{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:R6YLSZYAZIZVFZRHRCYDFCKCR3","short_pith_number":"pith:R6YLSZYA","canonical_record":{"source":{"id":"1405.2123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-08T23:33:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b42ad25e75dc8fb3d60645a28aeaf61e488c6325d28c065d712f97f3859abbd8","abstract_canon_sha256":"f5630ba3a3931cd137becc9a3d4948ece9d7ca3e8ea61c226266dc94a7956bb4"},"schema_version":"1.0"},"canonical_sha256":"8fb0b96700ca3352e62788b03289428ef9a1f0813042ff460ba309f903528ac3","source":{"kind":"arxiv","id":"1405.2123","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2123","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2123v2","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2123","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"R6YLSZYAZIZV","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R6YLSZYAZIZVFZRH","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R6YLSZYA","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:R6YLSZYAZIZVFZRHRCYDFCKCR3","target":"record","payload":{"canonical_record":{"source":{"id":"1405.2123","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-08T23:33:27Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"b42ad25e75dc8fb3d60645a28aeaf61e488c6325d28c065d712f97f3859abbd8","abstract_canon_sha256":"f5630ba3a3931cd137becc9a3d4948ece9d7ca3e8ea61c226266dc94a7956bb4"},"schema_version":"1.0"},"canonical_sha256":"8fb0b96700ca3352e62788b03289428ef9a1f0813042ff460ba309f903528ac3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:43:15.876063Z","signature_b64":"oPSq738i7KT85KYfXAvA5Hg+BpQg1jHAYIwFBkegFzFHwhta1FfRCWKBBg0MgBlBiTv8NhHQ3bd2czmllQ+CCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fb0b96700ca3352e62788b03289428ef9a1f0813042ff460ba309f903528ac3","last_reissued_at":"2026-05-18T01:43:15.875374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:43:15.875374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.2123","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":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7VUInLgkhXnirVIs3BGif1qRVHkyYYZc1M5l5a0gtLXLyjimbYiK2+s7f/JUEvscvXhtYJdZkkKOEE32PpYUBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:45:59.647758Z"},"content_sha256":"d81573a7677e1bb29add450df2d7dccac160f246140ceb8af233cd68b4e45981","schema_version":"1.0","event_id":"sha256:d81573a7677e1bb29add450df2d7dccac160f246140ceb8af233cd68b4e45981"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:R6YLSZYAZIZVFZRHRCYDFCKCR3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Global Aspects of Abelian Duality in Dimension Three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"hep-th","authors_text":"Chris Beasley","submitted_at":"2014-05-08T23:33:27Z","abstract_excerpt":"In three dimensions, an abelian gauge field is related by duality to a free, periodic scalar field. Though usually considered on Euclidean space, this duality can be extended to a general three-manifold M, in which case topological features of M become important. Here I comment upon several of these features as related to the partition function on M. In a companion article, arXiv:1405.2483, I discuss similarly the algebra of operators on a surface of genus g."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2123","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":"2026-05-18T01:43:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2SUIDVosW03PaiTcjjtFr9UIR5g9slFQgjavem4hi1zRfCRxblxgA1CPJB0CCeqjAmvBZVua0cVqj103LceDAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T14:45:59.648489Z"},"content_sha256":"1b2e60dd63351dafb35d542657b49c24579a1edcfef2b94468db7003846fda6b","schema_version":"1.0","event_id":"sha256:1b2e60dd63351dafb35d542657b49c24579a1edcfef2b94468db7003846fda6b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R6YLSZYAZIZVFZRHRCYDFCKCR3/bundle.json","state_url":"https://pith.science/pith/R6YLSZYAZIZVFZRHRCYDFCKCR3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R6YLSZYAZIZVFZRHRCYDFCKCR3/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":"2026-05-31T14:45:59Z","links":{"resolver":"https://pith.science/pith/R6YLSZYAZIZVFZRHRCYDFCKCR3","bundle":"https://pith.science/pith/R6YLSZYAZIZVFZRHRCYDFCKCR3/bundle.json","state":"https://pith.science/pith/R6YLSZYAZIZVFZRHRCYDFCKCR3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R6YLSZYAZIZVFZRHRCYDFCKCR3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:R6YLSZYAZIZVFZRHRCYDFCKCR3","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":"f5630ba3a3931cd137becc9a3d4948ece9d7ca3e8ea61c226266dc94a7956bb4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-08T23:33:27Z","title_canon_sha256":"b42ad25e75dc8fb3d60645a28aeaf61e488c6325d28c065d712f97f3859abbd8"},"schema_version":"1.0","source":{"id":"1405.2123","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.2123","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"arxiv_version","alias_value":"1405.2123v2","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.2123","created_at":"2026-05-18T01:43:15Z"},{"alias_kind":"pith_short_12","alias_value":"R6YLSZYAZIZV","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"R6YLSZYAZIZVFZRH","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"R6YLSZYA","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:1b2e60dd63351dafb35d542657b49c24579a1edcfef2b94468db7003846fda6b","target":"graph","created_at":"2026-05-18T01:43:15Z","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":"In three dimensions, an abelian gauge field is related by duality to a free, periodic scalar field. Though usually considered on Euclidean space, this duality can be extended to a general three-manifold M, in which case topological features of M become important. Here I comment upon several of these features as related to the partition function on M. In a companion article, arXiv:1405.2483, I discuss similarly the algebra of operators on a surface of genus g.","authors_text":"Chris Beasley","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-08T23:33:27Z","title":"Global Aspects of Abelian Duality in Dimension Three"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.2123","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:d81573a7677e1bb29add450df2d7dccac160f246140ceb8af233cd68b4e45981","target":"record","created_at":"2026-05-18T01:43:15Z","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":"f5630ba3a3931cd137becc9a3d4948ece9d7ca3e8ea61c226266dc94a7956bb4","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2014-05-08T23:33:27Z","title_canon_sha256":"b42ad25e75dc8fb3d60645a28aeaf61e488c6325d28c065d712f97f3859abbd8"},"schema_version":"1.0","source":{"id":"1405.2123","kind":"arxiv","version":2}},"canonical_sha256":"8fb0b96700ca3352e62788b03289428ef9a1f0813042ff460ba309f903528ac3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8fb0b96700ca3352e62788b03289428ef9a1f0813042ff460ba309f903528ac3","first_computed_at":"2026-05-18T01:43:15.875374Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:43:15.875374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"oPSq738i7KT85KYfXAvA5Hg+BpQg1jHAYIwFBkegFzFHwhta1FfRCWKBBg0MgBlBiTv8NhHQ3bd2czmllQ+CCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:43:15.876063Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.2123","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d81573a7677e1bb29add450df2d7dccac160f246140ceb8af233cd68b4e45981","sha256:1b2e60dd63351dafb35d542657b49c24579a1edcfef2b94468db7003846fda6b"],"state_sha256":"fdbcbf6b4d900ab1b584372ab277fcbe29556dc27650ba9debcab04e2131d28d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LfTSaLDlygjWfnRKlKmH5wnzH8aFNlE5Mkq0b36GIfiAupuy3rtSKnIkVVlyTp3ytnvTBKvzaImLA9jRZabQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T14:45:59.652217Z","bundle_sha256":"1c2ed5b1be133aa57f211754028e8b368766af5c8060f30984b2240fb7cdb97b"}}