{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:HJWHKJAUG6ITSOPAA6GCG6QF5K","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":"7ed62bf380b19380cdcd4bf9ff81f71c70413fa9015750507b186cc24e9172a7","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-01-30T08:20:38Z","title_canon_sha256":"544a068fa7adc407d4b6113f18881b00ffa6a31af6eeaad991e1b644051ab3bf"},"schema_version":"1.0","source":{"id":"1501.07693","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1501.07693","created_at":"2026-05-18T02:17:54Z"},{"alias_kind":"arxiv_version","alias_value":"1501.07693v2","created_at":"2026-05-18T02:17:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1501.07693","created_at":"2026-05-18T02:17:54Z"},{"alias_kind":"pith_short_12","alias_value":"HJWHKJAUG6IT","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_16","alias_value":"HJWHKJAUG6ITSOPA","created_at":"2026-05-18T12:29:25Z"},{"alias_kind":"pith_short_8","alias_value":"HJWHKJAU","created_at":"2026-05-18T12:29:25Z"}],"graph_snapshots":[{"event_id":"sha256:fbe881a86186e0b04639c3ac9f2e67a142682f754a06ac958c00fd2c73f1a23d","target":"graph","created_at":"2026-05-18T02:17:54Z","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 study the one dimensional branching Brownian motion starting at the origin and investigate the correlation between the rightmost ($X_{\\max}\\geq 0$) and leftmost ($X_{\\min} \\leq 0$) visited sites up to time $t$. At each time step the existing particles in the system either diffuse (with diffusion constant $D$), die (with rate $a$) or split into two particles (with rate $b$). We focus on the regime $b \\leq a$ where these two extreme values $X_{\\max}$ and $X_{\\min}$ are strongly correlated. We show that at large time $t$, the joint probability distribution function (PDF) of the two extreme poi","authors_text":"Gregory Schehr, Kabir Ramola, Satya N. Majumdar","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-01-30T08:20:38Z","title":"Spatial Extent of Branching Brownian Motion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.07693","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":"sha256:2692d4bcfd5ee6e5af25389f4da80de8a8e42a0fb6fe089039f6906152a1ac5f","target":"record","created_at":"2026-05-18T02:17:54Z","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":"7ed62bf380b19380cdcd4bf9ff81f71c70413fa9015750507b186cc24e9172a7","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.stat-mech","submitted_at":"2015-01-30T08:20:38Z","title_canon_sha256":"544a068fa7adc407d4b6113f18881b00ffa6a31af6eeaad991e1b644051ab3bf"},"schema_version":"1.0","source":{"id":"1501.07693","kind":"arxiv","version":2}},"canonical_sha256":"3a6c75241437913939e0078c237a05eaa5be99289a2bb0be83370432bab60444","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3a6c75241437913939e0078c237a05eaa5be99289a2bb0be83370432bab60444","first_computed_at":"2026-05-18T02:17:54.228030Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:54.228030Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+Am98FjJSORCW+TTJJozFYF0sQnB92SIg4ii7XL5rSG+7pZSNW8cg53zir1Pf8OI7pTz7GwMFp1E8Rp5jzC0CA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:54.228566Z","signed_message":"canonical_sha256_bytes"},"source_id":"1501.07693","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2692d4bcfd5ee6e5af25389f4da80de8a8e42a0fb6fe089039f6906152a1ac5f","sha256:fbe881a86186e0b04639c3ac9f2e67a142682f754a06ac958c00fd2c73f1a23d"],"state_sha256":"535b0ac783f2cc903774c270164c133a6995e4c9274b134fc7d1df4bc6ad5ada"}