{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2005:K6GQPQ2QNQEYD5L6N5B36QFWI5","short_pith_number":"pith:K6GQPQ2Q","canonical_record":{"source":{"id":"gr-qc/0507022","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T17:06:29Z","cross_cats_sorted":["astro-ph","hep-th"],"title_canon_sha256":"4723bfe742aabdb56902f16610fee14057a9305b6153fbe6005ca1102abb4c11","abstract_canon_sha256":"af7accba72704625fe40ede45f1e8eb9499b3289843189e8b42742be29108740"},"schema_version":"1.0"},"canonical_sha256":"578d07c3506c0981f57e6f43bf40b6477edb948940172d6a101cc5a3078a490e","source":{"kind":"arxiv","id":"gr-qc/0507022","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0507022","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0507022v3","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0507022","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"K6GQPQ2QNQEY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"K6GQPQ2QNQEYD5L6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"K6GQPQ2Q","created_at":"2026-05-18T12:25:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2005:K6GQPQ2QNQEYD5L6N5B36QFWI5","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0507022","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T17:06:29Z","cross_cats_sorted":["astro-ph","hep-th"],"title_canon_sha256":"4723bfe742aabdb56902f16610fee14057a9305b6153fbe6005ca1102abb4c11","abstract_canon_sha256":"af7accba72704625fe40ede45f1e8eb9499b3289843189e8b42742be29108740"},"schema_version":"1.0"},"canonical_sha256":"578d07c3506c0981f57e6f43bf40b6477edb948940172d6a101cc5a3078a490e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:06:45.428718Z","signature_b64":"5fhBwFe+Prx1+OwKphSTv7gtHUzJeSh51LfAPtHpuon5T8MWaAfvZ2XtLYmsrgaktCGajbr8ECj6ayI4ESxUDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"578d07c3506c0981f57e6f43bf40b6477edb948940172d6a101cc5a3078a490e","last_reissued_at":"2026-05-18T01:06:45.428237Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:06:45.428237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0507022","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":"2026-05-18T01:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QbNHnCshPpexOZjSMSjbSmktyx9SSZmeCLKkyTE5Vyh6Tmu4mbiIMv8HKjMTQrFeexb8sfMqNn94gGiqoUIDBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:34:40.880254Z"},"content_sha256":"71a370c0c9dbcf56d88d4602694221f38e408f0f378889ea20559d607c4102ea","schema_version":"1.0","event_id":"sha256:71a370c0c9dbcf56d88d4602694221f38e408f0f378889ea20559d607c4102ea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2005:K6GQPQ2QNQEYD5L6N5B36QFWI5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Some Statistical Mechanical Properties of Photon Black Holes","license":"","headline":"","cross_cats":["astro-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"C. S. Lopez-Monsalvo, R. A. Sussman, S. Mendoza, X. Hernandez","submitted_at":"2005-07-06T17:06:29Z","abstract_excerpt":"We show that if the total internal energy of a black hole is constructed as the sum of $N$ photons all having a fixed wavelength chosen to scale with the Schwarzschild radius as $\\lambda=\\alpha R_{s}$, then $N$ will scale with $R_{s}^{2}$. A statistical mechanical calculation of the configuration proposed yields (\\alpha = 4 \\pi^2 / \\ln(2)) and a total entropy of the system $S=k_{B}N \\ln(2)$, in agreement with the Bekenstein entropy of a black hole . It is shown that the critical temperature for Bose-Einstein condensation for relativistic particles of $\\lambda=\\alpha R_{s}$ is always well below"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0507022","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":"2026-05-18T01:06:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"z5vJ3CPmjb6iiTTuXouadB+Le2x5h9jYhaxdej5ZgVQe/aB25x3SJLmtO60Z2VjYc+8F0OOg/aa/F3HVFSCKDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T20:34:40.880976Z"},"content_sha256":"afe488d99cd1aeec1b327bcae169f39d5fe43e477b6b9c476eb5472a6f3af9a3","schema_version":"1.0","event_id":"sha256:afe488d99cd1aeec1b327bcae169f39d5fe43e477b6b9c476eb5472a6f3af9a3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K6GQPQ2QNQEYD5L6N5B36QFWI5/bundle.json","state_url":"https://pith.science/pith/K6GQPQ2QNQEYD5L6N5B36QFWI5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