{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:2M5PMDD74QUTR5UJKHPE6I2XVZ","short_pith_number":"pith:2M5PMDD7","canonical_record":{"source":{"id":"2411.17635","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-26T17:51:59Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"1a5276436cf644f101574abdff114f018edbcfc43a6606ea71fefe588b5668a0","abstract_canon_sha256":"36f33bb3919a204181c019fdf62347ea169864c922491af63f91a66afa4ceb08"},"schema_version":"1.0"},"canonical_sha256":"d33af60c7fe42938f68951de4f2357ae64020699e000094703e44ed3c99cca3b","source":{"kind":"arxiv","id":"2411.17635","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.17635","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"2411.17635v1","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17635","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"2M5PMDD74QUT","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_16","alias_value":"2M5PMDD74QUTR5UJ","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_8","alias_value":"2M5PMDD7","created_at":"2026-07-05T09:40:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:2M5PMDD74QUTR5UJKHPE6I2XVZ","target":"record","payload":{"canonical_record":{"source":{"id":"2411.17635","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-26T17:51:59Z","cross_cats_sorted":["math.AP","math.MP"],"title_canon_sha256":"1a5276436cf644f101574abdff114f018edbcfc43a6606ea71fefe588b5668a0","abstract_canon_sha256":"36f33bb3919a204181c019fdf62347ea169864c922491af63f91a66afa4ceb08"},"schema_version":"1.0"},"canonical_sha256":"d33af60c7fe42938f68951de4f2357ae64020699e000094703e44ed3c99cca3b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:40:49.889797Z","signature_b64":"ou/oaXnuN17tMPHRa4/gms/qZzGR4At2W+q8FGrkqcTLlnaAz8aBAdoIIGNdWQ5mqqX08JbKfAvBsmyupgKXAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d33af60c7fe42938f68951de4f2357ae64020699e000094703e44ed3c99cca3b","last_reissued_at":"2026-07-05T09:40:49.889435Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:40:49.889435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.17635","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":"2026-07-05T09:40:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0/UkxBZDAiHTdabscoNPvWBC+6uetBl4K7i6uCYdd86CVeqhBS81orpkzebCQoaOyeNBQWGDGZdvET5h5JmOBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:23:47.856373Z"},"content_sha256":"ae6e98ed5220ccaa56bf7a7b68ee482a28e7cbf2df0c1519b080bc6b22964b4c","schema_version":"1.0","event_id":"sha256:ae6e98ed5220ccaa56bf7a7b68ee482a28e7cbf2df0c1519b080bc6b22964b4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:2M5PMDD74QUTR5UJKHPE6I2XVZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational Dual Solutions of Chern-Simons Theory","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Ambar N. Sengupta, Amit Acharya, Janusz Ginster","submitted_at":"2024-11-26T17:51:59Z","abstract_excerpt":"A scheme for generating weakly lower semi-continuous action functionals corresponding to the Euler-Lagrange equations of Chern-Simons theory is described. Coercivity is deduced for such a functional in appropriate function spaces to prove the existence of a minimizer, which constitutes a solution to the Euler-Lagrange equations of Chern-Simons theory in a relaxed sense. A geometric analysis is also made, especially for the gauge group SU(2), relating connection forms on the bundle to corresponding forms in the dual scheme."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17635","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/2411.17635/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":"2026-07-05T09:40:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GmB3wTE0Gb58Js93HPMeE9ssen2PU+n9CnAPD7ejHC7mgYnOGErXPVZ4DE3mOd8+vgx2l8TIgs0//hdJevj4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T04:23:47.856780Z"},"content_sha256":"b393ec2d0542bbdc403dc8f934221cd44584f3c0fc3925cb6d6a0b6fb0f91da7","schema_version":"1.0","event_id":"sha256:b393ec2d0542bbdc403dc8f934221cd44584f3c0fc3925cb6d6a0b6fb0f91da7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2M5PMDD74QUTR5UJKHPE6I2XVZ/bundle.json","state_url":"https://pith.science/pith/2M5PMDD74QUTR5UJKHPE6I2XVZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