{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:UK5OHPKUHPNZHJTUB7T7IQ3OAP","short_pith_number":"pith:UK5OHPKU","canonical_record":{"source":{"id":"1509.02022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T13:07:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c3af92841ab3933ac991569690dee848247cf299adf1b331459b57c119242c1e","abstract_canon_sha256":"6b20163ccc3124f8183094af4fadd1872309f07a42416b3465f47ba9573cb436"},"schema_version":"1.0"},"canonical_sha256":"a2bae3bd543bdb93a6740fe7f4436e03e0baeedcbeaae9e24a35de95dfb61ee8","source":{"kind":"arxiv","id":"1509.02022","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02022","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02022v1","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02022","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"UK5OHPKUHPNZ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UK5OHPKUHPNZHJTU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UK5OHPKU","created_at":"2026-05-18T12:29:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:UK5OHPKUHPNZHJTUB7T7IQ3OAP","target":"record","payload":{"canonical_record":{"source":{"id":"1509.02022","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T13:07:40Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"c3af92841ab3933ac991569690dee848247cf299adf1b331459b57c119242c1e","abstract_canon_sha256":"6b20163ccc3124f8183094af4fadd1872309f07a42416b3465f47ba9573cb436"},"schema_version":"1.0"},"canonical_sha256":"a2bae3bd543bdb93a6740fe7f4436e03e0baeedcbeaae9e24a35de95dfb61ee8","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:49.910656Z","signature_b64":"HPBGNQQQRkBZ5VmkW5AX4am68K881WFwZxLa37fRSA5yp9/7SMMoGs1KYGhU5psASVRSqn5juWuHFf6dbi71Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2bae3bd543bdb93a6740fe7f4436e03e0baeedcbeaae9e24a35de95dfb61ee8","last_reissued_at":"2026-05-18T01:33:49.910067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:49.910067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1509.02022","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":"2026-05-18T01:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tXGxYobykfoCfdX5TUXj+sEsZnU6ATqVWw11EuNCJs2ArMNAInbB4YQbAEtWA4eLtbri2kH1BXWZVrU2l0NhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:14:59.776074Z"},"content_sha256":"50254bf5b8f7df4fe3b3f57dacef4397ecdac6c46b81b662e6fecd895ddb96df","schema_version":"1.0","event_id":"sha256:50254bf5b8f7df4fe3b3f57dacef4397ecdac6c46b81b662e6fecd895ddb96df"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:UK5OHPKUHPNZHJTUB7T7IQ3OAP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Helene Leman","submitted_at":"2015-09-07T13:07:40Z","abstract_excerpt":"We consider an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process when the population size grows to $+\\infty$ and the mutation probability decreases to $0$. We prove a convergence towards a jump process that jumps in the infinite dimensional space of the stable spat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02022","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":"2026-05-18T01:33:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MGN0S2FP/7n5boUzlkXirmCCDzDt4JcL+u/6aVplUfovPUQyMTOPfGjU7I+1sP9kPTqa8D+PEU9H0jaMgvXVDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T15:14:59.776498Z"},"content_sha256":"20ae1547a26d299bccb73474a8abf5ec1a96de55fe753b44b14501b143db1ed6","schema_version":"1.0","event_id":"sha256:20ae1547a26d299bccb73474a8abf5ec1a96de55fe753b44b14501b143db1ed6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/bundle.json","state_url":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/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":"2026-06-08T15:14:59Z","links":{"resolver":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP","bundle":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/bundle.json","state":"https://pith.science/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/UK5OHPKUHPNZHJTUB7T7IQ3OAP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:UK5OHPKUHPNZHJTUB7T7IQ3OAP","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":"6b20163ccc3124f8183094af4fadd1872309f07a42416b3465f47ba9573cb436","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T13:07:40Z","title_canon_sha256":"c3af92841ab3933ac991569690dee848247cf299adf1b331459b57c119242c1e"},"schema_version":"1.0","source":{"id":"1509.02022","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1509.02022","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"arxiv_version","alias_value":"1509.02022v1","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1509.02022","created_at":"2026-05-18T01:33:49Z"},{"alias_kind":"pith_short_12","alias_value":"UK5OHPKUHPNZ","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"UK5OHPKUHPNZHJTU","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"UK5OHPKU","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:20ae1547a26d299bccb73474a8abf5ec1a96de55fe753b44b14501b143db1ed6","target":"graph","created_at":"2026-05-18T01:33:49Z","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 an individual-based spatially structured population for Darwinian evolution in an asexual population. The individuals move randomly on a bounded continuous space according to a reflected brownian motion. The dynamics involves also a birth rate, a density-dependent logistic death rate and a probability of mutation at each birth event. We study the convergence of the microscopic process when the population size grows to $+\\infty$ and the mutation probability decreases to $0$. We prove a convergence towards a jump process that jumps in the infinite dimensional space of the stable spat","authors_text":"Helene Leman","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T13:07:40Z","title":"Convergence of an infinite dimensional stochastic process to a spatially structured trait substitution sequence"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.02022","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":"sha256:50254bf5b8f7df4fe3b3f57dacef4397ecdac6c46b81b662e6fecd895ddb96df","target":"record","created_at":"2026-05-18T01:33:49Z","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":"6b20163ccc3124f8183094af4fadd1872309f07a42416b3465f47ba9573cb436","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-09-07T13:07:40Z","title_canon_sha256":"c3af92841ab3933ac991569690dee848247cf299adf1b331459b57c119242c1e"},"schema_version":"1.0","source":{"id":"1509.02022","kind":"arxiv","version":1}},"canonical_sha256":"a2bae3bd543bdb93a6740fe7f4436e03e0baeedcbeaae9e24a35de95dfb61ee8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2bae3bd543bdb93a6740fe7f4436e03e0baeedcbeaae9e24a35de95dfb61ee8","first_computed_at":"2026-05-18T01:33:49.910067Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:49.910067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HPBGNQQQRkBZ5VmkW5AX4am68K881WFwZxLa37fRSA5yp9/7SMMoGs1KYGhU5psASVRSqn5juWuHFf6dbi71Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:49.910656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1509.02022","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50254bf5b8f7df4fe3b3f57dacef4397ecdac6c46b81b662e6fecd895ddb96df","sha256:20ae1547a26d299bccb73474a8abf5ec1a96de55fe753b44b14501b143db1ed6"],"state_sha256":"a94565ef73290f4df7d5c9d3d6893dd935e342b1b2c1518d8a2c2fafd5c19b2e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AOfK7ZXdwAh0ONTQ7b2GIYKGBmc1MRxNm8L1XAaZtXRy4yxuTbI3h8/Aix2qLIHAluEtLdFcOP/naGS9b/ZFBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T15:14:59.779094Z","bundle_sha256":"a10ea6d6989de815df203591e312460bd31cbd47e619f856b126465fef1d1829"}}