{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:ODEITOH4WA3AQVNYMDJMLB63VZ","short_pith_number":"pith:ODEITOH4","canonical_record":{"source":{"id":"1901.07848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-23T12:28:39Z","cross_cats_sorted":[],"title_canon_sha256":"ca1432651d9d82997079b74050c354ff24955775e6430af877574b10def6efc7","abstract_canon_sha256":"f84856d8a8d41c50e4c015053cb9525b0819bccf041d3a57e99b6bd3253672d7"},"schema_version":"1.0"},"canonical_sha256":"70c889b8fcb0360855b860d2c587dbae4ede8280625b4592cbd9560b0d87d164","source":{"kind":"arxiv","id":"1901.07848","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07848","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07848v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07848","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"ODEITOH4WA3A","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"ODEITOH4WA3AQVNY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"ODEITOH4","created_at":"2026-05-18T12:33:24Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:ODEITOH4WA3AQVNYMDJMLB63VZ","target":"record","payload":{"canonical_record":{"source":{"id":"1901.07848","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-23T12:28:39Z","cross_cats_sorted":[],"title_canon_sha256":"ca1432651d9d82997079b74050c354ff24955775e6430af877574b10def6efc7","abstract_canon_sha256":"f84856d8a8d41c50e4c015053cb9525b0819bccf041d3a57e99b6bd3253672d7"},"schema_version":"1.0"},"canonical_sha256":"70c889b8fcb0360855b860d2c587dbae4ede8280625b4592cbd9560b0d87d164","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:39.612474Z","signature_b64":"GG+HxFQx4H1rPsI22RjM+naqntxbBRLoqx+Nchkk8eDI7Y2Ado74RauMb6Rw38gBmxyJP5YM4H5MH8FT30+rAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"70c889b8fcb0360855b860d2c587dbae4ede8280625b4592cbd9560b0d87d164","last_reissued_at":"2026-05-17T23:55:39.612081Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:39.612081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1901.07848","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":"2026-05-17T23:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J1h9R9OwXIEEq7JwEdyb6UhPtoRlPW65Oa61NmlDvTwKvnaOlzytYx/e3TaO8ZIFu/ucH26gZZxh6d3YNXDdBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:42:44.471939Z"},"content_sha256":"25fb7f532a03f1c10f844441f6179c5e1db92299d174d6c55317b51bf923d2ad","schema_version":"1.0","event_id":"sha256:25fb7f532a03f1c10f844441f6179c5e1db92299d174d6c55317b51bf923d2ad"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:ODEITOH4WA3AQVNYMDJMLB63VZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Density dependent replicator-mutator models in directed evolution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Mario Veruete, Matthieu Alfaro","submitted_at":"2019-01-23T12:28:39Z","abstract_excerpt":"We analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal rescaling related to the Avron-Herbst formula [1] to give of a complete picture of the Cauchy problem. Besides its well-posedness, we provide an implicit/explicit expression of the solution, and analyze its large time behaviour. As a by product, we also solve a replicator-mutator model where the mutation coefficient is socially determined, in the sense that it i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07848","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":"2026-05-17T23:55:39Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yZKtE4qKCt+QKD7821noXDcNNkPrsB6NH+jUkOVA54R1Fe46oiYwmlE2VkCfJNBPOtNYXJUH+9UxumgGERu/Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T16:42:44.472653Z"},"content_sha256":"e5e852caba1e381c880402827c450cb897504563bbd39c045195636ac41d969b","schema_version":"1.0","event_id":"sha256:e5e852caba1e381c880402827c450cb897504563bbd39c045195636ac41d969b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ODEITOH4WA3AQVNYMDJMLB63VZ/bundle.json","state_url":"https://pith.science/pith/ODEITOH4WA3AQVNYMDJMLB63VZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ODEITOH4WA3AQVNYMDJMLB63VZ/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