{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:ULG4TDUKV47DHHJSBDWVZQU4CU","short_pith_number":"pith:ULG4TDUK","canonical_record":{"source":{"id":"2111.00473","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-31T11:50:33Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"05cddf5bf9e03730e3256020b6d5967a20b62d8f152bc85390fdaa74e4baf940","abstract_canon_sha256":"d3fb7fbfeb021a63aec15c87695172c2e79801971dd528b7e1cb03d0ac3628e4"},"schema_version":"1.0"},"canonical_sha256":"a2cdc98e8aaf3e339d3208ed5cc29c1539002ca9f2077841ffb60872d2750219","source":{"kind":"arxiv","id":"2111.00473","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.00473","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"2111.00473v4","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.00473","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"ULG4TDUKV47D","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"pith_short_16","alias_value":"ULG4TDUKV47DHHJS","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"pith_short_8","alias_value":"ULG4TDUK","created_at":"2026-07-05T04:44:41Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:ULG4TDUKV47DHHJSBDWVZQU4CU","target":"record","payload":{"canonical_record":{"source":{"id":"2111.00473","kind":"arxiv","version":4},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-31T11:50:33Z","cross_cats_sorted":["quant-ph"],"title_canon_sha256":"05cddf5bf9e03730e3256020b6d5967a20b62d8f152bc85390fdaa74e4baf940","abstract_canon_sha256":"d3fb7fbfeb021a63aec15c87695172c2e79801971dd528b7e1cb03d0ac3628e4"},"schema_version":"1.0"},"canonical_sha256":"a2cdc98e8aaf3e339d3208ed5cc29c1539002ca9f2077841ffb60872d2750219","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:44:41.273712Z","signature_b64":"J/HDYgiK/ETsETZecHJVP93VDFYwsAzR97OPv6OGpgdrRQAsc0Q9+pzUKhMTF7tH3NMZ3/lL8kqHKN7dk/GcBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2cdc98e8aaf3e339d3208ed5cc29c1539002ca9f2077841ffb60872d2750219","last_reissued_at":"2026-07-05T04:44:41.273286Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:44:41.273286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.00473","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T04:44:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2EKrgAzFAuxRBL6SylUKjpNX2Fp9aEg0rXFS3xZK16ESs0+Ij6zUpSxg9HvWEGlOQAY5TU4ryPvJmVLkp/pTCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T10:59:07.483818Z"},"content_sha256":"4026780de34d804de87952557feef3f327f1f9feeac463098944245be4961aa6","schema_version":"1.0","event_id":"sha256:4026780de34d804de87952557feef3f327f1f9feeac463098944245be4961aa6"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:ULG4TDUKV47DHHJSBDWVZQU4CU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Divergence Anomaly and Schwinger Terms: Towards a Consistent Theory of Anomalous Classical Fluid","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"hep-th","authors_text":"Arpan Krishna Mitra, Subir Ghosh","submitted_at":"2021-10-31T11:50:33Z","abstract_excerpt":"Anomaly, a generic feature of relativistic quantum field theory, is shown to be present in non-relativistic classical ideal fluid. A new result is the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms present in quantum field theory. We work in Hamiltonian framework where Eulerian dynamical variables obey an anomalous algebra (with Schwinger terms) that is inherited from modified Poisson brackets, with Berry curvature corrections, among Lagrangian discrete coordinates. The divergence anomaly appears in the Hamiltonian equations of motion. A generalized form"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.00473","kind":"arxiv","version":4},"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/2111.00473/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":"2026-07-05T04:44:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UY/iGXVO75SbjE7w8pbLPlISq7E2TpWRvNNt1dhmklLbXkhk36i1OYieEa8F1ZONhFlqOg4D5omF+EqHdgtuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T10:59:07.484309Z"},"content_sha256":"b2c88ad5ddd20e9310856aebb874ee50a00b4cde90b37194e737e45207ec9c9e","schema_version":"1.0","event_id":"sha256:b2c88ad5ddd20e9310856aebb874ee50a00b4cde90b37194e737e45207ec9c9e"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULG4TDUKV47DHHJSBDWVZQU4CU/bundle.json","state_url":"https://pith.science/pith/ULG4TDUKV47DHHJSBDWVZQU4CU