{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:DFG4H5NK7FQ7JCNOLAARJJFV4R","short_pith_number":"pith:DFG4H5NK","canonical_record":{"source":{"id":"2606.22001","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2026-06-20T11:53:39Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"dbfc530aa2710f21d5a1eaf829b67ee64369a600ca61abca602f3c48a6d6ff5e","abstract_canon_sha256":"41d6059653e42813db7deb952309c36dffca4fa254c903a377c1c851e55ab557"},"schema_version":"1.0"},"canonical_sha256":"194dc3f5aaf961f489ae580114a4b5e4524ea00667a0ef45020dd086ef27c8b9","source":{"kind":"arxiv","id":"2606.22001","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22001","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22001v1","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22001","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"DFG4H5NK7FQ7","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"pith_short_16","alias_value":"DFG4H5NK7FQ7JCNO","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"pith_short_8","alias_value":"DFG4H5NK","created_at":"2026-06-23T02:13:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:DFG4H5NK7FQ7JCNOLAARJJFV4R","target":"record","payload":{"canonical_record":{"source":{"id":"2606.22001","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2026-06-20T11:53:39Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"dbfc530aa2710f21d5a1eaf829b67ee64369a600ca61abca602f3c48a6d6ff5e","abstract_canon_sha256":"41d6059653e42813db7deb952309c36dffca4fa254c903a377c1c851e55ab557"},"schema_version":"1.0"},"canonical_sha256":"194dc3f5aaf961f489ae580114a4b5e4524ea00667a0ef45020dd086ef27c8b9","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:05.316801Z","signature_b64":"ynfSTU7TOi8luUBvfFe/a4SvJIE3Ai+2KM/g/O4O+ayJxrJBHxP4AeRb+TPk9OE77WCck9G7DX9AnQ6YBNOcCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"194dc3f5aaf961f489ae580114a4b5e4524ea00667a0ef45020dd086ef27c8b9","last_reissued_at":"2026-06-23T02:13:05.316370Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:05.316370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2606.22001","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":"2026-06-23T02:13:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Jflbs6FO4j+9rKRN2Eio0BjA6XlwwMO3voXYYZVUeHMHPSjSf1y6FUGoIaDPSoCUdO2z6jqX62akfLpl3fs7BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:53:44.290484Z"},"content_sha256":"4c9577c54c4da582a4ab5c9ba58857bda8e30e1c489493b1fb7027826d653181","schema_version":"1.0","event_id":"sha256:4c9577c54c4da582a4ab5c9ba58857bda8e30e1c489493b1fb7027826d653181"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:DFG4H5NK7FQ7JCNOLAARJJFV4R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolutionary Entropy Shapes Reproductive Lifespan in Age-Structured Populations","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"q-bio.PE","authors_text":"Henrique Oliveira, Jorge Buescu, Saber Elaydi","submitted_at":"2026-06-20T11:53:39Z","abstract_excerpt":"Evolutionary entropy measures the temporal organization of reproductive contributions along the life cycle of an age-structured population. We develop a mathematical and empirical framework showing that, in iteroparous animal populations represented by Leslie-type demographic matrices, reproductive windows are frequently organized near the age classes selected by entropy maximization.\n  Evolutionary entropy complements the classical net reproductive number and asymptotic growth rate: whereas these measure lifetime replacement and growth, entropy measures the temporal dispersion of the growth-a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22001","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/2606.22001/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":"2026-06-23T02:13:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"skB4xGD4sz8wElaEzviXj1/M+MZaYSiZ+FRKpQDDyq771Q8IixNeuQ73s6H3prdKDqBwhsz5FbMJmcCrOiSeBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T08:53:44.290844Z"},"content_sha256":"9b9f0532a8cd6c239c03d0e1e0c4309e6561b83921e386b7f1015b9cba509937","schema_version":"1.0","event_id":"sha256:9b9f0532a8cd6c239c03d0e1e0c4309e6561b83921e386b7f1015b9cba509937"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DFG4H5NK7FQ7JCNOLAARJJFV4R/bundle.json","state_url":"https://pith.science/pith/DFG4H5NK7FQ7JCNOLAARJJFV4R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DFG4H5NK7FQ7JCNOLAARJJFV4R/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":"2026-06-27T08:53:44Z","links":{"resolver":"https://pith.science/pith/DFG4H5NK7FQ7JCNOLAARJJFV4R","bundle":"https://pith.science/pith/DFG4H5NK7FQ7JCNOLAARJJFV4R/bundle.json","state":"https://pith.science/pith/DFG4H5NK7FQ7JCNOLAARJJFV4R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DFG4H5NK7FQ7JCNOLAARJJFV4R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:DFG4H5NK7FQ7JCNOLAARJJFV4R","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":"41d6059653e42813db7deb952309c36dffca4fa254c903a377c1c851e55ab557","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2026-06-20T11:53:39Z","title_canon_sha256":"dbfc530aa2710f21d5a1eaf829b67ee64369a600ca61abca602f3c48a6d6ff5e"},"schema_version":"1.0","source":{"id":"2606.22001","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.22001","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"2606.22001v1","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22001","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"DFG4H5NK7FQ7","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"pith_short_16","alias_value":"DFG4H5NK7FQ7JCNO","created_at":"2026-06-23T02:13:05Z"},{"alias_kind":"pith_short_8","alias_value":"DFG4H5NK","created_at":"2026-06-23T02:13:05Z"}],"graph_snapshots":[{"event_id":"sha256:9b9f0532a8cd6c239c03d0e1e0c4309e6561b83921e386b7f1015b9cba509937","target":"graph","created_at":"2026-06-23T02:13:05Z","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/2606.22001/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Evolutionary entropy measures the temporal organization of reproductive contributions along the life cycle of an age-structured population. We develop a mathematical and empirical framework showing that, in iteroparous animal populations represented by Leslie-type demographic matrices, reproductive windows are frequently organized near the age classes selected by entropy maximization.\n  Evolutionary entropy complements the classical net reproductive number and asymptotic growth rate: whereas these measure lifetime replacement and growth, entropy measures the temporal dispersion of the growth-a","authors_text":"Henrique Oliveira, Jorge Buescu, Saber Elaydi","cross_cats":["math.DS"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2026-06-20T11:53:39Z","title":"Evolutionary Entropy Shapes Reproductive Lifespan in Age-Structured Populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22001","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":"sha256:4c9577c54c4da582a4ab5c9ba58857bda8e30e1c489493b1fb7027826d653181","target":"record","created_at":"2026-06-23T02:13:05Z","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":"41d6059653e42813db7deb952309c36dffca4fa254c903a377c1c851e55ab557","cross_cats_sorted":["math.DS"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"q-bio.PE","submitted_at":"2026-06-20T11:53:39Z","title_canon_sha256":"dbfc530aa2710f21d5a1eaf829b67ee64369a600ca61abca602f3c48a6d6ff5e"},"schema_version":"1.0","source":{"id":"2606.22001","kind":"arxiv","version":1}},"canonical_sha256":"194dc3f5aaf961f489ae580114a4b5e4524ea00667a0ef45020dd086ef27c8b9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"194dc3f5aaf961f489ae580114a4b5e4524ea00667a0ef45020dd086ef27c8b9","first_computed_at":"2026-06-23T02:13:05.316370Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T02:13:05.316370Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ynfSTU7TOi8luUBvfFe/a4SvJIE3Ai+2KM/g/O4O+ayJxrJBHxP4AeRb+TPk9OE77WCck9G7DX9AnQ6YBNOcCQ==","signature_status":"signed_v1","signed_at":"2026-06-23T02:13:05.316801Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.22001","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4c9577c54c4da582a4ab5c9ba58857bda8e30e1c489493b1fb7027826d653181","sha256:9b9f0532a8cd6c239c03d0e1e0c4309e6561b83921e386b7f1015b9cba509937"],"state_sha256":"781b17d29ca3e658c42e4694b5da9659da566d1a058a3352c11362d9270e6a8d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"txBvfGEvU3FKrOrlnjPzvplgqPqYHMZIX7uzUak13qlO/71D5v9e39mCGidgxV739qPgPEUDRxiR+3iV5uluCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T08:53:44.292719Z","bundle_sha256":"c2c434b4602a942a8fced2986b8d6df6182116d3523ad245a74a011078f5c081"}}