{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:KYHYFCJV5GKU2JG2VS4AUX2QSG","short_pith_number":"pith:KYHYFCJV","canonical_record":{"source":{"id":"1907.05845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-12T17:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"bfecc41c8ceeb790739e54d9696331973fe918bd8eeb2617db7ba2e3fa4eb5fa","abstract_canon_sha256":"43642c65a46d75cac587051c5d686d06188ab0627a2206519c307795c2d213b2"},"schema_version":"1.0"},"canonical_sha256":"560f828935e9954d24daacb80a5f5091b4c80e946235de2af3451ff5c2d292df","source":{"kind":"arxiv","id":"1907.05845","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05845","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05845v1","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05845","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"KYHYFCJV5GKU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KYHYFCJV5GKU2JG2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KYHYFCJV","created_at":"2026-05-18T12:33:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:KYHYFCJV5GKU2JG2VS4AUX2QSG","target":"record","payload":{"canonical_record":{"source":{"id":"1907.05845","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-12T17:11:12Z","cross_cats_sorted":[],"title_canon_sha256":"bfecc41c8ceeb790739e54d9696331973fe918bd8eeb2617db7ba2e3fa4eb5fa","abstract_canon_sha256":"43642c65a46d75cac587051c5d686d06188ab0627a2206519c307795c2d213b2"},"schema_version":"1.0"},"canonical_sha256":"560f828935e9954d24daacb80a5f5091b4c80e946235de2af3451ff5c2d292df","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:44.224602Z","signature_b64":"WpAWwHPx+CM/6zJhPt1b5iClO7eE7WX58w5kmMoShTZyxNXLX5Q4MuHs4Uq9NIDPJIOeuBvJksthoUnL+hUgBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"560f828935e9954d24daacb80a5f5091b4c80e946235de2af3451ff5c2d292df","last_reissued_at":"2026-05-17T23:40:44.223947Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:44.223947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1907.05845","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yLvdCbuC3ZXIoP0rLyhfGc0LEAR2jwpOr5tFd7C63L8V8/wtDwnglxG+EIHy8PfRtU/ROFzYsWnkXLKgewAsAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:07:02.266509Z"},"content_sha256":"9947b79f8f4517e8a578b74becf9981c5b8ab5085c25ce2989ff720c76e3bc41","schema_version":"1.0","event_id":"sha256:9947b79f8f4517e8a578b74becf9981c5b8ab5085c25ce2989ff720c76e3bc41"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:KYHYFCJV5GKU2JG2VS4AUX2QSG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Kingman's coalescent with erosion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Amaury Lambert, Emmanuel Schertzer, F\\'elix Foutel-Rodier","submitted_at":"2019-07-12T17:11:12Z","abstract_excerpt":"Consider the Markov process taking values in the partitions of N such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate d. This is a special case of exchangeable fragmentation-coalescence process called Kingman's coalescent with erosion. We provide a new construction of the stationary distribution of this process as a sample from a standard flow of bridges. This allows us to give a representation of the asymptotic frequencies of this stationary distribution in terms of a sequence of hierarchically independent diffusions. Moreover,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05845","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:40:44Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SxcCpQuCG+wV4i5TEkMNSFAH5E2QSUQYC2ABX6cxrGefXRnqKnx1f5dF0/sW+lQ8gpc1kbGFPAXjLkjsVxReBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:07:02.266846Z"},"content_sha256":"643657916a87e4ab08a9383dfab3ed2ab6749c5530c4be3965e9b07d4bec9733","schema_version":"1.0","event_id":"sha256:643657916a87e4ab08a9383dfab3ed2ab6749c5530c4be3965e9b07d4bec9733"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/KYHYFCJV5GKU2JG2VS4AUX2QSG/bundle.json","state_url":"https://pith.science/pith/KYHYFCJV5GKU2JG2VS4AUX2QSG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/KYHYFCJV5GKU2JG2VS4AUX2QSG