{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:ASDJDFYK4C4C7LJUIGEOFDVKCW","short_pith_number":"pith:ASDJDFYK","canonical_record":{"source":{"id":"0706.3571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-06-25T07:17:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ead48b49423bff2b586c4e3379deee13399a38a19785456dc53cd09624eed925","abstract_canon_sha256":"ea7ea672a1de6b3cbe44e68772798ffc1a0a5294d37be7e8e9d4b571cdabb9d3"},"schema_version":"1.0"},"canonical_sha256":"048691970ae0b82fad344188e28eaa15b9b4e142ee1c1a4787f0296fd89322c7","source":{"kind":"arxiv","id":"0706.3571","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3571","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3571v2","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3571","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"ASDJDFYK4C4C","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ASDJDFYK4C4C7LJU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ASDJDFYK","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:ASDJDFYK4C4C7LJUIGEOFDVKCW","target":"record","payload":{"canonical_record":{"source":{"id":"0706.3571","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-06-25T07:17:03Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"ead48b49423bff2b586c4e3379deee13399a38a19785456dc53cd09624eed925","abstract_canon_sha256":"ea7ea672a1de6b3cbe44e68772798ffc1a0a5294d37be7e8e9d4b571cdabb9d3"},"schema_version":"1.0"},"canonical_sha256":"048691970ae0b82fad344188e28eaa15b9b4e142ee1c1a4787f0296fd89322c7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:40:47.868485Z","signature_b64":"i5kH5/MgIcwdVjEAp4GKOZphFTiVOVgEH1iWQUHLWL3Sn2N/E1XE81Fr8VvnGDf4lT/uabrsoOKe0BxJLGmuBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"048691970ae0b82fad344188e28eaa15b9b4e142ee1c1a4787f0296fd89322c7","last_reissued_at":"2026-05-18T02:40:47.867938Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:40:47.867938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0706.3571","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":"2026-05-18T02:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pf0gP5XagFmOT1yIH0+ANVDjiDXVnVXujHG55z4Xu4F9o58DFnVLkQBfWz6oxA41pL3rjV14HKRHG2PV1ox9Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:51:00.689677Z"},"content_sha256":"da05ac3c2a6c316178e2c9394f288a2958eb0f768e9f242a1f66d2d7411e3ae5","schema_version":"1.0","event_id":"sha256:da05ac3c2a6c316178e2c9394f288a2958eb0f768e9f242a1f66d2d7411e3ae5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:ASDJDFYK4C4C7LJUIGEOFDVKCW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Chern-Simons pre-quantization over four-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.SG","authors_text":"Tosiaki Kori","submitted_at":"2007-06-25T07:17:03Z","abstract_excerpt":"We introduce a pre-symplectic structure on the space of connections in a G-principal bundle over a four-manifold and a Hamiltonian action on it of the group of gauge transformations that are trivial on the boundary. The moment map is given by the square of curvature so that the 0-level set is the space of flat connections. Thus the moduli space of flat connections is endowed with a pre-symplectic structure. In case when the four-manifold is null-cobordant we shall construct, on the moduli space of connections, as well as on that of flat connections, a hermitian line bundle with connection whos"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3571","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":"2026-05-18T02:40:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"axc8J38Veg1BUniTBQCfVFjPabI1tMsHHFmgBldKzx0xXuwqXQ/nK8bsluW5ZA+gByEQla7/G7bg1OmdqQkFBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T15:51:00.690059Z"},"content_sha256":"bca48e1a6ea7b9af57a7656fdcd281f2b2106e70d4e68087330266ee1e2d126b","schema_version":"1.0","event_id":"sha256:bca48e1a6ea7b9af57a7656fdcd281f2b2106e70d4e68087330266ee1e2d126b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ASDJDFYK4C4C7LJUIGEOFDVKCW/bundle.json","state_url":"https://pith.science/pith/ASDJDFYK4C4C7LJUIGEOFDVKCW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ASDJDFYK4C4C7LJUIGEOFDVKCW/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":"2026-07-04T15:51:00Z","links":{"resolver":"https://pith.science/pith/ASDJDFYK4C4C7LJUIGEOFDVKCW","bundle":"https://pith.science/pith/ASDJDFYK4C4C7LJUIGEOFDVKCW/bundle.json","state":"https://pith.science/pith/ASDJDFYK4C4C7LJUIGEOFDVKCW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ASDJDFYK4C4C7LJUIGEOFDVKCW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:ASDJDFYK4C4C7LJUIGEOFDVKCW","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":"ea7ea672a1de6b3cbe44e68772798ffc1a0a5294d37be7e8e9d4b571cdabb9d3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-06-25T07:17:03Z","title_canon_sha256":"ead48b49423bff2b586c4e3379deee13399a38a19785456dc53cd09624eed925"},"schema_version":"1.0","source":{"id":"0706.3571","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0706.3571","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"arxiv_version","alias_value":"0706.3571v2","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0706.3571","created_at":"2026-05-18T02:40:47Z"},{"alias_kind":"pith_short_12","alias_value":"ASDJDFYK4C4C","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"ASDJDFYK4C4C7LJU","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"ASDJDFYK","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:bca48e1a6ea7b9af57a7656fdcd281f2b2106e70d4e68087330266ee1e2d126b","target":"graph","created_at":"2026-05-18T02:40:47Z","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 introduce a pre-symplectic structure on the space of connections in a G-principal bundle over a four-manifold and a Hamiltonian action on it of the group of gauge transformations that are trivial on the boundary. The moment map is given by the square of curvature so that the 0-level set is the space of flat connections. Thus the moduli space of flat connections is endowed with a pre-symplectic structure. In case when the four-manifold is null-cobordant we shall construct, on the moduli space of connections, as well as on that of flat connections, a hermitian line bundle with connection whos","authors_text":"Tosiaki Kori","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-06-25T07:17:03Z","title":"Chern-Simons pre-quantization over four-manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.3571","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:da05ac3c2a6c316178e2c9394f288a2958eb0f768e9f242a1f66d2d7411e3ae5","target":"record","created_at":"2026-05-18T02:40:47Z","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":"ea7ea672a1de6b3cbe44e68772798ffc1a0a5294d37be7e8e9d4b571cdabb9d3","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2007-06-25T07:17:03Z","title_canon_sha256":"ead48b49423bff2b586c4e3379deee13399a38a19785456dc53cd09624eed925"},"schema_version":"1.0","source":{"id":"0706.3571","kind":"arxiv","version":2}},"canonical_sha256":"048691970ae0b82fad344188e28eaa15b9b4e142ee1c1a4787f0296fd89322c7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"048691970ae0b82fad344188e28eaa15b9b4e142ee1c1a4787f0296fd89322c7","first_computed_at":"2026-05-18T02:40:47.867938Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:47.867938Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"i5kH5/MgIcwdVjEAp4GKOZphFTiVOVgEH1iWQUHLWL3Sn2N/E1XE81Fr8VvnGDf4lT/uabrsoOKe0BxJLGmuBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:47.868485Z","signed_message":"canonical_sha256_bytes"},"source_id":"0706.3571","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:da05ac3c2a6c316178e2c9394f288a2958eb0f768e9f242a1f66d2d7411e3ae5","sha256:bca48e1a6ea7b9af57a7656fdcd281f2b2106e70d4e68087330266ee1e2d126b"],"state_sha256":"a8d4a680209798a6b279ccf13ae6d503a5f309377d7d063e86946aee02741935"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4+ht7tcIbbgFk9YhaeME9MebgJ881NiJcDw8fFOaMo4bUyXc9rS+cBc9t7bXAhoKw03o22slZ93Ck+4ldmrlBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T15:51:00.692064Z","bundle_sha256":"96d156b5029cf26611bcb9d3fb913c44db26eb028f26c41e6700886f5bdb7eea"}}