2M5PMDD74QUTR5UJKHPE6I2XVZ/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":"2026-08-13T04:23:47Z","links":{"resolver":"https://pith.science/pith/2M5PMDD74QUTR5UJKHPE6I2XVZ","bundle":"https://pith.science/pith/2M5PMDD74QUTR5UJKHPE6I2XVZ/bundle.json","state":"https://pith.science/pith/2M5PMDD74QUTR5UJKHPE6I2XVZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2M5PMDD74QUTR5UJKHPE6I2XVZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:2M5PMDD74QUTR5UJKHPE6I2XVZ","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":"36f33bb3919a204181c019fdf62347ea169864c922491af63f91a66afa4ceb08","cross_cats_sorted":["math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-26T17:51:59Z","title_canon_sha256":"1a5276436cf644f101574abdff114f018edbcfc43a6606ea71fefe588b5668a0"},"schema_version":"1.0","source":{"id":"2411.17635","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.17635","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"arxiv_version","alias_value":"2411.17635v1","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.17635","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_12","alias_value":"2M5PMDD74QUT","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_16","alias_value":"2M5PMDD74QUTR5UJ","created_at":"2026-07-05T09:40:49Z"},{"alias_kind":"pith_short_8","alias_value":"2M5PMDD7","created_at":"2026-07-05T09:40:49Z"}],"graph_snapshots":[{"event_id":"sha256:b393ec2d0542bbdc403dc8f934221cd44584f3c0fc3925cb6d6a0b6fb0f91da7","target":"graph","created_at":"2026-07-05T09:40:49Z","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/2411.17635/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A scheme for generating weakly lower semi-continuous action functionals corresponding to the Euler-Lagrange equations of Chern-Simons theory is described. Coercivity is deduced for such a functional in appropriate function spaces to prove the existence of a minimizer, which constitutes a solution to the Euler-Lagrange equations of Chern-Simons theory in a relaxed sense. A geometric analysis is also made, especially for the gauge group SU(2), relating connection forms on the bundle to corresponding forms in the dual scheme.","authors_text":"Ambar N. Sengupta, Amit Acharya, Janusz Ginster","cross_cats":["math.AP","math.MP"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-26T17:51:59Z","title":"Variational Dual Solutions of Chern-Simons Theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.17635","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:ae6e98ed5220ccaa56bf7a7b68ee482a28e7cbf2df0c1519b080bc6b22964b4c","target":"record","created_at":"2026-07-05T09:40:49Z","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":"36f33bb3919a204181c019fdf62347ea169864c922491af63f91a66afa4ceb08","cross_cats_sorted":["math.AP","math.MP"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math-ph","submitted_at":"2024-11-26T17:51:59Z","title_canon_sha256":"1a5276436cf644f101574abdff114f018edbcfc43a6606ea71fefe588b5668a0"},"schema_version":"1.0","source":{"id":"2411.17635","kind":"arxiv","version":1}},"canonical_sha256":"d33af60c7fe42938f68951de4f2357ae64020699e000094703e44ed3c99cca3b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d33af60c7fe42938f68951de4f2357ae64020699e000094703e44ed3c99cca3b","first_computed_at":"2026-07-05T09:40:49.889435Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:40:49.889435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ou/oaXnuN17tMPHRa4/gms/qZzGR4At2W+q8FGrkqcTLlnaAz8aBAdoIIGNdWQ5mqqX08JbKfAvBsmyupgKXAA==","signature_status":"signed_v1","signed_at":"2026-07-05T09:40:49.889797Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.17635","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ae6e98ed5220ccaa56bf7a7b68ee482a28e7cbf2df0c1519b080bc6b22964b4c","sha256:b393ec2d0542bbdc403dc8f934221cd44584f3c0fc3925cb6d6a0b6fb0f91da7"],"state_sha256":"15278af2488843bc0895ebf36b14d357dbc8a024f59408e10f84c5ec24ebce45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DpjwNLuNW7y+mNKdf5VZ0hkBtQRQIA/dp2YbqNGwbd71qFPhTKwSTSx4TM3c2KRhK/JKWiUCwePrnPpPdtrzCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T04:23:47.859582Z","bundle_sha256":"3eb232f261b7709238f0274c3c982595e76f6b33874abf5f6159c0a03d4db03f"}}