{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:PXK45CCVF3AY5K26XNJV3NH5JA","short_pith_number":"pith:PXK45CCV","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"},"canonical_sha256":"7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024","source":{"kind":"arxiv","id":"1209.2016","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2016","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2016v3","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2016","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"PXK45CCVF3AY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PXK45CCVF3AY5K26","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PXK45CCV","created_at":"2026-05-18T12:27:18Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:PXK45CCVF3AY5K26XNJV3NH5JA","target":"record","payload":{"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"},"canonical_sha256":"7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024","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"},"source_kind":"arxiv","source_id":"1209.2016","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K27wskceM0C8jyjmjo7mHJw7rS7iRQS1oMtLcpnBocaCGyFeIEotUZtKkpqgO2s0eEv61QhAFEy0POfedRkhCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:19:31.616035Z"},"content_sha256":"7ddeb24eb196b685134046e23e8bb4fe4cf659d035e4489ae97d41182bda6a2f","schema_version":"1.0","event_id":"sha256:7ddeb24eb196b685134046e23e8bb4fe4cf659d035e4489ae97d41182bda6a2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:PXK45CCVF3AY5K26XNJV3NH5JA","target":"graph","payload":{"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:56:52Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rQZMsGU08af9J/YRy76HKXpLYYjf6YJY/zsX9bcqbUaAiIm6I21jybQYbiWXbtnTlbPssRM5Fu9UwZqz4/dgDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T10:19:31.616480Z"},"content_sha256":"317320ab5459fcdae64b32a9f321434a09c58a52d066e088f2613b262de8d20d","schema_version":"1.0","event_id":"sha256:317320ab5459fcdae64b32a9f321434a09c58a52d066e088f2613b262de8d20d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/bundle.json","state_url":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PXK45CCVF3AY5K26XNJV3NH5JA/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-28T10:19:31Z","links":{"resolver":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA","bundle":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/bundle.json","state":"https://pith.science/pith/PXK45CCVF3AY5K26XNJV3NH5JA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PXK45CCVF3AY5K26XNJV3NH5JA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:PXK45CCVF3AY5K26XNJV3NH5JA","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":"b03ec9c75dd8edba1669d0d31b2bba0ace5803fad29707e40de372f8ed9f414d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-06T17:47:16Z","title_canon_sha256":"886639793c41d5af37771f2d2f622d46712b58263b86879876e1a1c2b48482d3"},"schema_version":"1.0","source":{"id":"1209.2016","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1209.2016","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1209.2016v3","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1209.2016","created_at":"2026-05-18T00:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"PXK45CCVF3AY","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_16","alias_value":"PXK45CCVF3AY5K26","created_at":"2026-05-18T12:27:18Z"},{"alias_kind":"pith_short_8","alias_value":"PXK45CCV","created_at":"2026-05-18T12:27:18Z"}],"graph_snapshots":[{"event_id":"sha256:317320ab5459fcdae64b32a9f321434a09c58a52d066e088f2613b262de8d20d","target":"graph","created_at":"2026-05-18T00:56:52Z","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"},"paper":{"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","authors_text":"Andreas G. A. Pithis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-06T17:47:16Z","title":"The Gibbs paradox, Black hole entropy and the thermodynamics of isolated horizons"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.2016","kind":"arxiv","version":3},"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":"sha256:7ddeb24eb196b685134046e23e8bb4fe4cf659d035e4489ae97d41182bda6a2f","target":"record","created_at":"2026-05-18T00:56:52Z","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":"b03ec9c75dd8edba1669d0d31b2bba0ace5803fad29707e40de372f8ed9f414d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2012-09-06T17:47:16Z","title_canon_sha256":"886639793c41d5af37771f2d2f622d46712b58263b86879876e1a1c2b48482d3"},"schema_version":"1.0","source":{"id":"1209.2016","kind":"arxiv","version":3}},"canonical_sha256":"7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7dd5ce88552ec18eab5ebb535db4fd48384ab956b983d0e24258e5313dc22024","first_computed_at":"2026-05-18T00:56:52.497957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:56:52.497957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"poai4vz2sd05VMjIU4aA48qOucjOFEzcaGVdr84gzPz6X5MCyfborlDXGRlMNbvKS1AeFy3Da6Oww1NIrXPnDg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:56:52.498485Z","signed_message":"canonical_sha256_bytes"},"source_id":"1209.2016","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7ddeb24eb196b685134046e23e8bb4fe4cf659d035e4489ae97d41182bda6a2f","sha256:317320ab5459fcdae64b32a9f321434a09c58a52d066e088f2613b262de8d20d"],"state_sha256":"8205888c7fbe8eeff5931ef7948c69567efa310fad5dfefa7f01e8f3e481e5ae"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UUZ14n3pNHSVyCX1MwV4IJpw1sjY5HDbOD85MGjs2GEkObR3O9+uQy0DzbeIgRnE3Ox5RZtTGxYJgWA1JH7CCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T10:19:31.618202Z","bundle_sha256":"f62892fbf5b692ed240b650d0f05dc05e77a42c9e46aee675e60ba68a0439aca"}}