{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:ZEI44ZXYWAPYCGCPBROYKPLZD4","short_pith_number":"pith:ZEI44ZXY","canonical_record":{"source":{"id":"2411.09779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2024-11-14T19:47:19Z","cross_cats_sorted":["cs.NE","math.CT"],"title_canon_sha256":"77a9e35a88cf644e12d715e95a511fbe735ccc448198c750b96f8f9ef1823e90","abstract_canon_sha256":"0ff68b5a921215effded95259e3583f12d7376327e1610527fa5d08f8aeddc21"},"schema_version":"1.0"},"canonical_sha256":"c911ce66f8b01f81184f0c5d853d791f0157c91b305b6c9fa60918f42b4c8de2","source":{"kind":"arxiv","id":"2411.09779","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09779","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09779v1","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09779","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZEI44ZXYWAPY","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"pith_short_16","alias_value":"ZEI44ZXYWAPYCGCP","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"pith_short_8","alias_value":"ZEI44ZXY","created_at":"2026-07-05T09:35:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:ZEI44ZXYWAPYCGCPBROYKPLZD4","target":"record","payload":{"canonical_record":{"source":{"id":"2411.09779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2024-11-14T19:47:19Z","cross_cats_sorted":["cs.NE","math.CT"],"title_canon_sha256":"77a9e35a88cf644e12d715e95a511fbe735ccc448198c750b96f8f9ef1823e90","abstract_canon_sha256":"0ff68b5a921215effded95259e3583f12d7376327e1610527fa5d08f8aeddc21"},"schema_version":"1.0"},"canonical_sha256":"c911ce66f8b01f81184f0c5d853d791f0157c91b305b6c9fa60918f42b4c8de2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T09:35:38.088345Z","signature_b64":"jlzHZanx39a82zTT53MeM8wF+W1qwPCUyKlyUNdtenmv9BY9bwS1e4+9h2BWtxASGkgektLiPZa91oRmExt8Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c911ce66f8b01f81184f0c5d853d791f0157c91b305b6c9fa60918f42b4c8de2","last_reissued_at":"2026-07-05T09:35:38.087846Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T09:35:38.087846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2411.09779","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":"2026-07-05T09:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"jQClasHtjSjUwrtN78pmyoybp654IF7CUf4Hq8rW+K07or4JmvWz6HP3ZW50xRmZzRz5KRzSLW89QRZuYcHOCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T02:57:53.784849Z"},"content_sha256":"bd481847d1e3200d3bee11980ce6af29796988584b8a6f86d7f1c1d87d725aac","schema_version":"1.0","event_id":"sha256:bd481847d1e3200d3bee11980ce6af29796988584b8a6f86d7f1c1d87d725aac"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:ZEI44ZXYWAPYCGCPBROYKPLZD4","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Variational methods for Learning Multilevel Genetic Algorithms using the Kantorovich Monad","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NE","math.CT"],"primary_cat":"q-bio.PE","authors_text":"Anja M\\\"osch, Cameron Smith, Francesco Alesiani, Jonathan Warrell, Martin Renqiang Min","submitted_at":"2024-11-14T19:47:19Z","abstract_excerpt":"Levels of selection and multilevel evolutionary processes are essential concepts in evolutionary theory, and yet there is a lack of common mathematical models for these core ideas. Here, we propose a unified mathematical framework for formulating and optimizing multilevel evolutionary processes and genetic algorithms over arbitrarily many levels based on concepts from category theory and population genetics. We formulate a multilevel version of the Wright-Fisher process using this approach, and we show that this model can be analyzed to clarify key features of multilevel selection. Particularl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09779","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.09779/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T09:35:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Nt0TRVFAw/M9Tkc9LGppb8pf4kju062m1KV1GQBeDP4GZVktoGdT5s2Jf6uDwwfg7a0L1mOFzscnP068JOBKCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-15T02:57:53.785191Z"},"content_sha256":"39523018dd440ae55bb08a7834c3a473b24668efb19dff58e17af92826947161","schema_version":"1.0","event_id":"sha256:39523018dd440ae55bb08a7834c3a473b24668efb19dff58e17af92826947161"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZEI44ZXYWAPYCGCPBROYKPLZD4/bundle.json","state_url":"https://pith.science/pith/ZEI44ZXYWAPYCGCPBROYKPLZD4/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZEI44ZXYWAPYCGCPBROYKPLZD4/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":"2026-08-15T02:57:53Z","links":{"resolver":"https://pith.science/pith/ZEI44ZXYWAPYCGCPBROYKPLZD4","bundle":"https://pith.science/pith/ZEI44ZXYWAPYCGCPBROYKPLZD4/bundle.json","state":"https://pith.science/pith/ZEI44ZXYWAPYCGCPBROYKPLZD4/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZEI44ZXYWAPYCGCPBROYKPLZD4/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ZEI44ZXYWAPYCGCPBROYKPLZD4","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":"0ff68b5a921215effded95259e3583f12d7376327e1610527fa5d08f8aeddc21","cross_cats_sorted":["cs.NE","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2024-11-14T19:47:19Z","title_canon_sha256":"77a9e35a88cf644e12d715e95a511fbe735ccc448198c750b96f8f9ef1823e90"},"schema_version":"1.0","source":{"id":"2411.09779","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2411.09779","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"2411.09779v1","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.09779","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"ZEI44ZXYWAPY","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"pith_short_16","alias_value":"ZEI44ZXYWAPYCGCP","created_at":"2026-07-05T09:35:38Z"},{"alias_kind":"pith_short_8","alias_value":"ZEI44ZXY","created_at":"2026-07-05T09:35:38Z"}],"graph_snapshots":[{"event_id":"sha256:39523018dd440ae55bb08a7834c3a473b24668efb19dff58e17af92826947161","target":"graph","created_at":"2026-07-05T09:35:38Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2411.09779/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Levels of selection and multilevel evolutionary processes are essential concepts in evolutionary theory, and yet there is a lack of common mathematical models for these core ideas. Here, we propose a unified mathematical framework for formulating and optimizing multilevel evolutionary processes and genetic algorithms over arbitrarily many levels based on concepts from category theory and population genetics. We formulate a multilevel version of the Wright-Fisher process using this approach, and we show that this model can be analyzed to clarify key features of multilevel selection. Particularl","authors_text":"Anja M\\\"osch, Cameron Smith, Francesco Alesiani, Jonathan Warrell, Martin Renqiang Min","cross_cats":["cs.NE","math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2024-11-14T19:47:19Z","title":"Variational methods for Learning Multilevel Genetic Algorithms using the Kantorovich Monad"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.09779","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:bd481847d1e3200d3bee11980ce6af29796988584b8a6f86d7f1c1d87d725aac","target":"record","created_at":"2026-07-05T09:35:38Z","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":"0ff68b5a921215effded95259e3583f12d7376327e1610527fa5d08f8aeddc21","cross_cats_sorted":["cs.NE","math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2024-11-14T19:47:19Z","title_canon_sha256":"77a9e35a88cf644e12d715e95a511fbe735ccc448198c750b96f8f9ef1823e90"},"schema_version":"1.0","source":{"id":"2411.09779","kind":"arxiv","version":1}},"canonical_sha256":"c911ce66f8b01f81184f0c5d853d791f0157c91b305b6c9fa60918f42b4c8de2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c911ce66f8b01f81184f0c5d853d791f0157c91b305b6c9fa60918f42b4c8de2","first_computed_at":"2026-07-05T09:35:38.087846Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:35:38.087846Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jlzHZanx39a82zTT53MeM8wF+W1qwPCUyKlyUNdtenmv9BY9bwS1e4+9h2BWtxASGkgektLiPZa91oRmExt8Bw==","signature_status":"signed_v1","signed_at":"2026-07-05T09:35:38.088345Z","signed_message":"canonical_sha256_bytes"},"source_id":"2411.09779","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bd481847d1e3200d3bee11980ce6af29796988584b8a6f86d7f1c1d87d725aac","sha256:39523018dd440ae55bb08a7834c3a473b24668efb19dff58e17af92826947161"],"state_sha256":"cb608650993fe7255b18d29cf26091a797c0fa13b3a52a6c76c1ba35ab387fad"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"T/zdoSZP7HobVqfEK+9CkfSGPurGHv19X9TP9W58x6DXzLMMyaUM7Llts9FeJvlDWGSvpxym8MaBwOk+QSSFAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-15T02:57:53.787401Z","bundle_sha256":"e693c6d1c4ceb10cef830971c0241e3c4f61f92c15dfb457bb11118cfd58d010"}}