{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:4QVP77QYJLEIIKD5K6I3KUKOSI","short_pith_number":"pith:4QVP77QY","canonical_record":{"source":{"id":"1312.4879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-17T17:50:51Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"5434cf92da52d19482916f03f2c7f4e4e1691b498aae35919220510628fc9c45","abstract_canon_sha256":"5864d6daa43a79565717d0a14b8db99b251ed82bf7da4362d8e5d41a698e3b64"},"schema_version":"1.0"},"canonical_sha256":"e42afffe184ac884287d5791b5514e920a179a9f62e571a961c90604fb7e3e8e","source":{"kind":"arxiv","id":"1312.4879","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4879","created_at":"2026-05-18T01:45:45Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4879v2","created_at":"2026-05-18T01:45:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4879","created_at":"2026-05-18T01:45:45Z"},{"alias_kind":"pith_short_12","alias_value":"4QVP77QYJLEI","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4QVP77QYJLEIIKD5","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4QVP77QY","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:4QVP77QYJLEIIKD5K6I3KUKOSI","target":"record","payload":{"canonical_record":{"source":{"id":"1312.4879","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-17T17:50:51Z","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"title_canon_sha256":"5434cf92da52d19482916f03f2c7f4e4e1691b498aae35919220510628fc9c45","abstract_canon_sha256":"5864d6daa43a79565717d0a14b8db99b251ed82bf7da4362d8e5d41a698e3b64"},"schema_version":"1.0"},"canonical_sha256":"e42afffe184ac884287d5791b5514e920a179a9f62e571a961c90604fb7e3e8e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:45:45.077380Z","signature_b64":"FJMeijrpv9sA196YLYI8jpFpSA31TsqSJv+6YZvWX00NTJqG0WJ7FspMM07F8D+bw64FtwhwztzUb3pIHIGABg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e42afffe184ac884287d5791b5514e920a179a9f62e571a961c90604fb7e3e8e","last_reissued_at":"2026-05-18T01:45:45.076665Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:45:45.076665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.4879","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:45:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rDNT45YAl1fIGp9VkqLoYYzNwr5BPN8wh4gh0SoSRu4qTUgzfrQzEr1pWb+syPTgWPZ1ofrqTOPt1w/L+mcSCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:34:59.961084Z"},"content_sha256":"8a3c16d3a7412fe89aa3020dfee4d56200359d0235730c2b4455135d5565ca4b","schema_version":"1.0","event_id":"sha256:8a3c16d3a7412fe89aa3020dfee4d56200359d0235730c2b4455135d5565ca4b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:4QVP77QYJLEIIKD5K6I3KUKOSI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac operators on the Taub-NUT space, monopoles and SU(2) representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Bernd Schroers, Rogelio Jante","submitted_at":"2013-12-17T17:50:51Z","abstract_excerpt":"We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to a Dirac monopole. We show that the space of zero modes decomposes into a direct sum of irreducible SU(2) representations of all dimensions up to a bound determined by the spinor charge with respect to the abelian gauge group. Our decomposition provides an interpretation of an index formula due to Pope and provides a possible model for spin in recently propo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4879","kind":"arxiv","version":2},"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":"2026-05-18T01:45:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"noBhqGNaw8yrgaTz/ARPLEZ9SSjYZs748PtFzK/DXOfp6tViRVoo92IyCLqIvGBTX5Y94b1U4xrsoEr5IvYHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T00:34:59.961848Z"},"content_sha256":"3316c492037554bdcb1c2e7f9f875ccae655c0aa38c78e7b473710c959f96691","schema_version":"1.0","event_id":"sha256:3316c492037554bdcb1c2e7f9f875ccae655c0aa38c78e7b473710c959f96691"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4QVP77QYJLEIIKD5K6I3KUKOSI/bundle.json","state_url":"https://pith.science/pith/4QVP77QYJLEIIKD5K6I3KUKOSI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4QVP77QYJLEIIKD5K6I3KUKOSI/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":"2026-05-26T00:34:59Z","links":{"resolver":"https://pith.science/pith/4QVP77QYJLEIIKD5K6I3KUKOSI","bundle":"https://pith.science/pith/4QVP77QYJLEIIKD5K6I3KUKOSI/bundle.json","state":"https://pith.science/pith/4QVP77QYJLEIIKD5K6I3KUKOSI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4QVP77QYJLEIIKD5K6I3KUKOSI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:4QVP77QYJLEIIKD5K6I3KUKOSI","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":"5864d6daa43a79565717d0a14b8db99b251ed82bf7da4362d8e5d41a698e3b64","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-17T17:50:51Z","title_canon_sha256":"5434cf92da52d19482916f03f2c7f4e4e1691b498aae35919220510628fc9c45"},"schema_version":"1.0","source":{"id":"1312.4879","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.4879","created_at":"2026-05-18T01:45:45Z"},{"alias_kind":"arxiv_version","alias_value":"1312.4879v2","created_at":"2026-05-18T01:45:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4879","created_at":"2026-05-18T01:45:45Z"},{"alias_kind":"pith_short_12","alias_value":"4QVP77QYJLEI","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"4QVP77QYJLEIIKD5","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"4QVP77QY","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:3316c492037554bdcb1c2e7f9f875ccae655c0aa38c78e7b473710c959f96691","target":"graph","created_at":"2026-05-18T01:45:45Z","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 analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to a Dirac monopole. We show that the space of zero modes decomposes into a direct sum of irreducible SU(2) representations of all dimensions up to a bound determined by the spinor charge with respect to the abelian gauge group. Our decomposition provides an interpretation of an index formula due to Pope and provides a possible model for spin in recently propo","authors_text":"Bernd Schroers, Rogelio Jante","cross_cats":["gr-qc","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-17T17:50:51Z","title":"Dirac operators on the Taub-NUT space, monopoles and SU(2) representations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4879","kind":"arxiv","version":2},"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":"sha256:8a3c16d3a7412fe89aa3020dfee4d56200359d0235730c2b4455135d5565ca4b","target":"record","created_at":"2026-05-18T01:45:45Z","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":"5864d6daa43a79565717d0a14b8db99b251ed82bf7da4362d8e5d41a698e3b64","cross_cats_sorted":["gr-qc","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2013-12-17T17:50:51Z","title_canon_sha256":"5434cf92da52d19482916f03f2c7f4e4e1691b498aae35919220510628fc9c45"},"schema_version":"1.0","source":{"id":"1312.4879","kind":"arxiv","version":2}},"canonical_sha256":"e42afffe184ac884287d5791b5514e920a179a9f62e571a961c90604fb7e3e8e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e42afffe184ac884287d5791b5514e920a179a9f62e571a961c90604fb7e3e8e","first_computed_at":"2026-05-18T01:45:45.076665Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:45:45.076665Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FJMeijrpv9sA196YLYI8jpFpSA31TsqSJv+6YZvWX00NTJqG0WJ7FspMM07F8D+bw64FtwhwztzUb3pIHIGABg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:45:45.077380Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.4879","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a3c16d3a7412fe89aa3020dfee4d56200359d0235730c2b4455135d5565ca4b","sha256:3316c492037554bdcb1c2e7f9f875ccae655c0aa38c78e7b473710c959f96691"],"state_sha256":"bc4b6b2deb2a8e63173763f125296376ac448f74dd590a5c92bb72abcf514ea1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pv4/8b7lXG9xfwEFUwjyNXMgBXRX9B88Tpuu/olY2o08x43DaB+qb5pTnY8csAQQSHSg1PvrY+zy4eEtR/rAAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T00:34:59.965704Z","bundle_sha256":"c9d4dcfea2817e7abff0e1c55789ea612e2609f9359a9f1454e7bf617aaa0936"}}