsRVAQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:32:19.905828Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0411090","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a8a70be0a5695aa8d59d17964fe2fc6136fc77b1aeb318c9747b38430202648b","sha256:5bfe0f48453c441322b90c84d9cad1263be19116979cd1ef5ac5eded9ac8a872"],"state_sha256":"10ae687b42a21e667c3b27406a99460e2fa1e5c4a4d72a61b41699724ebcdb2b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cmElZ0iLpCpowlS12CMnWOblzwRn/Xtjafrczf58OLdZKlaZJ9IG7z/lADOE7vAWZB61pObMIuDdzncZYuwvBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-06T03:42:39.445198Z","bundle_sha256":"65a5c57b5ddec7015aec454b9529395b8b2a53fc4badf7919417aa509edd1d99"}}