{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:26OG3TK7QFJ2AX723XR7FX7SXS","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":"a91d4fb90ccaf623ad1726f6027fd78495de504de3d940995358e482d042f1e3","cross_cats_sorted":["math-ph","math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-02-15T18:46:40Z","title_canon_sha256":"03ef528272832606ce1ed847940be6849d2d435ab06f427d4085f090ffa6b77a"},"schema_version":"1.0","source":{"id":"2402.10190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.10190","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"arxiv_version","alias_value":"2402.10190v1","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.10190","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"pith_short_12","alias_value":"26OG3TK7QFJ2","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"pith_short_16","alias_value":"26OG3TK7QFJ2AX72","created_at":"2026-07-05T07:45:42Z"},{"alias_kind":"pith_short_8","alias_value":"26OG3TK7","created_at":"2026-07-05T07:45:42Z"}],"graph_snapshots":[{"event_id":"sha256:4b5c8b214292ea761ec44c08479406a4d7a62b5bae80ce6fdd29a1f82626e52c","target":"graph","created_at":"2026-07-05T07:45:42Z","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/2402.10190/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we prove that extremal black holes arise on the threshold of gravitational collapse. More precisely, we construct smooth one-parameter families of smooth, spherically symmetric solutions to the Einstein-Maxwell-Vlasov system which interpolate between dispersion and collapse and for which the critical solution is an extremal black hole. Physically, these solutions can be understood as beams of gravitationally self-interacting collisionless charged particles fired into Minkowski space from past infinity. Depending on the precise value of the parameter, we show that the Vlasov matt","authors_text":"Christoph Kehle, Ryan Unger","cross_cats":["math-ph","math.AP","math.DG","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-02-15T18:46:40Z","title":"Extremal black hole formation as a critical phenomenon"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.10190","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:e9da067c646e7b29a687e3225d56122e6bca4c478d5b2c59cf10c3332528a998","target":"record","created_at":"2026-07-05T07:45:42Z","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":"a91d4fb90ccaf623ad1726f6027fd78495de504de3d940995358e482d042f1e3","cross_cats_sorted":["math-ph","math.AP","math.DG","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2024-02-15T18:46:40Z","title_canon_sha256":"03ef528272832606ce1ed847940be6849d2d435ab06f427d4085f090ffa6b77a"},"schema_version":"1.0","source":{"id":"2402.10190","kind":"arxiv","version":1}},"canonical_sha256":"d79c6dcd5f8153a05ffadde3f2dff2bc97f6d0706670a2706a31f38b2d7ee58a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d79c6dcd5f8153a05ffadde3f2dff2bc97f6d0706670a2706a31f38b2d7ee58a","first_computed_at":"2026-07-05T07:45:42.525397Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T07:45:42.525397Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"6A+iGoj/S21GgLicbNUPzQVoO0oEB9ssn1p0MEjkE3TinTdMwBFNwNlYqOaW1TLiwiFYmanDqI7xzgnU5xedCw==","signature_status":"signed_v1","signed_at":"2026-07-05T07:45:42.525914Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.10190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9da067c646e7b29a687e3225d56122e6bca4c478d5b2c59cf10c3332528a998","sha256:4b5c8b214292ea761ec44c08479406a4d7a62b5bae80ce6fdd29a1f82626e52c"],"state_sha256":"feef4d4cfd1f3494b74bd56322318fe4550a47f7a2d4912eecad16ceb50384ed"}