":"2026-06-08T16:42:44Z","links":{"resolver":"https://pith.science/pith/ODEITOH4WA3AQVNYMDJMLB63VZ","bundle":"https://pith.science/pith/ODEITOH4WA3AQVNYMDJMLB63VZ/bundle.json","state":"https://pith.science/pith/ODEITOH4WA3AQVNYMDJMLB63VZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ODEITOH4WA3AQVNYMDJMLB63VZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:ODEITOH4WA3AQVNYMDJMLB63VZ","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":"f84856d8a8d41c50e4c015053cb9525b0819bccf041d3a57e99b6bd3253672d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-23T12:28:39Z","title_canon_sha256":"ca1432651d9d82997079b74050c354ff24955775e6430af877574b10def6efc7"},"schema_version":"1.0","source":{"id":"1901.07848","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1901.07848","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"arxiv_version","alias_value":"1901.07848v1","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.07848","created_at":"2026-05-17T23:55:39Z"},{"alias_kind":"pith_short_12","alias_value":"ODEITOH4WA3A","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_16","alias_value":"ODEITOH4WA3AQVNY","created_at":"2026-05-18T12:33:24Z"},{"alias_kind":"pith_short_8","alias_value":"ODEITOH4","created_at":"2026-05-18T12:33:24Z"}],"graph_snapshots":[{"event_id":"sha256:e5e852caba1e381c880402827c450cb897504563bbd39c045195636ac41d969b","target":"graph","created_at":"2026-05-17T23:55:39Z","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 analyze a replicator-mutator model arising in the context of directed evolution [23], where the selection term is modulated over time by the mean-fitness. We combine a Cumulant Generating Function approach [13] and a spatio-temporal rescaling related to the Avron-Herbst formula [1] to give of a complete picture of the Cauchy problem. Besides its well-posedness, we provide an implicit/explicit expression of the solution, and analyze its large time behaviour. As a by product, we also solve a replicator-mutator model where the mutation coefficient is socially determined, in the sense that it i","authors_text":"Mario Veruete, Matthieu Alfaro","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-23T12:28:39Z","title":"Density dependent replicator-mutator models in directed evolution"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07848","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":"sha256:25fb7f532a03f1c10f844441f6179c5e1db92299d174d6c55317b51bf923d2ad","target":"record","created_at":"2026-05-17T23:55:39Z","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":"f84856d8a8d41c50e4c015053cb9525b0819bccf041d3a57e99b6bd3253672d7","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2019-01-23T12:28:39Z","title_canon_sha256":"ca1432651d9d82997079b74050c354ff24955775e6430af877574b10def6efc7"},"schema_version":"1.0","source":{"id":"1901.07848","kind":"arxiv","version":1}},"canonical_sha256":"70c889b8fcb0360855b860d2c587dbae4ede8280625b4592cbd9560b0d87d164","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"70c889b8fcb0360855b860d2c587dbae4ede8280625b4592cbd9560b0d87d164","first_computed_at":"2026-05-17T23:55:39.612081Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:39.612081Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GG+HxFQx4H1rPsI22RjM+naqntxbBRLoqx+Nchkk8eDI7Y2Ado74RauMb6Rw38gBmxyJP5YM4H5MH8FT30+rAg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:39.612474Z","signed_message":"canonical_sha256_bytes"},"source_id":"1901.07848","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:25fb7f532a03f1c10f844441f6179c5e1db92299d174d6c55317b51bf923d2ad","sha256:e5e852caba1e381c880402827c450cb897504563bbd39c045195636ac41d969b"],"state_sha256":"49b0e0dd7903c47807a728173ca6fca2b57a237b51175fbd6d62077445158d01"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vn2K0yACwBzFDVJRUuMPaZVBXcegMvdXYoS5691h6jAlOz+97qz/MaB2Fs3RSZjBbpmDkc4zPFOe4VsZYohiCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T16:42:44.475903Z","bundle_sha256":"e577589bb8b5074194640d5bf605fda9fffa8e718717da1e8bda8743e46304cd"}}