{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:K3HDP6PBZP4TBVMTGJXHCZ7SNB","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":"8f030e362f5a0dcc806164d3e0f426533b4934db12e22ba867cdc6b2df5dc262","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-11-12T10:57:48Z","title_canon_sha256":"6a0cfac454487bb1fdbebf10a27ef49566d135701b4eb56d3810b90047a6865b"},"schema_version":"1.0","source":{"id":"0811.1863","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0811.1863","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"arxiv_version","alias_value":"0811.1863v3","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0811.1863","created_at":"2026-05-18T04:39:59Z"},{"alias_kind":"pith_short_12","alias_value":"K3HDP6PBZP4T","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"K3HDP6PBZP4TBVMT","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"K3HDP6PB","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:7b6c3c8e5e59b1c27bd4e2a91dda2437076e784fdbe47c07e1208997ab9bf083","target":"graph","created_at":"2026-05-18T04:39:59Z","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 $n+m$ nonintersecting Brownian bridges, with $n$ of them leaving from 0 at time $t=-1$ and returning to 0 at time $t=1$, while the $m$ remaining ones (wanderers) go from $m$ points $a_i$ to $m$ points $b_i$. First, we keep $m$ fixed and we scale $a_i,b_i$ appropriately with $n$. In the large-$n$ limit, we obtain a new Airy process with wanderers, in the neighborhood of $\\sqrt{2n}$, the approximate location of the rightmost particle in the absence of wanderers. This new process is governed by an Airy-type kernel, with a rational perturbation. Letting the number $m$ of wanderers tend to","authors_text":"Mark Adler, Patrik L. Ferrari, Pierre van Moerbeke","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-11-12T10:57:48Z","title":"Airy processes with wanderers and new universality classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0811.1863","kind":"arxiv","version":3},"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:baa52e6ab59dfaaae35124d7285603b75801489679ce363317f5ca061e8246e2","target":"record","created_at":"2026-05-18T04:39:59Z","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":"8f030e362f5a0dcc806164d3e0f426533b4934db12e22ba867cdc6b2df5dc262","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-11-12T10:57:48Z","title_canon_sha256":"6a0cfac454487bb1fdbebf10a27ef49566d135701b4eb56d3810b90047a6865b"},"schema_version":"1.0","source":{"id":"0811.1863","kind":"arxiv","version":3}},"canonical_sha256":"56ce37f9e1cbf930d593326e7167f268431b6f5b0fcb1ad3f17ee1be7bb6c905","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"56ce37f9e1cbf930d593326e7167f268431b6f5b0fcb1ad3f17ee1be7bb6c905","first_computed_at":"2026-05-18T04:39:59.719789Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:59.719789Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ebU/t6InqY1XLlJLQqlgBZ3h8e5oSxC50uAB7PCQkJ83TJX7Yfflv9KYkhQgrXs2XqjoVu1OQLMRPmXI0JdDCg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:59.720339Z","signed_message":"canonical_sha256_bytes"},"source_id":"0811.1863","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:baa52e6ab59dfaaae35124d7285603b75801489679ce363317f5ca061e8246e2","sha256:7b6c3c8e5e59b1c27bd4e2a91dda2437076e784fdbe47c07e1208997ab9bf083"],"state_sha256":"747361d31bba6c9bfe19686ce6b23dc8877425268bdde2ddb0ead644321f1bcd"}