{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1998:T7PAFCVREZBQKUFPB6E43SKITT","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":"e3e66f8b105126af30f7214128d69d9033a19cf78dae093927a916f4036bf5b6","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1998-10-02T04:56:33Z","title_canon_sha256":"124548833fb8cb2adc80939228f38da32144c23d0c46407e6db614c6e1921bc7"},"schema_version":"1.0","source":{"id":"gr-qc/9810006","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/9810006","created_at":"2026-07-04T17:28:36Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/9810006v1","created_at":"2026-07-04T17:28:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/9810006","created_at":"2026-07-04T17:28:36Z"},{"alias_kind":"pith_short_12","alias_value":"T7PAFCVREZBQ","created_at":"2026-07-04T17:28:36Z"},{"alias_kind":"pith_short_16","alias_value":"T7PAFCVREZBQKUFP","created_at":"2026-07-04T17:28:36Z"},{"alias_kind":"pith_short_8","alias_value":"T7PAFCVR","created_at":"2026-07-04T17:28:36Z"}],"graph_snapshots":[{"event_id":"sha256:00001fb0d84451a1e3acddb1b36e3d45f92987a08ee56fb12c17727e71e3f7cb","target":"graph","created_at":"2026-07-04T17:28:36Z","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/gr-qc/9810006/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider two non-statistical definitions of entropy for dynamic (non-stationary) black holes in spherical symmetry. The first is analogous to the original Clausius definition of thermodynamic entropy: there is a first law containing an energy-supply term which equals surface gravity times a total differential. The second is Wald's Noether-charge method, adapted to dynamic black holes by using the Kodama flow. Both definitions give the same answer for Einstein gravity: one-quarter the area of the trapping horizon.","authors_text":"Sean A. Hayward, Shinji Mukohyama & M. C. Ashworth","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"1998-10-02T04:56:33Z","title":"Dynamic black-hole entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/9810006","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":"sha256:9eb903fc69b4fe9b05763c3f6559167c41839f2d72af1eb8027db043a7df61c7","target":"record","created_at":"2026-07-04T17:28:36Z","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":"e3e66f8b105126af30f7214128d69d9033a19cf78dae093927a916f4036bf5b6","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"1998-10-02T04:56:33Z","title_canon_sha256":"124548833fb8cb2adc80939228f38da32144c23d0c46407e6db614c6e1921bc7"},"schema_version":"1.0","source":{"id":"gr-qc/9810006","kind":"arxiv","version":1}},"canonical_sha256":"9fde028ab126430550af0f89cdc9489ce1c4a3ce8e3edafefb6c677dcb752682","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fde028ab126430550af0f89cdc9489ce1c4a3ce8e3edafefb6c677dcb752682","first_computed_at":"2026-07-04T17:28:36.760973Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:28:36.760973Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vaGk8tKdY716nVvRx3Kw3mU7pdPHZk5EjYSXTyXyMEm3ubTcAHVfz3CMag7byIhTROZPbvdrGr7zk6SPSf3QBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:28:36.761406Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/9810006","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9eb903fc69b4fe9b05763c3f6559167c41839f2d72af1eb8027db043a7df61c7","sha256:00001fb0d84451a1e3acddb1b36e3d45f92987a08ee56fb12c17727e71e3f7cb"],"state_sha256":"30db22f58a1100596be93a46343a36fdd38f88b401c210cb91cdb0fc78aac097"}