{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2023:WTTUFTEIOSA4S7TGFSX6UIOSOH","short_pith_number":"pith:WTTUFTEI","canonical_record":{"source":{"id":"2307.09940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-07-19T12:32:09Z","cross_cats_sorted":[],"title_canon_sha256":"385928e726b0b82a93e5d2dc0838edc09e79b4dde5378842715a48544413c67d","abstract_canon_sha256":"b667b39fd2483df634c24ef2e3fa9f2480d2ca2edfccc0ac812a6d9809c50be9"},"schema_version":"1.0"},"canonical_sha256":"b4e742cc887481c97e662cafea21d271d16900fce8b64d6602ae2b86b5c41767","source":{"kind":"arxiv","id":"2307.09940","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.09940","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"arxiv_version","alias_value":"2307.09940v1","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.09940","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"pith_short_12","alias_value":"WTTUFTEIOSA4","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"pith_short_16","alias_value":"WTTUFTEIOSA4S7TG","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"pith_short_8","alias_value":"WTTUFTEI","created_at":"2026-07-05T06:32:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2023:WTTUFTEIOSA4S7TGFSX6UIOSOH","target":"record","payload":{"canonical_record":{"source":{"id":"2307.09940","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-07-19T12:32:09Z","cross_cats_sorted":[],"title_canon_sha256":"385928e726b0b82a93e5d2dc0838edc09e79b4dde5378842715a48544413c67d","abstract_canon_sha256":"b667b39fd2483df634c24ef2e3fa9f2480d2ca2edfccc0ac812a6d9809c50be9"},"schema_version":"1.0"},"canonical_sha256":"b4e742cc887481c97e662cafea21d271d16900fce8b64d6602ae2b86b5c41767","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:32:48.272451Z","signature_b64":"8stpyLRbxqdp/zmGQvyQUZRpkxlSpRvtff3r1Wv/70/5JjnVPioATq/yRQUAWKik8TuenKo7+t3hWLgZHWafBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4e742cc887481c97e662cafea21d271d16900fce8b64d6602ae2b86b5c41767","last_reissued_at":"2026-07-05T06:32:48.272055Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:32:48.272055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2307.09940","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":"2026-07-05T06:32:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3zYOFnvv8pW21GI5VZfIKjHv5+kffbC5V1kPrOVwlyoMlNwmN8hZ/htVnxcPqk7FX6ILaUUxB5wm7wKKu7tGDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:01:08.503755Z"},"content_sha256":"a0ae4e18688b49b79ba338a3f239ffa860a09dc84c36526a011c1d546a6c919c","schema_version":"1.0","event_id":"sha256:a0ae4e18688b49b79ba338a3f239ffa860a09dc84c36526a011c1d546a6c919c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2023:WTTUFTEIOSA4S7TGFSX6UIOSOH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Does genetic diversity help survival?","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fabio P. Machado, Luiz Renato Fontes, Rinaldo B. Schinazi","submitted_at":"2023-07-19T12:32:09Z","abstract_excerpt":"We introduce the following model for the evolution of a population. At every discrete time $j\\geq 0$ exactly one individual is introduced in the population and is assigned a death probability $c_j$ sampled from $C$, a fixed probability distribution. We think of $c_j$ as a genetic marker of this individual. At every time $n\\geq 1$ every individual in the population dies or not independently of each other with its corresponding death probability $c_j$. We show that the population size goes to infinity if and only if $E(1/C)=\\infty$. This is in sharp contrast with the model with constant $c$ and "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.09940","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/2307.09940/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":"2026-07-05T06:32:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/znZsPecoHLhSCIUvhnzg2iEll/X8qlmV1Uaxy0yAMvQM00vAZvgGKCprhlBTKdmCJCkzinO9EONVdMYpbyOAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-05T15:01:08.504432Z"},"content_sha256":"0f36dfadf82bed5730dd68308c39ced42da2173b18f4298ffb7c2184b85da243","schema_version":"1.0","event_id":"sha256:0f36dfadf82bed5730dd68308c39ced42da2173b18f4298ffb7c2184b85da243"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WTTUFTEIOSA4S7TGFSX6UIOSOH/bundle.json","state_url":"https://pith.