{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:US7IFDMMV6J74WNNEGKRLDCX72","short_pith_number":"pith:US7IFDMM","schema_version":"1.0","canonical_sha256":"a4be828d8caf93fe59ad2195158c57fe9e96e6ba0d4d7a407e38c6b96191adbc","source":{"kind":"arxiv","id":"1808.05445","version":2},"attestation_state":"computed","paper":{"title":"From $1$ to $6$: a finer analysis of perturbed 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":"2018-08-16T12:32:08Z","abstract_excerpt":"The logarithmic correction for the order of the maximum for two-speed branching Brownian motion changes discontinuously when approaching slopes $\\sigma_1^2=\\sigma_2^2=1$ which corresponds to standard branching Brownian motion. In this article we study this transition more closely by choosing $\\sigma_1^2=1\\pm t^{-\\alpha}$ and $\\sigma_2^2=1\\pm t^{-\\alpha}$. We show that the logarithmic correction for the order of the maximum now smoothly interpolates between the correction in the iid case $\\frac{1}{2\\sqrt 2}\\ln(t),\\;\\frac{3}{2\\sqrt 2}\\ln(t)$ and $\\frac{6}{2\\sqrt 2}\\ln(t)$ when $0<\\alpha<\\frac{1}"},"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":"1808.05445","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-08-16T12:32:08Z","cross_cats_sorted":[],"title_canon_sha256":"0f75fda94e818fa3cc869e1fee45dcae247009f105a124aaf6f19c71b74211f1","abstract_canon_sha256":"9285faecd3a776030ac71970b5a34bde3490c8c00b6dd72ffb9c4aec0e24a508"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:52.910583Z","signature_b64":"hiakT9vuagURTriytP0GZfTdyo3r12x8xTba5hH9N82pFhmh17ieMSuW6I+MnE5iT8w1b02aCC2Uv3ajA555BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a4be828d8caf93fe59ad2195158c57fe9e96e6ba0d4d7a407e38c6b96191adbc","last_reissued_at":"2026-05-17T23:45:52.910056Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:52.910056Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"From $1$ to $6$: a finer analysis of perturbed 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":"2018-08-16T12:32:08Z","abstract_excerpt":"The logarithmic correction for the order of the maximum for two-speed branching Brownian motion changes discontinuously when approaching slopes $\\sigma_1^2=\\sigma_2^2=1$ which corresponds to standard branching Brownian motion. In this article we study this transition more closely by choosing $\\sigma_1^2=1\\pm t^{-\\alpha}$ and $\\sigma_2^2=1\\pm t^{-\\alpha}$. We show that the logarithmic correction for the order of the maximum now smoothly interpolates between the correction in the iid case $\\frac{1}{2\\sqrt 2}\\ln(t),\\;\\frac{3}{2\\sqrt 2}\\ln(t)$ and $\\frac{6}{2\\sqrt 2}\\ln(t)$ when $0<\\alpha<\\frac{1}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05445","kind":"arxiv","version":2},"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":"1808.05445","created_at":"2026-05-17T23:45:52.910138+00:00"},{"alias_kind":"arxiv_version","alias_value":"1808.05445v2","created_at":"2026-05-17T23:45:52.910138+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.05445","created_at":"2026-05-17T23:45:52.910138+00:00"},{"alias_kind":"pith_short_12","alias_value":"US7IFDMMV6J7","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_16","alias_value":"US7IFDMMV6J74WNN","created_at":"2026-05-18T12:32:56.356000+00:00"},{"alias_kind":"pith_short_8","alias_value":"US7IFDMM","created_at":"2026-05-18T12:32:56.356000+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/US7IFDMMV6J74WNNEGKRLDCX72","json":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72.json","graph_json":"https://pith.science/api/pith-number/US7IFDMMV6J74WNNEGKRLDCX72/graph.json","events_json":"https://pith.science/api/pith-number/US7IFDMMV6J74WNNEGKRLDCX72/events.json","paper":"https://pith.science/paper/US7IFDMM"},"agent_actions":{"view_html":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72","download_json":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72.json","view_paper":"https://pith.science/paper/US7IFDMM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1808.05445&json=true","fetch_graph":"https://pith.science/api/pith-number/US7IFDMMV6J74WNNEGKRLDCX72/graph.json","fetch_events":"https://pith.science/api/pith-number/US7IFDMMV6J74WNNEGKRLDCX72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72/action/storage_attestation","attest_author":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72/action/author_attestation","sign_citation":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72/action/citation_signature","submit_replication":"https://pith.science/pith/US7IFDMMV6J74WNNEGKRLDCX72/action/replication_record"}},"created_at":"2026-05-17T23:45:52.910138+00:00","updated_at":"2026-05-17T23:45:52.910138+00:00"}