{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:PQ3KPBNZYT6R3Y5DRFKT7WEBMT","short_pith_number":"pith:PQ3KPBNZ","canonical_record":{"source":{"id":"1406.5876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-23T11:55:38Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"9b9fa6a9940948e6051ccc30e417d5ebd529d99900cb241cf2e2b216aedb87b9","abstract_canon_sha256":"82b79b0c348840c6a840f585325ddfeae9976ea8f9d71b01f2a1f65d36821e13"},"schema_version":"1.0"},"canonical_sha256":"7c36a785b9c4fd1de3a389553fd88164c9c76974f1a0fb84ffd6f19617602111","source":{"kind":"arxiv","id":"1406.5876","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5876","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5876v2","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5876","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"pith_short_12","alias_value":"PQ3KPBNZYT6R","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQ3KPBNZYT6R3Y5D","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQ3KPBNZ","created_at":"2026-05-18T12:28:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:PQ3KPBNZYT6R3Y5DRFKT7WEBMT","target":"record","payload":{"canonical_record":{"source":{"id":"1406.5876","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-23T11:55:38Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"9b9fa6a9940948e6051ccc30e417d5ebd529d99900cb241cf2e2b216aedb87b9","abstract_canon_sha256":"82b79b0c348840c6a840f585325ddfeae9976ea8f9d71b01f2a1f65d36821e13"},"schema_version":"1.0"},"canonical_sha256":"7c36a785b9c4fd1de3a389553fd88164c9c76974f1a0fb84ffd6f19617602111","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:31.915146Z","signature_b64":"8BU3eGmp2JFHFuafdDDn7bjhE92MgdoewXZvQk4ux7mJljuqFavuU97Nki4h1xOAlzDSm64ViVe6F/Iag4pGCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7c36a785b9c4fd1de3a389553fd88164c9c76974f1a0fb84ffd6f19617602111","last_reissued_at":"2026-05-18T02:30:31.914495Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:31.914495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1406.5876","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":"2026-05-18T02:30:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"c2Xu97Wkb65zAi8j8I2aUc/sHrdWhdZHj7BBzk5JBiYxHqws1Ym/JVUxr/pxJqcfIr/rM1XCY9u19S/ITtZRAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:23:28.809094Z"},"content_sha256":"4daddd6ca7b71b20945c4272e49d360bfd16d72fd974af14911dd08634384ab3","schema_version":"1.0","event_id":"sha256:4daddd6ca7b71b20945c4272e49d360bfd16d72fd974af14911dd08634384ab3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:PQ3KPBNZYT6R3Y5DRFKT7WEBMT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Spatial Evolutionary Games with small selection coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Rick Durrett","submitted_at":"2014-06-23T11:55:38Z","abstract_excerpt":"Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\\sigma^2I$. The games we consider have payoff matrices of the form ${\\bf 1} + wG$ where ${\\bf 1}$ is matrix of all 1's and $w$ is small and positive. Since our population size $N=\\infty$, we call our selection small rather than weak which usually means $w =O(1/N)$.\n  The key to studying these games is the fact that when the dynamics are suitably rescaled in space and time the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5876","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":"2026-05-18T02:30:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"N53ui7yIkIxHku6SdQSO6H3CO9ka5CxbkAYTHnpsDazFti6YpRgA5jSJDDFqzRhD1jgkTv1gRwkCLc0nbrjzCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T04:23:28.809466Z"},"content_sha256":"c9165f82d72fc4303bce70eac01f3fb95b70257b8ab25753c5e20368f4a8f841","schema_version":"1.0","event_id":"sha256:c9165f82d72fc4303bce70eac01f3fb95b70257b8ab25753c5e20368f4a8f841"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PQ3KPBNZYT6R3Y5DRFKT7WEBMT/bundle.json","state_url":"https://pith.science/pith/PQ3KPBNZYT6R3Y5DRFKT7WEBMT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PQ3KPBNZYT6R3Y5DRFKT7WEBMT/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":"2026-06-02T04:23:28Z","links":{"resolver":"https://pith.science/pith/PQ3KPBNZYT6R3Y5DRFKT7WEBMT","bundle":"https://pith.science/pith/PQ3KPBNZYT6R3Y5DRFKT7WEBMT/bundle.json","state":"https://pith.science/pith/PQ3KPBNZYT6R3Y5DRFKT7WEBMT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PQ3KPBNZYT6R3Y5DRFKT7WEBMT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:PQ3KPBNZYT6R3Y5DRFKT7WEBMT","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":"82b79b0c348840c6a840f585325ddfeae9976ea8f9d71b01f2a1f65d36821e13","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-23T11:55:38Z","title_canon_sha256":"9b9fa6a9940948e6051ccc30e417d5ebd529d99900cb241cf2e2b216aedb87b9"},"schema_version":"1.0","source":{"id":"1406.5876","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1406.5876","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"arxiv_version","alias_value":"1406.5876v2","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1406.5876","created_at":"2026-05-18T02:30:31Z"},{"alias_kind":"pith_short_12","alias_value":"PQ3KPBNZYT6R","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"PQ3KPBNZYT6R3Y5D","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"PQ3KPBNZ","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:c9165f82d72fc4303bce70eac01f3fb95b70257b8ab25753c5e20368f4a8f841","target":"graph","created_at":"2026-05-18T02:30:31Z","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":"Here we will use results of Cox, Durrett, and Perkins for voter model perturbations to study spatial evolutionary games on $Z^d$, $d\\ge 3$ when the interaction kernel is finite range, symmetric, and has covariance matrix $\\sigma^2I$. The games we consider have payoff matrices of the form ${\\bf 1} + wG$ where ${\\bf 1}$ is matrix of all 1's and $w$ is small and positive. Since our population size $N=\\infty$, we call our selection small rather than weak which usually means $w =O(1/N)$.\n  The key to studying these games is the fact that when the dynamics are suitably rescaled in space and time the","authors_text":"Rick Durrett","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-23T11:55:38Z","title":"Spatial Evolutionary Games with small selection coefficients"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5876","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":"sha256:4daddd6ca7b71b20945c4272e49d360bfd16d72fd974af14911dd08634384ab3","target":"record","created_at":"2026-05-18T02:30:31Z","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":"82b79b0c348840c6a840f585325ddfeae9976ea8f9d71b01f2a1f65d36821e13","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-06-23T11:55:38Z","title_canon_sha256":"9b9fa6a9940948e6051ccc30e417d5ebd529d99900cb241cf2e2b216aedb87b9"},"schema_version":"1.0","source":{"id":"1406.5876","kind":"arxiv","version":2}},"canonical_sha256":"7c36a785b9c4fd1de3a389553fd88164c9c76974f1a0fb84ffd6f19617602111","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7c36a785b9c4fd1de3a389553fd88164c9c76974f1a0fb84ffd6f19617602111","first_computed_at":"2026-05-18T02:30:31.914495Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:30:31.914495Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8BU3eGmp2JFHFuafdDDn7bjhE92MgdoewXZvQk4ux7mJljuqFavuU97Nki4h1xOAlzDSm64ViVe6F/Iag4pGCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:30:31.915146Z","signed_message":"canonical_sha256_bytes"},"source_id":"1406.5876","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4daddd6ca7b71b20945c4272e49d360bfd16d72fd974af14911dd08634384ab3","sha256:c9165f82d72fc4303bce70eac01f3fb95b70257b8ab25753c5e20368f4a8f841"],"state_sha256":"110d24f008d68ee86acffc7568530fae9dadb0310f6c71b7e5e2cb29074737f6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1hgj6BfD9R99fdDXfPcIaWZyO5NXhEcMO8GOD/dEAt/OwiOH9rzTg+MtK30nNWMp8udbDZ4qdEgW9z6fWUtoAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T04:23:28.811529Z","bundle_sha256":"d778857fb5705881891f56f88aa628ca1a86e0bb59ae036a5dbeebdbcd1f6935"}}