{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NAC6YVPF5N2LO4O6LRIEHVJU7W","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":"dba0d9f9ffec0d3438dec46a2aab54bb4fa1b8c0dff2a178de481a41879dfc36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-26T18:19:49Z","title_canon_sha256":"844ff74e9d156e2e976cdd470faf72a5d649f8bdd3d9e0d339b6943f4007bf23"},"schema_version":"1.0","source":{"id":"1406.6971","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.6971","created_at":"2026-05-18T02:40:01Z"},{"alias_kind":"arxiv_version","alias_value":"1406.6971v2","created_at":"2026-05-18T02:40:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.6971","created_at":"2026-05-18T02:40:01Z"},{"alias_kind":"pith_short_12","alias_value":"NAC6YVPF5N2L","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NAC6YVPF5N2LO4O6","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NAC6YVPF","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:113108ff3d1bc4c0d6c0d30819cfde366e523ba768a28022c007e762581b5055","target":"graph","created_at":"2026-05-18T02:40:01Z","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":"This paper is a complement to the studies on the minimum of a real-valued branching random walk. In the boundary case (Biggins, Kyprianou 2005), A\\\"{i}d\\'ekon in a seminal paper (2013) obtained the convergence in law of the minimum after a suitable renormalization. We study here the situation when the log-generating function of the branching random walk explodes at some positive point and it cannot be reduced to the boundary case. In the associated thermodynamics framework this corresponds to a first order phase transition, while the boundary case corresponds to a second order phase transition","authors_text":"Julien Barral, Thomas Madaule, Yueyun Hu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-26T18:19:49Z","title":"The minimum of a branching random walk outside the boundary case"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6971","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":"sha256:58198d2f8394b354ddba3d279898322ad111833317bd3ff8481eb4e55b8323cb","target":"record","created_at":"2026-05-18T02:40:01Z","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":"dba0d9f9ffec0d3438dec46a2aab54bb4fa1b8c0dff2a178de481a41879dfc36","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-26T18:19:49Z","title_canon_sha256":"844ff74e9d156e2e976cdd470faf72a5d649f8bdd3d9e0d339b6943f4007bf23"},"schema_version":"1.0","source":{"id":"1406.6971","kind":"arxiv","version":2}},"canonical_sha256":"6805ec55e5eb74b771de5c5043d534fd9499e441209a72083e988d3a0a83d709","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6805ec55e5eb74b771de5c5043d534fd9499e441209a72083e988d3a0a83d709","first_computed_at":"2026-05-18T02:40:01.717022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:40:01.717022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"M2KIRmLiOI8uo/kBQeqwZvpNiEtudNujM+L0zu2ckIjkZS1BHfhCu/q9fF147+MmJYHp/CALOVk8Bztv08LPCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:40:01.717620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.6971","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:58198d2f8394b354ddba3d279898322ad111833317bd3ff8481eb4e55b8323cb","sha256:113108ff3d1bc4c0d6c0d30819cfde366e523ba768a28022c007e762581b5055"],"state_sha256":"33efee0d84c5952cac5322f54d7e5347c430f12c42ad062d67e038a73ef5b6e7"}