{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:DBE3YLZNJ2Y4NZRAM4M4M56KNM","short_pith_number":"pith:DBE3YLZN","schema_version":"1.0","canonical_sha256":"1849bc2f2d4eb1c6e6206719c677ca6b2546c19a61bc17b1b417c3dbc7cde4b6","source":{"kind":"arxiv","id":"1308.1868","version":4},"attestation_state":"computed","paper":{"title":"The extremal process of two-speed branching Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Bovier, Lisa Hartung","submitted_at":"2013-08-08T15:02:36Z","abstract_excerpt":"We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is $\\sigma_1$ for $s\\leq bt$ and $\\sigma_2$ when $bt\\leq s\\leq t$. In the case $\\sigma_1>\\sigma_2$, the process is the concatenation of two BBM extremal processes, as expected. In the case $\\sigma_1<\\sigma_2$, a new family of cluster point processes arises, that are similar, but distinctively different from the BBM process. Our proofs follow the strategy of "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1308.1868","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-08-08T15:02:36Z","cross_cats_sorted":[],"title_canon_sha256":"425acea1ed5af28747f8bdbf3252877421e422b8f7a4db43fcd25a07e74b179c","abstract_canon_sha256":"671b763c6b65e9523e9ccc55f6687deae0b5835aee5abc4b53374eafccce9fb8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:04:22.383887Z","signature_b64":"0EX3zitwtpwlm/lDjfQ182z9CwvnBZj/V93kk1NeGzFYeg3xUuWk/u41wlPIxz9PtkTf92YiimGc+Xcv6JGIDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1849bc2f2d4eb1c6e6206719c677ca6b2546c19a61bc17b1b417c3dbc7cde4b6","last_reissued_at":"2026-05-18T03:04:22.383329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:04:22.383329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The extremal process of two-speed branching Brownian motion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anton Bovier, Lisa Hartung","submitted_at":"2013-08-08T15:02:36Z","abstract_excerpt":"We construct and describe the extremal process for variable speed branching Brownian motion, studied recently by Fang and Zeitouni, for the case of piecewise constant speeds; in fact for simplicity we concentrate on the case when the speed is $\\sigma_1$ for $s\\leq bt$ and $\\sigma_2$ when $bt\\leq s\\leq t$. In the case $\\sigma_1>\\sigma_2$, the process is the concatenation of two BBM extremal processes, as expected. In the case $\\sigma_1<\\sigma_2$, a new family of cluster point processes arises, that are similar, but distinctively different from the BBM process. Our proofs follow the strategy of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1868","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1308.1868","created_at":"2026-05-18T03:04:22.383413+00:00"},{"alias_kind":"arxiv_version","alias_value":"1308.1868v4","created_at":"2026-05-18T03:04:22.383413+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1868","created_at":"2026-05-18T03:04:22.383413+00:00"},{"alias_kind":"pith_short_12","alias_value":"DBE3YLZNJ2Y4","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"DBE3YLZNJ2Y4NZRA","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"DBE3YLZN","created_at":"2026-05-18T12:27:40.988391+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM","json":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM.json","graph_json":"https://pith.science/api/pith-number/DBE3YLZNJ2Y4NZRAM4M4M56KNM/graph.json","events_json":"https://pith.science/api/pith-number/DBE3YLZNJ2Y4NZRAM4M4M56KNM/events.json","paper":"https://pith.science/paper/DBE3YLZN"},"agent_actions":{"view_html":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM","download_json":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM.json","view_paper":"https://pith.science/paper/DBE3YLZN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1308.1868&json=true","fetch_graph":"https://pith.science/api/pith-number/DBE3YLZNJ2Y4NZRAM4M4M56KNM/graph.json","fetch_events":"https://pith.science/api/pith-number/DBE3YLZNJ2Y4NZRAM4M4M56KNM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM/action/storage_attestation","attest_author":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM/action/author_attestation","sign_citation":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM/action/citation_signature","submit_replication":"https://pith.science/pith/DBE3YLZNJ2Y4NZRAM4M4M56KNM/action/replication_record"}},"created_at":"2026-05-18T03:04:22.383413+00:00","updated_at":"2026-05-18T03:04:22.383413+00:00"}