{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:NCYU5PLH4VZ7KWSVSOV3GLXHKH","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":"1e994c7f7f98d1381475d36081a5f0f95b894739bc647e5830c62077915d3e92","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-12-01T17:33:08Z","title_canon_sha256":"118f0f18d25fbdf72232f4cf00f6a459ed136a51e70d14b978ec7e1e42c88f1f"},"schema_version":"1.0","source":{"id":"2512.01916","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2512.01916","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"arxiv_version","alias_value":"2512.01916v2","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2512.01916","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_12","alias_value":"NCYU5PLH4VZ7","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_16","alias_value":"NCYU5PLH4VZ7KWSV","created_at":"2026-05-21T01:04:19Z"},{"alias_kind":"pith_short_8","alias_value":"NCYU5PLH","created_at":"2026-05-21T01:04:19Z"}],"graph_snapshots":[{"event_id":"sha256:e0bf6f8ced00c0eb288a106c4de13dcc42c25a647a667cbd4c1ff57158998c31","target":"graph","created_at":"2026-05-21T01:04:19Z","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/2512.01916/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In extended black hole thermodynamics, the cosmological constant and other couplings are treated as thermodynamic variables, yielding the first law $\\tilde{\\delta}M = T\\tilde{\\delta}S+\\Omega\\tilde{\\delta}J +\\mathcal{V} \\tilde{\\delta}P+\\cdots$, where $P\\equiv -\\frac{\\Lambda}{8\\pi}$. A long-standing conceptual gap in this framework is that, unlike $M$, $T$, $S$, $\\Omega$, and $J$, the thermodynamic volume $\\mathcal{V} $ lacks a first-principles definition and can only be deduced from other thermodynamic quantities. This deficiency indicates that the underlying origin of $\\mathcal{V} $ remains po","authors_text":"Hongbao Zhang, Yong Xiao, Yu Tian, Yu-Xiao Liu","cross_cats":["hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-12-01T17:33:08Z","title":"Explicit and covariant formula for thermodynamic volume in extended black hole thermodynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2512.01916","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":"sha256:3ff83bd1c5fcc19ea791d41d66101d05de048c21c2dc4e4ad280942279fffeda","target":"record","created_at":"2026-05-21T01:04:19Z","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":"1e994c7f7f98d1381475d36081a5f0f95b894739bc647e5830c62077915d3e92","cross_cats_sorted":["hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2025-12-01T17:33:08Z","title_canon_sha256":"118f0f18d25fbdf72232f4cf00f6a459ed136a51e70d14b978ec7e1e42c88f1f"},"schema_version":"1.0","source":{"id":"2512.01916","kind":"arxiv","version":2}},"canonical_sha256":"68b14ebd67e573f55a5593abb32ee751de73b3e0778685dc8b499cae63f76a1c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"68b14ebd67e573f55a5593abb32ee751de73b3e0778685dc8b499cae63f76a1c","first_computed_at":"2026-05-21T01:04:19.338179Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-21T01:04:19.338179Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aMgN6UxAan3xYb6E5zCngruaFDHH32KlDkKA0kTOU/gwd8m6rncl0F465Zsmbv0BsGbl2O+wg/oG8BTGMkDdCQ==","signature_status":"signed_v1","signed_at":"2026-05-21T01:04:19.338983Z","signed_message":"canonical_sha256_bytes"},"source_id":"2512.01916","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3ff83bd1c5fcc19ea791d41d66101d05de048c21c2dc4e4ad280942279fffeda","sha256:e0bf6f8ced00c0eb288a106c4de13dcc42c25a647a667cbd4c1ff57158998c31"],"state_sha256":"c2e186733a075667ea5b2846d5fb74276653302f95dfffb38ba0e121aa0f6a48"}