{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Z6FGP2FGGKJMSZGV6AIY7SUHDS","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":"7aea146bed31e555496e2c533320dfc0b19b5086aa6726028efb5ef4817f9cdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T17:51:02Z","title_canon_sha256":"b16c661a616f42d881d03265bf8fb13a975e80986837c75b39be6caa3f3d6ee6"},"schema_version":"1.0","source":{"id":"1202.4715","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.4715","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"arxiv_version","alias_value":"1202.4715v1","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.4715","created_at":"2026-05-18T04:01:50Z"},{"alias_kind":"pith_short_12","alias_value":"Z6FGP2FGGKJM","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_16","alias_value":"Z6FGP2FGGKJMSZGV","created_at":"2026-05-18T12:27:30Z"},{"alias_kind":"pith_short_8","alias_value":"Z6FGP2FG","created_at":"2026-05-18T12:27:30Z"}],"graph_snapshots":[{"event_id":"sha256:f9b6b5581cf1561884fbcc245caaef887e540aad367955c79b0654ef42bc63ac","target":"graph","created_at":"2026-05-18T04:01:50Z","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 consider a general class of discrete, two-dimensional Markov chains modeling the dynamics of a population with two types, without mutation or immigration, and neutral in the sense that type has no influence on each individual's birth or death parameters. We prove that all the eigenvectors of the corresponding transition matrix or infinitesimal generator \\Pi\\ can be expressed as the product of \"universal\" polynomials of two variables, depending on each type's size but not on the specific transitions of the dynamics, and functions depending only on the total population size. These eigenvector","authors_text":"Laurent Miclo, Nicolas Champagnat, Persi Diaconis","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T17:51:02Z","title":"On Dirichlet eigenvectors for neutral two-dimensional Markov chains"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.4715","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:e080ce435ae16d26b474b7e2341cf855465f0283da73258e782d803a9ad3d324","target":"record","created_at":"2026-05-18T04:01:50Z","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":"7aea146bed31e555496e2c533320dfc0b19b5086aa6726028efb5ef4817f9cdf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-02-21T17:51:02Z","title_canon_sha256":"b16c661a616f42d881d03265bf8fb13a975e80986837c75b39be6caa3f3d6ee6"},"schema_version":"1.0","source":{"id":"1202.4715","kind":"arxiv","version":1}},"canonical_sha256":"cf8a67e8a63292c964d5f0118fca871ca4646061eb20c51a3705593dac0100db","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf8a67e8a63292c964d5f0118fca871ca4646061eb20c51a3705593dac0100db","first_computed_at":"2026-05-18T04:01:50.006403Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:01:50.006403Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"T6lazqxBRNjzrqjw118diZVHJN5y5JCfonVb1s5XMvdZroCjI/ekcPyc6G/tGKLiJ3ZJyGl+j5ZdRCD/vM0yAA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:01:50.006868Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.4715","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e080ce435ae16d26b474b7e2341cf855465f0283da73258e782d803a9ad3d324","sha256:f9b6b5581cf1561884fbcc245caaef887e540aad367955c79b0654ef42bc63ac"],"state_sha256":"dcec349c18d317bd664a6056f7d54b541ce4e9d1ea6c05c7e95711dda6e33f19"}