{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:YXLXDPZD7ELGOWWCEG65CTOXCY","short_pith_number":"pith:YXLXDPZD","canonical_record":{"source":{"id":"1701.06193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-22T17:27:25Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"8e5e658e2c6014909b07d9c5af421b53bd8bfa45f9d911b87f634c15f00309d4","abstract_canon_sha256":"fa66a90950c11fb60e9744fdffc97f7b710bfb238a286bf8d010913a09acf3fa"},"schema_version":"1.0"},"canonical_sha256":"c5d771bf23f916675ac221bdd14dd7160c2830e35609eea2da009ab55bb5fa4c","source":{"kind":"arxiv","id":"1701.06193","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06193","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06193v2","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06193","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"pith_short_12","alias_value":"YXLXDPZD7ELG","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YXLXDPZD7ELGOWWC","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YXLXDPZD","created_at":"2026-05-18T12:31:56Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:YXLXDPZD7ELGOWWCEG65CTOXCY","target":"record","payload":{"canonical_record":{"source":{"id":"1701.06193","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-22T17:27:25Z","cross_cats_sorted":["gr-qc"],"title_canon_sha256":"8e5e658e2c6014909b07d9c5af421b53bd8bfa45f9d911b87f634c15f00309d4","abstract_canon_sha256":"fa66a90950c11fb60e9744fdffc97f7b710bfb238a286bf8d010913a09acf3fa"},"schema_version":"1.0"},"canonical_sha256":"c5d771bf23f916675ac221bdd14dd7160c2830e35609eea2da009ab55bb5fa4c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:33.644089Z","signature_b64":"4ioSUCVmcurOsL932pHE8q88/3BR+bO44iCaeQyCG+wGETuRXj8IOVYqOUBEsI4u3JjbRYV9vz56iey+DO/PCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c5d771bf23f916675ac221bdd14dd7160c2830e35609eea2da009ab55bb5fa4c","last_reissued_at":"2026-05-18T00:51:33.643484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:33.643484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.06193","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:51:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lgY01wN6U9yPpP6oYtuOlfbGOdeFyyyNpyLEeFwCRHuJwvt8nhnDBwslJ/BtClT3xp9iu/7htu3SDTYpwpXJDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:26:21.008914Z"},"content_sha256":"d5b9c28af54ddb35c5035ff5d98502211655e3a62e60281c764789df9e144357","schema_version":"1.0","event_id":"sha256:d5b9c28af54ddb35c5035ff5d98502211655e3a62e60281c764789df9e144357"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:YXLXDPZD7ELGOWWCEG65CTOXCY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Statistical mechanics of gravitons in a box and the black hole entropy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"hep-th","authors_text":"Stefano Viaggiu","submitted_at":"2017-01-22T17:27:25Z","abstract_excerpt":"This paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index $\\ell$ similar to the harmonic oscillator one is obtained and a statistical study is performed. The mean energy $<E>$ results as a sum of two discrete Planck distributions with different dependent frequencies. As an important application, we derive the semiclassical Bekenstein-Hawking entropy formula for a static Schwarzschild black hole by only requiring that the black hole int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06193","kind":"arxiv","version":2},"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":"2026-05-18T00:51:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyxYoQ+tFiWXjJg2EzFpvEC6Sx1bQnIPbLD+6hkUGgMDMC4qV3MaIVAbJ1BiRyFJAGrWijiIPf4HfuPZdS7FBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T17:26:21.009260Z"},"content_sha256":"ba5270da6991ad7f714c681eddb20bdc477155f330f1de7834c1d77072582c00","schema_version":"1.0","event_id":"sha256:ba5270da6991ad7f714c681eddb20bdc477155f330f1de7834c1d77072582c00"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/YXLXDPZD7ELGOWWCEG65CTOXCY/bundle.json","state_url":"https://pith.science/pith/YXLXDPZD7ELGOWWCEG65CTOXCY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/YXLXDPZD7ELGOWWCEG65CTOXCY/