{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:IFJWFXPM4JTOVYZ7QREMPT2GGC","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":"447424a1f4bbcf967c4ba7e5b2874682a7dacfe93f44eac77986cdca34bf849d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-09T01:57:07Z","title_canon_sha256":"0b042ac600cfefe0add1e1b01a4c7ef0465fc43035670b731f37a229388f2446"},"schema_version":"1.0","source":{"id":"1507.02345","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.02345","created_at":"2026-05-18T01:35:29Z"},{"alias_kind":"arxiv_version","alias_value":"1507.02345v2","created_at":"2026-05-18T01:35:29Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.02345","created_at":"2026-05-18T01:35:29Z"},{"alias_kind":"pith_short_12","alias_value":"IFJWFXPM4JTO","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"IFJWFXPM4JTOVYZ7","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"IFJWFXPM","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:1e6ab031182e3d2614294b67d6625e00d28b2e6529ed00243f76ce9c38872385","target":"graph","created_at":"2026-05-18T01:35:29Z","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 obtain sharp asymptotic estimates for hitting probabilities of a critical branching Brownian motion in one dimension with killing at 0 We also obtain sharp asymptotic formulas for the tail probabilities of the number of particles killed at 0. In the special case of double-or-nothing branching, we give exact formulas for both the hitting probabilities, in terms of elliptic functions, and the distribution of the number of killed particles.","authors_text":"Bowei Zheng, Steven P. Lalley","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-09T01:57:07Z","title":"Critical Branching Brownian Motion with Killing"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.02345","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:bdee69d5a9cc706a47fdb914a1aa0cbca20ec906689de4c28cfda7cbc50867a4","target":"record","created_at":"2026-05-18T01:35:29Z","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":"447424a1f4bbcf967c4ba7e5b2874682a7dacfe93f44eac77986cdca34bf849d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-09T01:57:07Z","title_canon_sha256":"0b042ac600cfefe0add1e1b01a4c7ef0465fc43035670b731f37a229388f2446"},"schema_version":"1.0","source":{"id":"1507.02345","kind":"arxiv","version":2}},"canonical_sha256":"415362ddece266eae33f8448c7cf463092f869b930c702a4613bbcfde4fd7a38","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"415362ddece266eae33f8448c7cf463092f869b930c702a4613bbcfde4fd7a38","first_computed_at":"2026-05-18T01:35:29.586005Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:29.586005Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EDv99gJps2wvgWr5ishMJ2kDYfuPH/ewBG2VVolf+jtVHmRR0xneGgJn+aUrtlJG8jojcBE4fX+xAdskmggjDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:29.586653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.02345","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bdee69d5a9cc706a47fdb914a1aa0cbca20ec906689de4c28cfda7cbc50867a4","sha256:1e6ab031182e3d2614294b67d6625e00d28b2e6529ed00243f76ce9c38872385"],"state_sha256":"4072ac07b1adf17593f74458c732788301251a5eb64f133840c0c5619c1aed6b"}