{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:UKCUO5VAZB4JFJWQXZ5GC2ZWPL","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":"a2e9025750ac84a6f840616c34a825a65451050eaa8a4ae774839fd1ea06ab32","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-28T20:21:27Z","title_canon_sha256":"8dfd856a4b74cf9f8c0029833909d4464b7821728b87f76c23389f9b07877dfc"},"schema_version":"1.0","source":{"id":"2606.29590","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.29590","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"arxiv_version","alias_value":"2606.29590v1","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.29590","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_12","alias_value":"UKCUO5VAZB4J","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_16","alias_value":"UKCUO5VAZB4JFJWQ","created_at":"2026-06-30T01:18:13Z"},{"alias_kind":"pith_short_8","alias_value":"UKCUO5VA","created_at":"2026-06-30T01:18:13Z"}],"graph_snapshots":[{"event_id":"sha256:660c0cd5266dcbc3177b3dd35ce2083c05316b8aabe40ec282d8aacc21f63958","target":"graph","created_at":"2026-06-30T01:18:13Z","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/2606.29590/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The threshold and scaling laws of gravitational critical collapse depend sensitively on the matter equation of state. We investigate how these quantities are modified by a generic feature of dense matter that is absent from the radiation fluid commonly assumed in primordial black hole (PBH) studies: pressure stiffening as a maximum density is approached. As an analytically tractable proxy, we adopt the closed-form equation of state of a single-occupancy lattice gas, \\(p=-T\\ln(1-\\rho)\\), which exhibits a density-dependent sound speed and a saturation density. Using general-relativistic simulati","authors_text":"Benaoumeur Bakhti","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-28T20:21:27Z","title":"Saturation Equations of State in Critical Gravitational Collapse: The Primordial Black Hole Threshold"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.29590","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:eb6d5304cfa919ab791be2285f1b2974bd84923308c65cd0a5229868d42e35bf","target":"record","created_at":"2026-06-30T01:18:13Z","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":"a2e9025750ac84a6f840616c34a825a65451050eaa8a4ae774839fd1ea06ab32","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"gr-qc","submitted_at":"2026-06-28T20:21:27Z","title_canon_sha256":"8dfd856a4b74cf9f8c0029833909d4464b7821728b87f76c23389f9b07877dfc"},"schema_version":"1.0","source":{"id":"2606.29590","kind":"arxiv","version":1}},"canonical_sha256":"a2854776a0c87892a6d0be7a616b367ad4de91db01905de7c38f8dd02acab62e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2854776a0c87892a6d0be7a616b367ad4de91db01905de7c38f8dd02acab62e","first_computed_at":"2026-06-30T01:18:13.287640Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-30T01:18:13.287640Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3rn+s/c42pk4HXA4297k1jzeX1QDBXii00SoJcoKwMzg7yHRZ5MIe2EE6iaSs8T7muFbHi3pzOXFr3qBYIWZDg==","signature_status":"signed_v1","signed_at":"2026-06-30T01:18:13.288247Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.29590","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb6d5304cfa919ab791be2285f1b2974bd84923308c65cd0a5229868d42e35bf","sha256:660c0cd5266dcbc3177b3dd35ce2083c05316b8aabe40ec282d8aacc21f63958"],"state_sha256":"7309848686e9391ac571cddea1c8384a39e76266fc1e6b134dd9b816b326b4ff"}