science/pith/WTTUFTEIOSA4S7TGFSX6UIOSOH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WTTUFTEIOSA4S7TGFSX6UIOSOH/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":"2026-07-05T15:01:08Z","links":{"resolver":"https://pith.science/pith/WTTUFTEIOSA4S7TGFSX6UIOSOH","bundle":"https://pith.science/pith/WTTUFTEIOSA4S7TGFSX6UIOSOH/bundle.json","state":"https://pith.science/pith/WTTUFTEIOSA4S7TGFSX6UIOSOH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WTTUFTEIOSA4S7TGFSX6UIOSOH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:WTTUFTEIOSA4S7TGFSX6UIOSOH","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":"b667b39fd2483df634c24ef2e3fa9f2480d2ca2edfccc0ac812a6d9809c50be9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-07-19T12:32:09Z","title_canon_sha256":"385928e726b0b82a93e5d2dc0838edc09e79b4dde5378842715a48544413c67d"},"schema_version":"1.0","source":{"id":"2307.09940","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2307.09940","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"arxiv_version","alias_value":"2307.09940v1","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2307.09940","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"pith_short_12","alias_value":"WTTUFTEIOSA4","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"pith_short_16","alias_value":"WTTUFTEIOSA4S7TG","created_at":"2026-07-05T06:32:48Z"},{"alias_kind":"pith_short_8","alias_value":"WTTUFTEI","created_at":"2026-07-05T06:32:48Z"}],"graph_snapshots":[{"event_id":"sha256:0f36dfadf82bed5730dd68308c39ced42da2173b18f4298ffb7c2184b85da243","target":"graph","created_at":"2026-07-05T06:32:48Z","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/2307.09940/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce the following model for the evolution of a population. At every discrete time $j\\geq 0$ exactly one individual is introduced in the population and is assigned a death probability $c_j$ sampled from $C$, a fixed probability distribution. We think of $c_j$ as a genetic marker of this individual. At every time $n\\geq 1$ every individual in the population dies or not independently of each other with its corresponding death probability $c_j$. We show that the population size goes to infinity if and only if $E(1/C)=\\infty$. This is in sharp contrast with the model with constant $c$ and ","authors_text":"Fabio P. Machado, Luiz Renato Fontes, Rinaldo B. Schinazi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-07-19T12:32:09Z","title":"Does genetic diversity help survival?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2307.09940","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:a0ae4e18688b49b79ba338a3f239ffa860a09dc84c36526a011c1d546a6c919c","target":"record","created_at":"2026-07-05T06:32:48Z","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":"b667b39fd2483df634c24ef2e3fa9f2480d2ca2edfccc0ac812a6d9809c50be9","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-07-19T12:32:09Z","title_canon_sha256":"385928e726b0b82a93e5d2dc0838edc09e79b4dde5378842715a48544413c67d"},"schema_version":"1.0","source":{"id":"2307.09940","kind":"arxiv","version":1}},"canonical_sha256":"b4e742cc887481c97e662cafea21d271d16900fce8b64d6602ae2b86b5c41767","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4e742cc887481c97e662cafea21d271d16900fce8b64d6602ae2b86b5c41767","first_computed_at":"2026-07-05T06:32:48.272055Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T06:32:48.272055Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8stpyLRbxqdp/zmGQvyQUZRpkxlSpRvtff3r1Wv/70/5JjnVPioATq/yRQUAWKik8TuenKo7+t3hWLgZHWafBQ==","signature_status":"signed_v1","signed_at":"2026-07-05T06:32:48.272451Z","signed_message":"canonical_sha256_bytes"},"source_id":"2307.09940","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a0ae4e18688b49b79ba338a3f239ffa860a09dc84c36526a011c1d546a6c919c","sha256:0f36dfadf82bed5730dd68308c39ced42da2173b18f4298ffb7c2184b85da243"],"state_sha256":"bf49de789cf1ffa4c35026e5726c5439354b0b096ca98a8e791efca068e8e5ec"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CcJHcef9Lt4wGasWaAj3TTlJnShMflY2CDCP+JzrfMCtyufOtPOAT2TZ4qaOvGV6sGH5U98VwJrUSfvBr3JECA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-05T15:01:08.507865Z","bundle_sha256":"1aa0b3b66ba2f6fb1c3ce3bfaa566f3e8a4b72ca8ab107ba5410646923d8f764"}}