{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:VMXYSAQLM77ZOUE7MUB2QIMLJW","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":"634553f90b086441bc4da08915752db4ca7508dadf479991d80ef6faa999ced4","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-05T15:52:37Z","title_canon_sha256":"0abd381ed5b783c017a9deffc441103d8b4ef0e50675c80f9fd249a51015e7d8"},"schema_version":"1.0","source":{"id":"1705.02277","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1705.02277","created_at":"2026-05-18T00:35:20Z"},{"alias_kind":"arxiv_version","alias_value":"1705.02277v1","created_at":"2026-05-18T00:35:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1705.02277","created_at":"2026-05-18T00:35:20Z"},{"alias_kind":"pith_short_12","alias_value":"VMXYSAQLM77Z","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_16","alias_value":"VMXYSAQLM77ZOUE7","created_at":"2026-05-18T12:31:49Z"},{"alias_kind":"pith_short_8","alias_value":"VMXYSAQL","created_at":"2026-05-18T12:31:49Z"}],"graph_snapshots":[{"event_id":"sha256:b940020e6ea18ec7518303cbbe84fa9776bdacd987243038682596a3020e430e","target":"graph","created_at":"2026-05-18T00:35:20Z","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 have shown recently how to calculate the large deviation function of the position $X_{\\max}(t) $ of the right most particle of a branching Brownian motion at time $t$. This large deviation function exhibits a phase transition at a certain negative velocity. Here we extend this result to more general branching random walks and show that the probability distribution of $X_{\\max}(t)$ has, asymptotically in time, a prefactor characterized by non trivial power law.","authors_text":"Bernard Derrida, Zhan Shi","cross_cats":["cond-mat.stat-mech","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-05T15:52:37Z","title":"Slower deviations of the branching Brownian motion and of branching random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.02277","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:c8cb2af77edc2ddf9dbcc0dac2c6b2d6e88bd2ae7860b82e45552983bd7bb74d","target":"record","created_at":"2026-05-18T00:35:20Z","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":"634553f90b086441bc4da08915752db4ca7508dadf479991d80ef6faa999ced4","cross_cats_sorted":["cond-mat.stat-mech","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2017-05-05T15:52:37Z","title_canon_sha256":"0abd381ed5b783c017a9deffc441103d8b4ef0e50675c80f9fd249a51015e7d8"},"schema_version":"1.0","source":{"id":"1705.02277","kind":"arxiv","version":1}},"canonical_sha256":"ab2f89020b67ff97509f6503a8218b4d87a9a5972347012ea6ae0ceb26e87ae5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab2f89020b67ff97509f6503a8218b4d87a9a5972347012ea6ae0ceb26e87ae5","first_computed_at":"2026-05-18T00:35:20.745233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:35:20.745233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"b4ksfG5K1cr+4h7+aRUN27ritWAUtlw+Ykrf4cZuKgBhrJQVkhzq2c4oOFfOlLQKDELYgpOqPxEio0zm7FcQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:35:20.745723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1705.02277","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8cb2af77edc2ddf9dbcc0dac2c6b2d6e88bd2ae7860b82e45552983bd7bb74d","sha256:b940020e6ea18ec7518303cbbe84fa9776bdacd987243038682596a3020e430e"],"state_sha256":"ca431650a6067d473d92bb2c13e5f9b81ca37a1becb63c1631da3dce3b83f4ab"}