{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:SP7O3AHP4JOPBDPTITKVYAXEXT","short_pith_number":"pith:SP7O3AHP","canonical_record":{"source":{"id":"1312.2942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-12-10T20:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"7507043788900821680f59a4b2cacd1673e32cb151a9cb7f42cbf6b47553e240","abstract_canon_sha256":"2a53a5a7df2ace295f1dd07bce3028b16372ccdf7625ec708fe5d86d3cbb1de2"},"schema_version":"1.0"},"canonical_sha256":"93feed80efe25cf08df344d55c02e4bcc07308aaa89018abc0bc4c06dc532330","source":{"kind":"arxiv","id":"1312.2942","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2942","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2942v1","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2942","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"SP7O3AHP4JOP","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SP7O3AHP4JOPBDPT","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SP7O3AHP","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:SP7O3AHP4JOPBDPTITKVYAXEXT","target":"record","payload":{"canonical_record":{"source":{"id":"1312.2942","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-12-10T20:46:39Z","cross_cats_sorted":[],"title_canon_sha256":"7507043788900821680f59a4b2cacd1673e32cb151a9cb7f42cbf6b47553e240","abstract_canon_sha256":"2a53a5a7df2ace295f1dd07bce3028b16372ccdf7625ec708fe5d86d3cbb1de2"},"schema_version":"1.0"},"canonical_sha256":"93feed80efe25cf08df344d55c02e4bcc07308aaa89018abc0bc4c06dc532330","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:33.093546Z","signature_b64":"3szSt2UYiwfqGd7v2C05tDH4E8eIQCmB2HFo7YIi4ISgQRM0bVZ4iRHB9YOw1jr5//abe0Jl91A9AKre0W9uCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93feed80efe25cf08df344d55c02e4bcc07308aaa89018abc0bc4c06dc532330","last_reissued_at":"2026-05-18T00:00:33.093079Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:33.093079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.2942","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":"2026-05-18T00:00:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wfPdcuKTzRW83iOqtkftg9epCh715SxZFQFzyVi7V9urdCaYtjOZYbWijBjyG2fcDlBXvjv9PDytALhXVRCWCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:28:30.452017Z"},"content_sha256":"ddee138b9bbd45743830fd61f76ff2378e43c93bf1b346a5b5db508e095fcaa5","schema_version":"1.0","event_id":"sha256:ddee138b9bbd45743830fd61f76ff2378e43c93bf1b346a5b5db508e095fcaa5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:SP7O3AHP4JOPBDPTITKVYAXEXT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolutionary Game Dynamics in Populations with Heterogeneous Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Christoph Hauert, Feng Fu, Wes Maciejewski","submitted_at":"2013-12-10T20:46:39Z","abstract_excerpt":"Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of hetero"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2942","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":"2026-05-18T00:00:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pQyqSUSXBAOAsDDqI2tsu0OMlGxA7JrkUE0Hcckx7Wi5HSYxdedXir/ZTQCY/RZj89qRj+x2ZjFX1Lm5MaiPDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:28:30.452382Z"},"content_sha256":"c2a37ce857f5d88bc0568bc96c888e4c60e5eef97dc5cfabee1b6a024a478fe3","schema_version":"1.0","event_id":"sha256:c2a37ce857f5d88bc0568bc96c888e4c60e5eef97dc5cfabee1b6a024a478fe3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/SP7O3AHP4JOPBDPTITKVYAXEXT/bundle.json","state_url":"https://pith.science/pith/SP7O3AHP4JOPBDPTITKVYAXEXT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/SP7O3AHP4JOPBDPTITKVYAXEXT/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":"2026-06-25T18:28:30Z","links":{"resolver":"https://pith.science/pith/SP7O3AHP4JOPBDPTITKVYAXEXT","bundle":"https://pith.science/pith/SP7O3AHP4JOPBDPTITKVYAXEXT/bundle.json","state":"https://pith.science/pith/SP7O3AHP4JOPBDPTITKVYAXEXT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/SP7O3AHP4JOPBDPTITKVYAXEXT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:SP7O3AHP4JOPBDPTITKVYAXEXT","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":"2a53a5a7df2ace295f1dd07bce3028b16372ccdf7625ec708fe5d86d3cbb1de2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-12-10T20:46:39Z","title_canon_sha256":"7507043788900821680f59a4b2cacd1673e32cb151a9cb7f42cbf6b47553e240"},"schema_version":"1.0","source":{"id":"1312.2942","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.2942","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"arxiv_version","alias_value":"1312.2942v1","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.2942","created_at":"2026-05-18T00:00:33Z"},{"alias_kind":"pith_short_12","alias_value":"SP7O3AHP4JOP","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"SP7O3AHP4JOPBDPT","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"SP7O3AHP","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:c2a37ce857f5d88bc0568bc96c888e4c60e5eef97dc5cfabee1b6a024a478fe3","target":"graph","created_at":"2026-05-18T00:00:33Z","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":"Evolutionary graph theory is a well established framework for modelling the evolution of social behaviours in structured populations. An emerging consensus in this field is that graphs that exhibit heterogeneity in the number of connections between individuals are more conducive to the spread of cooperative behaviours. In this article we show that such a conclusion largely depends on the individual-level interactions that take place. In particular, averaging payoffs garnered through game interactions rather than accumulating the payoffs can altogether remove the cooperative advantage of hetero","authors_text":"Christoph Hauert, Feng Fu, Wes Maciejewski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-12-10T20:46:39Z","title":"Evolutionary Game Dynamics in Populations with Heterogeneous Structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2942","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:ddee138b9bbd45743830fd61f76ff2378e43c93bf1b346a5b5db508e095fcaa5","target":"record","created_at":"2026-05-18T00:00:33Z","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":"2a53a5a7df2ace295f1dd07bce3028b16372ccdf7625ec708fe5d86d3cbb1de2","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2013-12-10T20:46:39Z","title_canon_sha256":"7507043788900821680f59a4b2cacd1673e32cb151a9cb7f42cbf6b47553e240"},"schema_version":"1.0","source":{"id":"1312.2942","kind":"arxiv","version":1}},"canonical_sha256":"93feed80efe25cf08df344d55c02e4bcc07308aaa89018abc0bc4c06dc532330","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"93feed80efe25cf08df344d55c02e4bcc07308aaa89018abc0bc4c06dc532330","first_computed_at":"2026-05-18T00:00:33.093079Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:33.093079Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3szSt2UYiwfqGd7v2C05tDH4E8eIQCmB2HFo7YIi4ISgQRM0bVZ4iRHB9YOw1jr5//abe0Jl91A9AKre0W9uCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:33.093546Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.2942","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ddee138b9bbd45743830fd61f76ff2378e43c93bf1b346a5b5db508e095fcaa5","sha256:c2a37ce857f5d88bc0568bc96c888e4c60e5eef97dc5cfabee1b6a024a478fe3"],"state_sha256":"312b5298b2b7ae63a20c32f6fa16f4acc2d686ff6717f29fe34910a0787cdf9d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gMBB70bEBaP0REycTvPaZ0M2YUkrMxCbE4TzeUD6Gn4tPwFCMLzk4sDeO0p5AN4YuF1X0pxV8TAT7WV9zwbyBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:28:30.454370Z","bundle_sha256":"92950096c5ea5889ff334b5d21fac84a8a5b97ec5de6b09c4d647e6b37aa4bcc"}}