{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GY344JVC4ZSBJQDCK4X4DWSXWK","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":"83bb7ebac482ba6c27b43d4f1a5cbb457d62c04f209c22eec98c6b6049520dd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-16T09:37:48Z","title_canon_sha256":"6db98596e195d2b02f9cee79c4af95644ef757b30539236d667e00219b2806d4"},"schema_version":"1.0","source":{"id":"1507.04506","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.04506","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"arxiv_version","alias_value":"1507.04506v2","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.04506","created_at":"2026-05-17T23:45:53Z"},{"alias_kind":"pith_short_12","alias_value":"GY344JVC4ZSB","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GY344JVC4ZSBJQDC","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GY344JVC","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:4b9dd8fa7a7a69960caef40d6bd8802f049bf352cc7d36176204528bef78b09b","target":"graph","created_at":"2026-05-17T23:45:53Z","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":"Consider a branching random walk on the real line. Madaule showed the renormalized trajectory of an individual selected according to the critical Gibbs measure converges in law to a Brownian meander. Besides, Chen proved that the renormalized trajectory leading to the leftmost individual at time $n$ converges in law to a standard Brownian excursion. In this article, we prove that the renormalized trajectory of an individual selected according to a supercritical Gibbs measure also converges in law toward the Brownian excursion. Moreover, refinements of this results enables to express the probab","authors_text":"Bastien Mallein, Thomas Madaule, Xinxin Chen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-16T09:37:48Z","title":"On the trajectory of an individual chosen according to supercritical Gibbs measure in the branching random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04506","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":"sha256:576a7e1343d806026b0311b34e97f53c3b004880f7c5fbf6ffbdcd1fb6fbb9f6","target":"record","created_at":"2026-05-17T23:45:53Z","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":"83bb7ebac482ba6c27b43d4f1a5cbb457d62c04f209c22eec98c6b6049520dd9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-07-16T09:37:48Z","title_canon_sha256":"6db98596e195d2b02f9cee79c4af95644ef757b30539236d667e00219b2806d4"},"schema_version":"1.0","source":{"id":"1507.04506","kind":"arxiv","version":2}},"canonical_sha256":"3637ce26a2e66414c062572fc1da57b2ae74f2e243ca2db255997aa290a39a34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3637ce26a2e66414c062572fc1da57b2ae74f2e243ca2db255997aa290a39a34","first_computed_at":"2026-05-17T23:45:53.762853Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:45:53.762853Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"xhm3I0ywxuMuA6EzAma7FCUyUkYaCgDwNlXXHcqtoX1IQymL88C74B0XAGX34R9gVnDvfsgO+WnCQoG8vmKvBQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:45:53.763293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.04506","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:576a7e1343d806026b0311b34e97f53c3b004880f7c5fbf6ffbdcd1fb6fbb9f6","sha256:4b9dd8fa7a7a69960caef40d6bd8802f049bf352cc7d36176204528bef78b09b"],"state_sha256":"402b12bcd7005bfb589f6607ea4812e166c3bb8dae271c6276e6999df8c9ee29"}