{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:NDZEM4ORML2NJMW3NUC2ZJDSUA","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":"2aeb6e348b14a0434bce50e467d9e9a446790da2ea703e54168910c33de456b4","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-11-14T16:33:41Z","title_canon_sha256":"e4b77748db19f71e9fd1b24f21f6d1f4913273d495c8354355f386180676a046"},"schema_version":"1.0","source":{"id":"1911.06224","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1911.06224","created_at":"2026-07-05T01:50:57Z"},{"alias_kind":"arxiv_version","alias_value":"1911.06224v2","created_at":"2026-07-05T01:50:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1911.06224","created_at":"2026-07-05T01:50:57Z"},{"alias_kind":"pith_short_12","alias_value":"NDZEM4ORML2N","created_at":"2026-07-05T01:50:57Z"},{"alias_kind":"pith_short_16","alias_value":"NDZEM4ORML2NJMW3","created_at":"2026-07-05T01:50:57Z"},{"alias_kind":"pith_short_8","alias_value":"NDZEM4OR","created_at":"2026-07-05T01:50:57Z"}],"graph_snapshots":[{"event_id":"sha256:33359c386f6da375c7909dec5ae6ea90c5ae21fa1f7d1ecf518069c64a4f3056","target":"graph","created_at":"2026-07-05T01:50:57Z","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/1911.06224/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A general-covariant statistical framework capable of describing classical fluctuations of the gravitational field is a thorny open problem in theoretical physics, yet ultimately necessary to understand the nature of the gravitational interaction and a key to quantum gravity. Inspired by Souriau's symplectic generalization of the Maxwell-Boltzmann-Gibbs equilibrium in Lie group thermodynamics, we investigate a spacetime-covariant formulation of statistical mechanics for parametrized first-order field theories, as a simplified model sharing essential general covariant features with canonical gen","authors_text":"Fabio M. Mele, Goffredo Chirco, Marco Laudato","cross_cats":["gr-qc","hep-th","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-11-14T16:33:41Z","title":"Covariant Momentum Map Thermodynamics for Parametrized Field Theories"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1911.06224","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:c93458d95222df7d678f2aa421d091cf123e9515b534a11f99987936ba3b3c73","target":"record","created_at":"2026-07-05T01:50:57Z","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":"2aeb6e348b14a0434bce50e467d9e9a446790da2ea703e54168910c33de456b4","cross_cats_sorted":["gr-qc","hep-th","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-11-14T16:33:41Z","title_canon_sha256":"e4b77748db19f71e9fd1b24f21f6d1f4913273d495c8354355f386180676a046"},"schema_version":"1.0","source":{"id":"1911.06224","kind":"arxiv","version":2}},"canonical_sha256":"68f24671d162f4d4b2db6d05aca472a00d68f4519ffbffa3f1a00b269a4b373e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68f24671d162f4d4b2db6d05aca472a00d68f4519ffbffa3f1a00b269a4b373e","first_computed_at":"2026-07-05T01:50:57.460411Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:50:57.460411Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"779Ih9I3WFrLkCmZFjXiFzWWnf0mU7nJDS6U2jKdbYcDvx7YSVEJWEzWk1ghB6do43vAn653CBlk+0JBaV/FCg==","signature_status":"signed_v1","signed_at":"2026-07-05T01:50:57.460849Z","signed_message":"canonical_sha256_bytes"},"source_id":"1911.06224","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c93458d95222df7d678f2aa421d091cf123e9515b534a11f99987936ba3b3c73","sha256:33359c386f6da375c7909dec5ae6ea90c5ae21fa1f7d1ecf518069c64a4f3056"],"state_sha256":"ac1f73d00c612abfb1b8640f99556a90ceb9f9344363230653a2c347ced9c9ce"}