{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:CWB237TTXKUM4FEVY2UHYNHQRD","short_pith_number":"pith:CWB237TT","canonical_record":{"source":{"id":"1807.09153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T14:38:58Z","cross_cats_sorted":["math.AP","q-bio.PE"],"title_canon_sha256":"dccf47764748ca387ee9a87ea6185414e29a64212d703c935a9216ed7893de95","abstract_canon_sha256":"9987e0cbeba37fcf544444e6d5beb3f34e1c740f611551145195e431c9301ec5"},"schema_version":"1.0"},"canonical_sha256":"1583adfe73baa8ce1495c6a87c34f088c5576e0d80c958b692b91b1b15abc28d","source":{"kind":"arxiv","id":"1807.09153","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09153","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09153v1","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09153","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"CWB237TTXKUM","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CWB237TTXKUM4FEV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CWB237TT","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:CWB237TTXKUM4FEVY2UHYNHQRD","target":"record","payload":{"canonical_record":{"source":{"id":"1807.09153","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T14:38:58Z","cross_cats_sorted":["math.AP","q-bio.PE"],"title_canon_sha256":"dccf47764748ca387ee9a87ea6185414e29a64212d703c935a9216ed7893de95","abstract_canon_sha256":"9987e0cbeba37fcf544444e6d5beb3f34e1c740f611551145195e431c9301ec5"},"schema_version":"1.0"},"canonical_sha256":"1583adfe73baa8ce1495c6a87c34f088c5576e0d80c958b692b91b1b15abc28d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:09:56.624647Z","signature_b64":"fyt4v/J8ke1nJY/Gi3wZ+bM0D4LWLLA9To5qNr4DjJEHpvuH1iXoo72SPQXNezzh851KDZvOCnxXwbzkL2aiCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1583adfe73baa8ce1495c6a87c34f088c5576e0d80c958b692b91b1b15abc28d","last_reissued_at":"2026-05-18T00:09:56.623927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:09:56.623927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.09153","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":"2026-05-18T00:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vuwu1PcBoQ1DiG/+nLeTa3v9v5TFcHc1yXGndKMhMg4wzLyYuckZ/e2Cr7TZOGIlxwByyqa73IBdTt2D2EPSCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:16:37.237844Z"},"content_sha256":"40350796927448f9d8ca98275d05967870a910036fb029412480f5001aa8cd1e","schema_version":"1.0","event_id":"sha256:40350796927448f9d8ca98275d05967870a910036fb029412480f5001aa8cd1e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:CWB237TTXKUM4FEVY2UHYNHQRD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coagulation-transport equations and the nested coalescents","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","q-bio.PE"],"primary_cat":"math.PR","authors_text":"Amaury Lambert, Emmanuel Schertzer","submitted_at":"2018-07-24T14:38:58Z","abstract_excerpt":"The nested Kingman coalescent describes the dynamics of particles (called genes) contained in larger components (called species), where pairs of species coalesce at constant rate and pairs of genes coalesce at constant rate provided they lie within the same species. We prove that starting from $rn$ species, the empirical distribution of species masses (numbers of genes$/n$) at time $t/n$ converges as $n\\to\\infty$ to a solution of the deterministic coagulation-transport equation $$\n  \\partial_t d \\ = \\ \\partial_x ( \\psi d ) \\ + \\ a(t)\\left(d\\star d - d \\right), $$ where $\\psi(x) = cx^2$, $\\star"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09153","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":"2026-05-18T00:09:56Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IPQmhMbbfH2xNPrim4qudpdKp59blNC4lkEyhpbb5AH5DZJbrtj5Esyxfvclw23h6vakT5Qwv39Pi5WWY00qDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T23:16:37.238184Z"},"content_sha256":"51cbb92567ef137ddfab97af68bf9fd318d5686461161990108e8d26b74b2360","schema_version":"1.0","event_id":"sha256:51cbb92567ef137ddfab97af68bf9fd318d5686461161990108e8d26b74b2360"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CWB237TTXKUM4FEVY2UHYNHQRD/bundle.json","state_url":"https://pith.science/pith/CWB237TTXKUM4FEVY2UHYNHQRD