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":"2026-06-02T17:26:21Z","links":{"resolver":"https://pith.science/pith/YXLXDPZD7ELGOWWCEG65CTOXCY","bundle":"https://pith.science/pith/YXLXDPZD7ELGOWWCEG65CTOXCY/bundle.json","state":"https://pith.science/pith/YXLXDPZD7ELGOWWCEG65CTOXCY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/YXLXDPZD7ELGOWWCEG65CTOXCY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:YXLXDPZD7ELGOWWCEG65CTOXCY","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":"fa66a90950c11fb60e9744fdffc97f7b710bfb238a286bf8d010913a09acf3fa","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-22T17:27:25Z","title_canon_sha256":"8e5e658e2c6014909b07d9c5af421b53bd8bfa45f9d911b87f634c15f00309d4"},"schema_version":"1.0","source":{"id":"1701.06193","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.06193","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"arxiv_version","alias_value":"1701.06193v2","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.06193","created_at":"2026-05-18T00:51:33Z"},{"alias_kind":"pith_short_12","alias_value":"YXLXDPZD7ELG","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_16","alias_value":"YXLXDPZD7ELGOWWC","created_at":"2026-05-18T12:31:56Z"},{"alias_kind":"pith_short_8","alias_value":"YXLXDPZD","created_at":"2026-05-18T12:31:56Z"}],"graph_snapshots":[{"event_id":"sha256:ba5270da6991ad7f714c681eddb20bdc477155f330f1de7834c1d77072582c00","target":"graph","created_at":"2026-05-18T00:51:33Z","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 paper is devoted to the study of the statistical mechanics of trapped gravitons obtained by 'trapping' a spherical gravitational wave in a box. As a consequence, a discrete spectrum dependent on the Legendre index $\\ell$ similar to the harmonic oscillator one is obtained and a statistical study is performed. The mean energy $<E>$ results as a sum of two discrete Planck distributions with different dependent frequencies. As an important application, we derive the semiclassical Bekenstein-Hawking entropy formula for a static Schwarzschild black hole by only requiring that the black hole int","authors_text":"Stefano Viaggiu","cross_cats":["gr-qc"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-22T17:27:25Z","title":"Statistical mechanics of gravitons in a box and the black hole entropy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.06193","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:d5b9c28af54ddb35c5035ff5d98502211655e3a62e60281c764789df9e144357","target":"record","created_at":"2026-05-18T00:51:33Z","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":"fa66a90950c11fb60e9744fdffc97f7b710bfb238a286bf8d010913a09acf3fa","cross_cats_sorted":["gr-qc"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2017-01-22T17:27:25Z","title_canon_sha256":"8e5e658e2c6014909b07d9c5af421b53bd8bfa45f9d911b87f634c15f00309d4"},"schema_version":"1.0","source":{"id":"1701.06193","kind":"arxiv","version":2}},"canonical_sha256":"c5d771bf23f916675ac221bdd14dd7160c2830e35609eea2da009ab55bb5fa4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5d771bf23f916675ac221bdd14dd7160c2830e35609eea2da009ab55bb5fa4c","first_computed_at":"2026-05-18T00:51:33.643484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:51:33.643484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4ioSUCVmcurOsL932pHE8q88/3BR+bO44iCaeQyCG+wGETuRXj8IOVYqOUBEsI4u3JjbRYV9vz56iey+DO/PCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:51:33.644089Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.06193","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d5b9c28af54ddb35c5035ff5d98502211655e3a62e60281c764789df9e144357","sha256:ba5270da6991ad7f714c681eddb20bdc477155f330f1de7834c1d77072582c00"],"state_sha256":"a910f8f98060a8319c023f8cb1e0ced7dad6a0ad9ce250b36de14b75687cb49e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xRfremit8oBtX78KemXBc9aKiDgQzKxNVGD4o8hVjMFETVG/A5x1F8mr1T1SEhaljRbcbNcDLx4u9mSGrTtEBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T17:26:21.012430Z","bundle_sha256":"e4fdf3032291f8f020e10ff8a6fb6438586b6fe2888e55f639594f51d7580ab9"}}