{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2023:UPXTKYYYKRHCKDRGTXZH2R3SAY","short_pith_number":"pith:UPXTKYYY","schema_version":"1.0","canonical_sha256":"a3ef356318544e250e269df27d4772061b727cfbefc7a27dacd82ff6050aabdd","source":{"kind":"arxiv","id":"2310.12897","version":1},"attestation_state":"computed","paper":{"title":"Critical exponential tiltings for size-conditioned multitype Bienaym\\'e--Galton--Watson trees","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paul Th\\'evenin","submitted_at":"2023-10-19T16:48:15Z","abstract_excerpt":"We consider here multitype Bienaym\\'e--Galton--Watson trees, under the conditioning that the numbers of vertices of given type satisfy some linear relations. We prove that, under some smoothness conditions on the offspring distribution $\\mathbf{\\zeta}$, there exists a critical offspring distribution $\\tilde{\\mathbf{\\zeta}}$ such that the trees with offspring distribution $\\mathbf{\\zeta}$ and $\\tilde{\\mathbf{\\zeta}}$ have the same law under our conditioning. This allows us in a second time to characterize the local limit of such trees, as their size goes to infinity. Our main tool is a notion o"},"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":"2310.12897","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/publicdomain/zero/1.0/","primary_cat":"math.PR","submitted_at":"2023-10-19T16:48:15Z","cross_cats_sorted":[],"title_canon_sha256":"846ba2f4d4d1f0d93fde31d689ca33cd45371be5cad3be8226be3348b127df30","abstract_canon_sha256":"0a7a683847a4003cb6b02d3ce99e836d3e2ca448e0a8533d6139435f7a2372b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T07:02:44.100889Z","signature_b64":"H+jzskMvykEvD5QS6YZA5yh67zcW263uTK27utJKy3rMU2mzuF3WAChiov7WLkM3fkJwODP1uczLPDhd67JtDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a3ef356318544e250e269df27d4772061b727cfbefc7a27dacd82ff6050aabdd","last_reissued_at":"2026-07-05T07:02:44.100395Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T07:02:44.100395Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Critical exponential tiltings for size-conditioned multitype Bienaym\\'e--Galton--Watson trees","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Paul Th\\'evenin","submitted_at":"2023-10-19T16:48:15Z","abstract_excerpt":"We consider here multitype Bienaym\\'e--Galton--Watson trees, under the conditioning that the numbers of vertices of given type satisfy some linear relations. We prove that, under some smoothness conditions on the offspring distribution $\\mathbf{\\zeta}$, there exists a critical offspring distribution $\\tilde{\\mathbf{\\zeta}}$ such that the trees with offspring distribution $\\mathbf{\\zeta}$ and $\\tilde{\\mathbf{\\zeta}}$ have the same law under our conditioning. This allows us in a second time to characterize the local limit of such trees, as their size goes to infinity. Our main tool is a notion o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.12897","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2310.12897/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2310.12897","created_at":"2026-07-05T07:02:44.100471+00:00"},{"alias_kind":"arxiv_version","alias_value":"2310.12897v1","created_at":"2026-07-05T07:02:44.100471+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.12897","created_at":"2026-07-05T07:02:44.100471+00:00"},{"alias_kind":"pith_short_12","alias_value":"UPXTKYYYKRHC","created_at":"2026-07-05T07:02:44.100471+00:00"},{"alias_kind":"pith_short_16","alias_value":"UPXTKYYYKRHCKDRG","created_at":"2026-07-05T07:02:44.100471+00:00"},{"alias_kind":"pith_short_8","alias_value":"UPXTKYYY","created_at":"2026-07-05T07:02:44.100471+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/UPXTKYYYKRHCKDRGTXZH2R3SAY","json":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY.json","graph_json":"https://pith.science/api/pith-number/UPXTKYYYKRHCKDRGTXZH2R3SAY/graph.json","events_json":"https://pith.science/api/pith-number/UPXTKYYYKRHCKDRGTXZH2R3SAY/events.json","paper":"https://pith.science/paper/UPXTKYYY"},"agent_actions":{"view_html":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY","download_json":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY.json","view_paper":"https://pith.science/paper/UPXTKYYY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2310.12897&json=true","fetch_graph":"https://pith.science/api/pith-number/UPXTKYYYKRHCKDRGTXZH2R3SAY/graph.json","fetch_events":"https://pith.science/api/pith-number/UPXTKYYYKRHCKDRGTXZH2R3SAY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY/action/storage_attestation","attest_author":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY/action/author_attestation","sign_citation":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY/action/citation_signature","submit_replication":"https://pith.science/pith/UPXTKYYYKRHCKDRGTXZH2R3SAY/action/replication_record"}},"created_at":"2026-07-05T07:02:44.100471+00:00","updated_at":"2026-07-05T07:02:44.100471+00:00"}