{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:PXK45CCVF3AY5K26XNJV3NH5JA","short_pith_number":"pith:PXK45CCV","schema_version":"1.0","canonical_sha256":"7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024","source":{"kind":"arxiv","id":"1209.2016","version":3},"attestation_state":"computed","paper":{"title":"The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Andreas G. A. Pithis","submitted_at":"2012-09-06T17:47:16Z","abstract_excerpt":"This letter presents a new, solely thermodynamical argument for considering the states of the quantum isolated horizon of a black hole as distinguishable. We claim that only if the states are distinguishable, the thermodynamic entropy is an extensive quantity and can be well-defined. To show this, we make a comparison with a classical ideal gas system whose statistical description makes only sense if an additional 1/N!-factor is included in the state counting in order to cure the Gibbs paradox. The case of the statistical description of a quantum isolated horizon is elaborated, to make the cla"},"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":"1209.2016","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-06T17:47:16Z","cross_cats_sorted":[],"title_canon_sha256":"886639793c41d5af37771f2d2f622d46712b58263b86879876e1a1c2b48482d3","abstract_canon_sha256":"b03ec9c75dd8edba1669d0d31b2bba0ace5803fad29707e40de372f8ed9f414d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:56:52.498485Z","signature_b64":"poai4vz2sd05VMjIU4aA48qOucjOFEzcaGVdr84gzPz6X5MCyfborlDXGRlMNbvKS1AeFy3Da6Oww1NIrXPnDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024","last_reissued_at":"2026-05-18T00:56:52.497957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:56:52.497957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Andreas G. A. Pithis","submitted_at":"2012-09-06T17:47:16Z","abstract_excerpt":"This letter presents a new, solely thermodynamical argument for considering the states of the quantum isolated horizon of a black hole as distinguishable. We claim that only if the states are distinguishable, the thermodynamic entropy is an extensive quantity and can be well-defined. To show this, we make a comparison with a classical ideal gas system whose statistical description makes only sense if an additional 1/N!-factor is included in the state counting in order to cure the Gibbs paradox. The case of the statistical description of a quantum isolated horizon is elaborated, to make the cla"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2016","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1209.2016","created_at":"2026-05-18T00:56:52.498038+00:00"},{"alias_kind":"arxiv_version","alias_value":"1209.2016v3","created_at":"2026-05-18T00:56:52.498038+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2016","created_at":"2026-05-18T00:56:52.498038+00:00"},{"alias_kind":"pith_short_12","alias_value":"PXK45CCVF3AY","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"PXK45CCVF3AY5K26","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"PXK45CCV","created_at":"2026-05-18T12:27:18.751474+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/PXK45CCVF3AY5K26XNJV3NH5JA","json":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA.json","graph_json":"https://pith.science/api/pith-number/PXK45CCVF3AY5K26XNJV3NH5JA/graph.json","events_json":"https://pith.science/api/pith-number/PXK45CCVF3AY5K26XNJV3NH5JA/events.json","paper":"https://pith.science/paper/PXK45CCV"},"agent_actions":{"view_html":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA","download_json":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA.json","view_paper":"https://pith.science/paper/PXK45CCV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1209.2016&json=true","fetch_graph":"https://pith.science/api/pith-number/PXK45CCVF3AY5K26XNJV3NH5JA/graph.json","fetch_events":"https://pith.science/api/pith-number/PXK45CCVF3AY5K26XNJV3NH5JA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/action/storage_attestation","attest_author":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/action/author_attestation","sign_citation":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/action/citation_signature","submit_replication":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/action/replication_record"}},"created_at":"2026-05-18T00:56:52.498038+00:00","updated_at":"2026-05-18T00:56:52.498038+00:00"}