{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:3BGFVWYJMJVCETPCLQGSAO4JE5","short_pith_number":"pith:3BGFVWYJ","schema_version":"1.0","canonical_sha256":"d84c5adb09626a224de25c0d203b892763453cdce80353fce3cfb5313fc2ce9f","source":{"kind":"arxiv","id":"2606.30507","version":1},"attestation_state":"computed","paper":{"title":"The Role of the Volume in Black Hole Thermodynamics","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"William Ballik","submitted_at":"2026-06-29T16:13:54Z","abstract_excerpt":"Gibbons et al. [arXiv:hep-th/0408217] found the energy $E$ of Kerr--anti-de Sitter black holes by integrating the first law of black hole thermodynamics. They found that $E$ corresponds to the Ashtekar--Magnon--Das (AMD) energy associated with an asymptotically nonrotating frame, whereas the AMD ``energy'' which I will call $F$ associated with an asymptotically rotating frame does not satisfy the first law. In Cveti\\v{c} et al. [arXiv:1012.2888], the first law was extended by interpreting $E$ as an enthalpy and $\\Lambda$ as being proportional to a pressure. The term conjugate to the pressure w"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.30507","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-29T16:13:54Z","cross_cats_sorted":[],"title_canon_sha256":"7da9df8b64a0bd150892903d55b3248f4ae4a08b44d47d942591c2d6cc8848d7","abstract_canon_sha256":"f348256519d4cb570e495008682e0cbf8414e9ae7fd67d0362638a1745b6e523"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-30T02:18:18.101008Z","signature_b64":"Jdi+GZ3YBj32INoon36ghIcOIQDfby8DRuM9/cYE/6P46+m4G0xfcrYxwYnc/YQnW/94Lm1E2aUY61B8/i+6Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d84c5adb09626a224de25c0d203b892763453cdce80353fce3cfb5313fc2ce9f","last_reissued_at":"2026-06-30T02:18:18.100435Z","signature_status":"signed_v1","first_computed_at":"2026-06-30T02:18:18.100435Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Role of the Volume in Black Hole Thermodynamics","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"William Ballik","submitted_at":"2026-06-29T16:13:54Z","abstract_excerpt":"Gibbons et al. [arXiv:hep-th/0408217] found the energy $E$ of Kerr--anti-de Sitter black holes by integrating the first law of black hole thermodynamics. They found that $E$ corresponds to the Ashtekar--Magnon--Das (AMD) energy associated with an asymptotically nonrotating frame, whereas the AMD ``energy'' which I will call $F$ associated with an asymptotically rotating frame does not satisfy the first law. In Cveti\\v{c} et al. [arXiv:1012.2888], the first law was extended by interpreting $E$ as an enthalpy and $\\Lambda$ as being proportional to a pressure. The term conjugate to the pressure w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30507","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/2606.30507/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.30507","created_at":"2026-06-30T02:18:18.100527+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.30507v1","created_at":"2026-06-30T02:18:18.100527+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.30507","created_at":"2026-06-30T02:18:18.100527+00:00"},{"alias_kind":"pith_short_12","alias_value":"3BGFVWYJMJVC","created_at":"2026-06-30T02:18:18.100527+00:00"},{"alias_kind":"pith_short_16","alias_value":"3BGFVWYJMJVCETPC","created_at":"2026-06-30T02:18:18.100527+00:00"},{"alias_kind":"pith_short_8","alias_value":"3BGFVWYJ","created_at":"2026-06-30T02:18:18.100527+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5","json":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5.json","graph_json":"https://pith.science/api/pith-number/3BGFVWYJMJVCETPCLQGSAO4JE5/graph.json","events_json":"https://pith.science/api/pith-number/3BGFVWYJMJVCETPCLQGSAO4JE5/events.json","paper":"https://pith.science/paper/3BGFVWYJ"},"agent_actions":{"view_html":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5","download_json":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5.json","view_paper":"https://pith.science/paper/3BGFVWYJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.30507&json=true","fetch_graph":"https://pith.science/api/pith-number/3BGFVWYJMJVCETPCLQGSAO4JE5/graph.json","fetch_events":"https://pith.science/api/pith-number/3BGFVWYJMJVCETPCLQGSAO4JE5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5/action/storage_attestation","attest_author":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5/action/author_attestation","sign_citation":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5/action/citation_signature","submit_replication":"https://pith.science/pith/3BGFVWYJMJVCETPCLQGSAO4JE5/action/replication_record"}},"created_at":"2026-06-30T02:18:18.100527+00:00","updated_at":"2026-06-30T02:18:18.100527+00:00"}