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CWB237TTXKUM4FEVY2UHYNHQRD/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":"2026-06-26T23:16:37Z","links":{"resolver":"https://pith.science/pith/CWB237TTXKUM4FEVY2UHYNHQRD","bundle":"https://pith.science/pith/CWB237TTXKUM4FEVY2UHYNHQRD/bundle.json","state":"https://pith.science/pith/CWB237TTXKUM4FEVY2UHYNHQRD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CWB237TTXKUM4FEVY2UHYNHQRD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CWB237TTXKUM4FEVY2UHYNHQRD","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":"9987e0cbeba37fcf544444e6d5beb3f34e1c740f611551145195e431c9301ec5","cross_cats_sorted":["math.AP","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T14:38:58Z","title_canon_sha256":"dccf47764748ca387ee9a87ea6185414e29a64212d703c935a9216ed7893de95"},"schema_version":"1.0","source":{"id":"1807.09153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.09153","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"arxiv_version","alias_value":"1807.09153v1","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.09153","created_at":"2026-05-18T00:09:56Z"},{"alias_kind":"pith_short_12","alias_value":"CWB237TTXKUM","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CWB237TTXKUM4FEV","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CWB237TT","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:51cbb92567ef137ddfab97af68bf9fd318d5686461161990108e8d26b74b2360","target":"graph","created_at":"2026-05-18T00:09:56Z","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":"The nested Kingman coalescent describes the dynamics of particles (called genes) contained in larger components (called species), where pairs of species coalesce at constant rate and pairs of genes coalesce at constant rate provided they lie within the same species. We prove that starting from $rn$ species, the empirical distribution of species masses (numbers of genes$/n$) at time $t/n$ converges as $n\\to\\infty$ to a solution of the deterministic coagulation-transport equation $$\n  \\partial_t d \\ = \\ \\partial_x ( \\psi d ) \\ + \\ a(t)\\left(d\\star d - d \\right), $$ where $\\psi(x) = cx^2$, $\\star","authors_text":"Amaury Lambert, Emmanuel Schertzer","cross_cats":["math.AP","q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T14:38:58Z","title":"Coagulation-transport equations and the nested coalescents"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09153","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":"sha256:40350796927448f9d8ca98275d05967870a910036fb029412480f5001aa8cd1e","target":"record","created_at":"2026-05-18T00:09:56Z","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":"9987e0cbeba37fcf544444e6d5beb3f34e1c740f611551145195e431c9301ec5","cross_cats_sorted":["math.AP","q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-07-24T14:38:58Z","title_canon_sha256":"dccf47764748ca387ee9a87ea6185414e29a64212d703c935a9216ed7893de95"},"schema_version":"1.0","source":{"id":"1807.09153","kind":"arxiv","version":1}},"canonical_sha256":"1583adfe73baa8ce1495c6a87c34f088c5576e0d80c958b692b91b1b15abc28d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1583adfe73baa8ce1495c6a87c34f088c5576e0d80c958b692b91b1b15abc28d","first_computed_at":"2026-05-18T00:09:56.623927Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:09:56.623927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fyt4v/J8ke1nJY/Gi3wZ+bM0D4LWLLA9To5qNr4DjJEHpvuH1iXoo72SPQXNezzh851KDZvOCnxXwbzkL2aiCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:09:56.624647Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.09153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:40350796927448f9d8ca98275d05967870a910036fb029412480f5001aa8cd1e","sha256:51cbb92567ef137ddfab97af68bf9fd318d5686461161990108e8d26b74b2360"],"state_sha256":"cfd1a5377866cca5ec2feaf3b76a002f430f8be3ed7b541dc5e26640e1ca08fe"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kUOEonP+HzwrY7qhqca5mhZJI514yyFwMoqDkOdmER55W6dFxLSvmCZuMLgh587wUASX1VMf32FukwsJi/rVCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T23:16:37.240037Z","bundle_sha256":"54356d0f02d6cfc011f35b22b54530187887e0d4cd21639bb6992b9c724f8246"}}