{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:ZKDGAECXSW62CWM5WTKEFHHCTY","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":"8d8ba32a3718793fed7a23a0c5ae6fa4f299f3f400be5f4580e3f1dcebdd893e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-05-16T17:59:21Z","title_canon_sha256":"ef3ab0597e78c032da00b997577c681c9f623ed7f424247816be0e2a9f9b29cb"},"schema_version":"1.0","source":{"id":"2505.11585","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2505.11585","created_at":"2026-07-05T11:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"2505.11585v1","created_at":"2026-07-05T11:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2505.11585","created_at":"2026-07-05T11:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"ZKDGAECXSW62","created_at":"2026-07-05T11:04:24Z"},{"alias_kind":"pith_short_16","alias_value":"ZKDGAECXSW62CWM5","created_at":"2026-07-05T11:04:24Z"},{"alias_kind":"pith_short_8","alias_value":"ZKDGAECX","created_at":"2026-07-05T11:04:24Z"}],"graph_snapshots":[{"event_id":"sha256:9df4e24f32acb6120b569237675213066c36d7fb97a51a774c9b5a51def6a200","target":"graph","created_at":"2026-07-05T11:04:24Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2505.11585/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The issue of defining the volume of black holes has significant implications for quantum gravity. Drawing on concepts from quantum theory and general relativity, several motivations for introducing discreteness in geometry can be proposed. However, to seriously consider any proposal for a discrete geometry, the identification problem and the challenge of defining a distance function within such a geometry must be addressed. This paper proposes the faithful embedding of sets representing spaces in finite geometry -- a specific type of discrete geometry characterized by a finite set of points --","authors_text":"Arkady Bolotin","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-05-16T17:59:21Z","title":"Finite geometry and black hole stability: Embedding discrete space into classical manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2505.11585","kind":"arxiv","version":1},"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":"sha256:7b9ab7e3d6ab30e8b96a94beb2d950edd026fe390171ac3ec8124365475ab6ff","target":"record","created_at":"2026-07-05T11:04:24Z","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":"8d8ba32a3718793fed7a23a0c5ae6fa4f299f3f400be5f4580e3f1dcebdd893e","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2025-05-16T17:59:21Z","title_canon_sha256":"ef3ab0597e78c032da00b997577c681c9f623ed7f424247816be0e2a9f9b29cb"},"schema_version":"1.0","source":{"id":"2505.11585","kind":"arxiv","version":1}},"canonical_sha256":"ca8660105795bda1599db4d4429ce29e190ec180d74d39bf34850b2d6895f992","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ca8660105795bda1599db4d4429ce29e190ec180d74d39bf34850b2d6895f992","first_computed_at":"2026-07-05T11:04:24.049367Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:04:24.049367Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"rrpmdCfpc+p0eDYzv1ekn62c5w1rKa0lr/dZkN09kUuhGuKIrRG8yVXyVuWbVtsRneIMJri+inDkIR7D0fBnDA==","signature_status":"signed_v1","signed_at":"2026-07-05T11:04:24.049908Z","signed_message":"canonical_sha256_bytes"},"source_id":"2505.11585","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7b9ab7e3d6ab30e8b96a94beb2d950edd026fe390171ac3ec8124365475ab6ff","sha256:9df4e24f32acb6120b569237675213066c36d7fb97a51a774c9b5a51def6a200"],"state_sha256":"2bf8b6e4c82dd99344dc0adb63ad43484ce6d3883667ae4b0afdf8ec666cc6b1"}