K6GQPQ2QNQEYD5L6N5B36QFWI5/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":"2026-06-06T20:34:40Z","links":{"resolver":"https://pith.science/pith/K6GQPQ2QNQEYD5L6N5B36QFWI5","bundle":"https://pith.science/pith/K6GQPQ2QNQEYD5L6N5B36QFWI5/bundle.json","state":"https://pith.science/pith/K6GQPQ2QNQEYD5L6N5B36QFWI5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K6GQPQ2QNQEYD5L6N5B36QFWI5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:K6GQPQ2QNQEYD5L6N5B36QFWI5","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":"af7accba72704625fe40ede45f1e8eb9499b3289843189e8b42742be29108740","cross_cats_sorted":["astro-ph","hep-th"],"license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T17:06:29Z","title_canon_sha256":"4723bfe742aabdb56902f16610fee14057a9305b6153fbe6005ca1102abb4c11"},"schema_version":"1.0","source":{"id":"gr-qc/0507022","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0507022","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0507022v3","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0507022","created_at":"2026-05-18T01:06:45Z"},{"alias_kind":"pith_short_12","alias_value":"K6GQPQ2QNQEY","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_16","alias_value":"K6GQPQ2QNQEYD5L6","created_at":"2026-05-18T12:25:53Z"},{"alias_kind":"pith_short_8","alias_value":"K6GQPQ2Q","created_at":"2026-05-18T12:25:53Z"}],"graph_snapshots":[{"event_id":"sha256:afe488d99cd1aeec1b327bcae169f39d5fe43e477b6b9c476eb5472a6f3af9a3","target":"graph","created_at":"2026-05-18T01:06:45Z","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":"We show that if the total internal energy of a black hole is constructed as the sum of $N$ photons all having a fixed wavelength chosen to scale with the Schwarzschild radius as $\\lambda=\\alpha R_{s}$, then $N$ will scale with $R_{s}^{2}$. A statistical mechanical calculation of the configuration proposed yields (\\alpha = 4 \\pi^2 / \\ln(2)) and a total entropy of the system $S=k_{B}N \\ln(2)$, in agreement with the Bekenstein entropy of a black hole . It is shown that the critical temperature for Bose-Einstein condensation for relativistic particles of $\\lambda=\\alpha R_{s}$ is always well below","authors_text":"C. S. Lopez-Monsalvo, R. A. Sussman, S. Mendoza, X. Hernandez","cross_cats":["astro-ph","hep-th"],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T17:06:29Z","title":"Some Statistical Mechanical Properties of Photon Black Holes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0507022","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":"sha256:71a370c0c9dbcf56d88d4602694221f38e408f0f378889ea20559d607c4102ea","target":"record","created_at":"2026-05-18T01:06:45Z","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":"af7accba72704625fe40ede45f1e8eb9499b3289843189e8b42742be29108740","cross_cats_sorted":["astro-ph","hep-th"],"license":"","primary_cat":"gr-qc","submitted_at":"2005-07-06T17:06:29Z","title_canon_sha256":"4723bfe742aabdb56902f16610fee14057a9305b6153fbe6005ca1102abb4c11"},"schema_version":"1.0","source":{"id":"gr-qc/0507022","kind":"arxiv","version":3}},"canonical_sha256":"578d07c3506c0981f57e6f43bf40b6477edb948940172d6a101cc5a3078a490e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"578d07c3506c0981f57e6f43bf40b6477edb948940172d6a101cc5a3078a490e","first_computed_at":"2026-05-18T01:06:45.428237Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:06:45.428237Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"5fhBwFe+Prx1+OwKphSTv7gtHUzJeSh51LfAPtHpuon5T8MWaAfvZ2XtLYmsrgaktCGajbr8ECj6ayI4ESxUDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:06:45.428718Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0507022","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71a370c0c9dbcf56d88d4602694221f38e408f0f378889ea20559d607c4102ea","sha256:afe488d99cd1aeec1b327bcae169f39d5fe43e477b6b9c476eb5472a6f3af9a3"],"state_sha256":"106a7e3f43679b08bde8d58ec0b1ecc04aee56f40c187d183bf67d206e2a7a6b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6w98CihOKs1ruj1yQd+ziYI0XWHjxj/Vj+HrLfDN8M6LfENe3nLqeIziJ5ySmrPkrXaX/vNKhw1DuBt2xVDKBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T20:34:40.884405Z","bundle_sha256":"0a54756a2aeb83a0a9f23c7ee535bc585b90f40bfeaaa088ac6c1ac4a6afc32c"}}