{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:ZBINUBFC6ZPFFF22VSFKO6DMZG","short_pith_number":"pith:ZBINUBFC","canonical_record":{"source":{"id":"1803.09146","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2018-03-24T18:40:29Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"26dd59b73897899662c15d9044a3e41ffadcaf5dcd7c7897a48ac99b275bc9b8","abstract_canon_sha256":"80ad981bfb4f9a944491a794eb34879b4de5767a404edeba95857ce50782f435"},"schema_version":"1.0"},"canonical_sha256":"c850da04a2f65e52975aac8aa7786cc996f1c551f145eb2f757211b15b09598d","source":{"kind":"arxiv","id":"1803.09146","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09146","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09146v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09146","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZBINUBFC6ZPF","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZBINUBFC6ZPFFF22","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZBINUBFC","created_at":"2026-05-18T12:33:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:ZBINUBFC6ZPFFF22VSFKO6DMZG","target":"record","payload":{"canonical_record":{"source":{"id":"1803.09146","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2018-03-24T18:40:29Z","cross_cats_sorted":["physics.soc-ph"],"title_canon_sha256":"26dd59b73897899662c15d9044a3e41ffadcaf5dcd7c7897a48ac99b275bc9b8","abstract_canon_sha256":"80ad981bfb4f9a944491a794eb34879b4de5767a404edeba95857ce50782f435"},"schema_version":"1.0"},"canonical_sha256":"c850da04a2f65e52975aac8aa7786cc996f1c551f145eb2f757211b15b09598d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:56:48.201535Z","signature_b64":"P/ka2y7ZOY6ABp/lHBFyJwG9iF2MtncR/gffv0/X4y0PjMlzU5xlzWaFUKoUIWGx1PogPgg/nkkLxpoud+lUCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c850da04a2f65e52975aac8aa7786cc996f1c551f145eb2f757211b15b09598d","last_reissued_at":"2026-05-17T23:56:48.201113Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:56:48.201113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1803.09146","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Iu9L5WJMTtE4IARHSYG/GewDVx1o0Xhuaaj/qfPSNS/rEV7BW94H40vLSfOk1z8Wf4LYr3OEGcXRXrl2tFhVAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:16:52.142496Z"},"content_sha256":"eb279ebc3260602ac41b27e50b914338b2598e3c62ee3e763d9883652320e80c","schema_version":"1.0","event_id":"sha256:eb279ebc3260602ac41b27e50b914338b2598e3c62ee3e763d9883652320e80c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:ZBINUBFC6ZPFFF22VSFKO6DMZG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Replicator equation on networks with degree regular communities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["physics.soc-ph"],"primary_cat":"q-bio.PE","authors_text":"Daniele Cassese","submitted_at":"2018-03-24T18:40:29Z","abstract_excerpt":"The replicator equation is one of the fundamental tools to study evolutionary dynamics in well-mixed populations. This paper contributes to the literature on evolutionary graph theory, providing a version of the replicator equation for a family of connected networks with communities, where nodes in the same community have the same degree. This replicator equation is applied to the study of different classes of games, exploring the impact of the graph structure on the equilibria of the evolutionary dynamics."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09146","kind":"arxiv","version":2},"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":"2026-05-17T23:56:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kkcwf4SURrb3YDbTG5ryt3MA1oHaIc0hKYj3VgZ3Q3iociV9EjBDphB5FJmxy0Jj3o1WC3U5xsX4jcp+/WHICg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:16:52.143217Z"},"content_sha256":"caa16358af5c073a87461efa1cbd4ea16d186370cff609f989ecb79565c872c6","schema_version":"1.0","event_id":"sha256:caa16358af5c073a87461efa1cbd4ea16d186370cff609f989ecb79565c872c6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ZBINUBFC6ZPFFF22VSFKO6DMZG/bundle.json","state_url":"https://pith.science/pith/ZBINUBFC6ZPFFF22VSFKO6DMZG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ZBINUBFC6ZPFFF22VSFKO6DMZG/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":"2026-05-26T21:16:52Z","links":{"resolver":"https://pith.science/pith/ZBINUBFC6ZPFFF22VSFKO6DMZG","bundle":"https://pith.science/pith/ZBINUBFC6ZPFFF22VSFKO6DMZG/bundle.json","state":"https://pith.science/pith/ZBINUBFC6ZPFFF22VSFKO6DMZG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ZBINUBFC6ZPFFF22VSFKO6DMZG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:ZBINUBFC6ZPFFF22VSFKO6DMZG","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":"80ad981bfb4f9a944491a794eb34879b4de5767a404edeba95857ce50782f435","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2018-03-24T18:40:29Z","title_canon_sha256":"26dd59b73897899662c15d9044a3e41ffadcaf5dcd7c7897a48ac99b275bc9b8"},"schema_version":"1.0","source":{"id":"1803.09146","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.09146","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"arxiv_version","alias_value":"1803.09146v2","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.09146","created_at":"2026-05-17T23:56:48Z"},{"alias_kind":"pith_short_12","alias_value":"ZBINUBFC6ZPF","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_16","alias_value":"ZBINUBFC6ZPFFF22","created_at":"2026-05-18T12:33:04Z"},{"alias_kind":"pith_short_8","alias_value":"ZBINUBFC","created_at":"2026-05-18T12:33:04Z"}],"graph_snapshots":[{"event_id":"sha256:caa16358af5c073a87461efa1cbd4ea16d186370cff609f989ecb79565c872c6","target":"graph","created_at":"2026-05-17T23:56:48Z","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"},"paper":{"abstract_excerpt":"The replicator equation is one of the fundamental tools to study evolutionary dynamics in well-mixed populations. This paper contributes to the literature on evolutionary graph theory, providing a version of the replicator equation for a family of connected networks with communities, where nodes in the same community have the same degree. This replicator equation is applied to the study of different classes of games, exploring the impact of the graph structure on the equilibria of the evolutionary dynamics.","authors_text":"Daniele Cassese","cross_cats":["physics.soc-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2018-03-24T18:40:29Z","title":"Replicator equation on networks with degree regular communities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09146","kind":"arxiv","version":2},"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:eb279ebc3260602ac41b27e50b914338b2598e3c62ee3e763d9883652320e80c","target":"record","created_at":"2026-05-17T23:56:48Z","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":"80ad981bfb4f9a944491a794eb34879b4de5767a404edeba95857ce50782f435","cross_cats_sorted":["physics.soc-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2018-03-24T18:40:29Z","title_canon_sha256":"26dd59b73897899662c15d9044a3e41ffadcaf5dcd7c7897a48ac99b275bc9b8"},"schema_version":"1.0","source":{"id":"1803.09146","kind":"arxiv","version":2}},"canonical_sha256":"c850da04a2f65e52975aac8aa7786cc996f1c551f145eb2f757211b15b09598d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c850da04a2f65e52975aac8aa7786cc996f1c551f145eb2f757211b15b09598d","first_computed_at":"2026-05-17T23:56:48.201113Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:56:48.201113Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"P/ka2y7ZOY6ABp/lHBFyJwG9iF2MtncR/gffv0/X4y0PjMlzU5xlzWaFUKoUIWGx1PogPgg/nkkLxpoud+lUCQ==","signature_status":"signed_v1","signed_at":"2026-05-17T23:56:48.201535Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.09146","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eb279ebc3260602ac41b27e50b914338b2598e3c62ee3e763d9883652320e80c","sha256:caa16358af5c073a87461efa1cbd4ea16d186370cff609f989ecb79565c872c6"],"state_sha256":"b4a0d41977117c436b7bc2c200091f514e745f0ce5bcd79ec9807cda71684deb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YhI4wJKuI676pnzxZmc1JILNq7XSuRffCD5L3KJnhXl/9dHT50evmukqp4Or7uKsGERI4nYuLjx7/KQkzsroBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:16:52.147261Z","bundle_sha256":"d76cc2ade7567ec1670465a1b54656ad0480e8aa11e2f6db0593446afb3b7d82"}}