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-26T23:07:02Z","links":{"resolver":"https://pith.science/pith/KYHYFCJV5GKU2JG2VS4AUX2QSG","bundle":"https://pith.science/pith/KYHYFCJV5GKU2JG2VS4AUX2QSG/bundle.json","state":"https://pith.science/pith/KYHYFCJV5GKU2JG2VS4AUX2QSG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/KYHYFCJV5GKU2JG2VS4AUX2QSG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:KYHYFCJV5GKU2JG2VS4AUX2QSG","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":"43642c65a46d75cac587051c5d686d06188ab0627a2206519c307795c2d213b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-12T17:11:12Z","title_canon_sha256":"bfecc41c8ceeb790739e54d9696331973fe918bd8eeb2617db7ba2e3fa4eb5fa"},"schema_version":"1.0","source":{"id":"1907.05845","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1907.05845","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"arxiv_version","alias_value":"1907.05845v1","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1907.05845","created_at":"2026-05-17T23:40:44Z"},{"alias_kind":"pith_short_12","alias_value":"KYHYFCJV5GKU","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_16","alias_value":"KYHYFCJV5GKU2JG2","created_at":"2026-05-18T12:33:21Z"},{"alias_kind":"pith_short_8","alias_value":"KYHYFCJV","created_at":"2026-05-18T12:33:21Z"}],"graph_snapshots":[{"event_id":"sha256:643657916a87e4ab08a9383dfab3ed2ab6749c5530c4be3965e9b07d4bec9733","target":"graph","created_at":"2026-05-17T23:40:44Z","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 the Markov process taking values in the partitions of N such that each pair of blocks merges at rate one, and each integer is eroded, i.e., becomes a singleton block, at rate d. This is a special case of exchangeable fragmentation-coalescence process called Kingman's coalescent with erosion. We provide a new construction of the stationary distribution of this process as a sample from a standard flow of bridges. This allows us to give a representation of the asymptotic frequencies of this stationary distribution in terms of a sequence of hierarchically independent diffusions. Moreover,","authors_text":"Amaury Lambert, Emmanuel Schertzer, F\\'elix Foutel-Rodier","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-12T17:11:12Z","title":"Kingman's coalescent with erosion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.05845","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":"sha256:9947b79f8f4517e8a578b74becf9981c5b8ab5085c25ce2989ff720c76e3bc41","target":"record","created_at":"2026-05-17T23:40:44Z","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":"43642c65a46d75cac587051c5d686d06188ab0627a2206519c307795c2d213b2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-07-12T17:11:12Z","title_canon_sha256":"bfecc41c8ceeb790739e54d9696331973fe918bd8eeb2617db7ba2e3fa4eb5fa"},"schema_version":"1.0","source":{"id":"1907.05845","kind":"arxiv","version":1}},"canonical_sha256":"560f828935e9954d24daacb80a5f5091b4c80e946235de2af3451ff5c2d292df","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"560f828935e9954d24daacb80a5f5091b4c80e946235de2af3451ff5c2d292df","first_computed_at":"2026-05-17T23:40:44.223947Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:44.223947Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WpAWwHPx+CM/6zJhPt1b5iClO7eE7WX58w5kmMoShTZyxNXLX5Q4MuHs4Uq9NIDPJIOeuBvJksthoUnL+hUgBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:44.224602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1907.05845","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9947b79f8f4517e8a578b74becf9981c5b8ab5085c25ce2989ff720c76e3bc41","sha256:643657916a87e4ab08a9383dfab3ed2ab6749c5530c4be3965e9b07d4bec9733"],"state_sha256":"c6b9e800ebdf8233542fee3683b027f347b0da1f94bd230d627bb721c936bfe4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jZJf/w+0ueZGx5Dz2jGBQR0VaLBpvRPopY2C/cCp+Cnu+rRdort/A4Iy4vzOPeSLKk6XBzdElj4jE+QdI8k7DQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:07:02.269170Z","bundle_sha256":"0bfc8f0a2a0745f901729bc20f07d289de13552af82830eefa8d03c879623cca"}}