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULG4TDUKV47DHHJSBDWVZQU4CU/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":"2026-08-09T10:59:07Z","links":{"resolver":"https://pith.science/pith/ULG4TDUKV47DHHJSBDWVZQU4CU","bundle":"https://pith.science/pith/ULG4TDUKV47DHHJSBDWVZQU4CU/bundle.json","state":"https://pith.science/pith/ULG4TDUKV47DHHJSBDWVZQU4CU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULG4TDUKV47DHHJSBDWVZQU4CU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:ULG4TDUKV47DHHJSBDWVZQU4CU","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":"d3fb7fbfeb021a63aec15c87695172c2e79801971dd528b7e1cb03d0ac3628e4","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-31T11:50:33Z","title_canon_sha256":"05cddf5bf9e03730e3256020b6d5967a20b62d8f152bc85390fdaa74e4baf940"},"schema_version":"1.0","source":{"id":"2111.00473","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.00473","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"arxiv_version","alias_value":"2111.00473v4","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.00473","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"pith_short_12","alias_value":"ULG4TDUKV47D","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"pith_short_16","alias_value":"ULG4TDUKV47DHHJS","created_at":"2026-07-05T04:44:41Z"},{"alias_kind":"pith_short_8","alias_value":"ULG4TDUK","created_at":"2026-07-05T04:44:41Z"}],"graph_snapshots":[{"event_id":"sha256:b2c88ad5ddd20e9310856aebb874ee50a00b4cde90b37194e737e45207ec9c9e","target":"graph","created_at":"2026-07-05T04:44:41Z","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/2111.00473/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Anomaly, a generic feature of relativistic quantum field theory, is shown to be present in non-relativistic classical ideal fluid. A new result is the presence of anomalous terms in current algebra, an obvious analogue of Schwinger terms present in quantum field theory. We work in Hamiltonian framework where Eulerian dynamical variables obey an anomalous algebra (with Schwinger terms) that is inherited from modified Poisson brackets, with Berry curvature corrections, among Lagrangian discrete coordinates. The divergence anomaly appears in the Hamiltonian equations of motion. A generalized form","authors_text":"Arpan Krishna Mitra, Subir Ghosh","cross_cats":["quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-31T11:50:33Z","title":"Divergence Anomaly and Schwinger Terms: Towards a Consistent Theory of Anomalous Classical Fluid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.00473","kind":"arxiv","version":4},"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":"sha256:4026780de34d804de87952557feef3f327f1f9feeac463098944245be4961aa6","target":"record","created_at":"2026-07-05T04:44:41Z","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":"d3fb7fbfeb021a63aec15c87695172c2e79801971dd528b7e1cb03d0ac3628e4","cross_cats_sorted":["quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"hep-th","submitted_at":"2021-10-31T11:50:33Z","title_canon_sha256":"05cddf5bf9e03730e3256020b6d5967a20b62d8f152bc85390fdaa74e4baf940"},"schema_version":"1.0","source":{"id":"2111.00473","kind":"arxiv","version":4}},"canonical_sha256":"a2cdc98e8aaf3e339d3208ed5cc29c1539002ca9f2077841ffb60872d2750219","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2cdc98e8aaf3e339d3208ed5cc29c1539002ca9f2077841ffb60872d2750219","first_computed_at":"2026-07-05T04:44:41.273286Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:44:41.273286Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/HDYgiK/ETsETZecHJVP93VDFYwsAzR97OPv6OGpgdrRQAsc0Q9+pzUKhMTF7tH3NMZ3/lL8kqHKN7dk/GcBg==","signature_status":"signed_v1","signed_at":"2026-07-05T04:44:41.273712Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.00473","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4026780de34d804de87952557feef3f327f1f9feeac463098944245be4961aa6","sha256:b2c88ad5ddd20e9310856aebb874ee50a00b4cde90b37194e737e45207ec9c9e"],"state_sha256":"42ecc4dafaff15fb5a8dc5ef08bd60da113a4f4ffcce8e2ab1f28fc865125486"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QV1NAFIErWtIfC3MKqPNS7zZNQTrXckQVs6CaBzA+T5qQbty3BKUK5yzhfozXQ+JtI1E48wq/nVkj5+/kOCUDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T10:59:07.487981Z","bundle_sha256":"4e04c87f7458fa3ad651ff6c57046f403855293f545d6cc43321bacc72503be6"}}