{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:J2C6NSWQRISQVKQG74IGQMIYLT","short_pith_number":"pith:J2C6NSWQ","canonical_record":{"source":{"id":"1204.3966","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"q-bio.PE","submitted_at":"2012-04-18T03:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"d64e76ad66a951185241cb76e412ed6bdfe634088c2e1edcac080b27dc379954","abstract_canon_sha256":"1f8b01daf47bea1d2fb760ef5c6b058136701e22e9ce2dabb1365410fecbb610"},"schema_version":"1.0"},"canonical_sha256":"4e85e6cad08a250aaa06ff106831185cfab38005e60323a491255af1a3a88450","source":{"kind":"arxiv","id":"1204.3966","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3966","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3966v1","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3966","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"J2C6NSWQRISQ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"J2C6NSWQRISQVKQG","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"J2C6NSWQ","created_at":"2026-05-18T12:27:09Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:J2C6NSWQRISQVKQG74IGQMIYLT","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3966","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"q-bio.PE","submitted_at":"2012-04-18T03:17:37Z","cross_cats_sorted":[],"title_canon_sha256":"d64e76ad66a951185241cb76e412ed6bdfe634088c2e1edcac080b27dc379954","abstract_canon_sha256":"1f8b01daf47bea1d2fb760ef5c6b058136701e22e9ce2dabb1365410fecbb610"},"schema_version":"1.0"},"canonical_sha256":"4e85e6cad08a250aaa06ff106831185cfab38005e60323a491255af1a3a88450","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:57:38.153088Z","signature_b64":"lYrHVopzek7bIRsveb4cTX1eU7BZW2MIBUTOrILn7DytRuM9/GxS7fbjO6JUChvEnat8LKSDuHRPvziWp8K2CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4e85e6cad08a250aaa06ff106831185cfab38005e60323a491255af1a3a88450","last_reissued_at":"2026-05-18T03:57:38.152419Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:57:38.152419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3966","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":"2026-05-18T03:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FDlVAdIOCuaPtGGP/+kufs9RcC7hJKRQtlSrj7/wQi0reJ20x+jQ9AfI82mhKsio7No2n8xG2xhO4Wm3x70lCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:12:38.991024Z"},"content_sha256":"c06c360d8fe56e7c0d8a7bcfd50fcf13ff3e5d2bfdb65a1486207529376f1822","schema_version":"1.0","event_id":"sha256:c06c360d8fe56e7c0d8a7bcfd50fcf13ff3e5d2bfdb65a1486207529376f1822"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:J2C6NSWQRISQVKQG74IGQMIYLT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The \\sigma law of evolutionary dynamics in community-structured populations","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"q-bio.PE","authors_text":"Changbing Tang, Jingyuan Zhan, Lang Cao, Xiang Li","submitted_at":"2012-04-18T03:17:37Z","abstract_excerpt":"Evolutionary game dynamics in finite populations provides a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call {\\sigma} law, describes how to determine the selection between two competing strategies: in most evolutionary processes with two strategies, A and B, strategy A is favored over B in weak selection if and only if {\\sigma}R + S > T + {\\sigma}P. This relationship holds for a wide variety of structured populations with mutation rate and weak selection under certain assumptions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3966","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":"2026-05-18T03:57:38Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"M5dt4d7HSbxPz3eBP+rGI8ZEV4P7iHPR+Y3vfm528hu2Rp24TyczQU1gbPQYsN4BPGZME+hiyFVSEaz99GHlAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T19:12:38.991379Z"},"content_sha256":"ef7b8b86b68b0c9b039eb743dd90e76a6466ab443c39e12c1d3a611e479bf529","schema_version":"1.0","event_id":"sha256:ef7b8b86b68b0c9b039eb743dd90e76a6466ab443c39e12c1d3a611e479bf529"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/J2C6NSWQRISQVKQG74IGQMIYLT/bundle.json","state_url":"https://pith.science/pith/J2C6NSWQRISQVKQG74IGQMIYLT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/J2C6NSWQRISQVKQG74IGQMIYLT/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":"2026-06-02T19:12:38Z","links":{"resolver":"https://pith.science/pith/J2C6NSWQRISQVKQG74IGQMIYLT","bundle":"https://pith.science/pith/J2C6NSWQRISQVKQG74IGQMIYLT/bundle.json","state":"https://pith.science/pith/J2C6NSWQRISQVKQG74IGQMIYLT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/J2C6NSWQRISQVKQG74IGQMIYLT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:J2C6NSWQRISQVKQG74IGQMIYLT","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":"1f8b01daf47bea1d2fb760ef5c6b058136701e22e9ce2dabb1365410fecbb610","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"q-bio.PE","submitted_at":"2012-04-18T03:17:37Z","title_canon_sha256":"d64e76ad66a951185241cb76e412ed6bdfe634088c2e1edcac080b27dc379954"},"schema_version":"1.0","source":{"id":"1204.3966","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3966","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3966v1","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3966","created_at":"2026-05-18T03:57:38Z"},{"alias_kind":"pith_short_12","alias_value":"J2C6NSWQRISQ","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"J2C6NSWQRISQVKQG","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"J2C6NSWQ","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ef7b8b86b68b0c9b039eb743dd90e76a6466ab443c39e12c1d3a611e479bf529","target":"graph","created_at":"2026-05-18T03:57:38Z","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 game dynamics in finite populations provides a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call {\\sigma} law, describes how to determine the selection between two competing strategies: in most evolutionary processes with two strategies, A and B, strategy A is favored over B in weak selection if and only if {\\sigma}R + S > T + {\\sigma}P. This relationship holds for a wide variety of structured populations with mutation rate and weak selection under certain assumptions","authors_text":"Changbing Tang, Jingyuan Zhan, Lang Cao, Xiang Li","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"q-bio.PE","submitted_at":"2012-04-18T03:17:37Z","title":"The \\sigma law of evolutionary dynamics in community-structured populations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3966","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:c06c360d8fe56e7c0d8a7bcfd50fcf13ff3e5d2bfdb65a1486207529376f1822","target":"record","created_at":"2026-05-18T03:57:38Z","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":"1f8b01daf47bea1d2fb760ef5c6b058136701e22e9ce2dabb1365410fecbb610","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"q-bio.PE","submitted_at":"2012-04-18T03:17:37Z","title_canon_sha256":"d64e76ad66a951185241cb76e412ed6bdfe634088c2e1edcac080b27dc379954"},"schema_version":"1.0","source":{"id":"1204.3966","kind":"arxiv","version":1}},"canonical_sha256":"4e85e6cad08a250aaa06ff106831185cfab38005e60323a491255af1a3a88450","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4e85e6cad08a250aaa06ff106831185cfab38005e60323a491255af1a3a88450","first_computed_at":"2026-05-18T03:57:38.152419Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:57:38.152419Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lYrHVopzek7bIRsveb4cTX1eU7BZW2MIBUTOrILn7DytRuM9/GxS7fbjO6JUChvEnat8LKSDuHRPvziWp8K2CA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:57:38.153088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3966","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c06c360d8fe56e7c0d8a7bcfd50fcf13ff3e5d2bfdb65a1486207529376f1822","sha256:ef7b8b86b68b0c9b039eb743dd90e76a6466ab443c39e12c1d3a611e479bf529"],"state_sha256":"79dc13e0e6f9adcecc778cc0b8308216cd1fb54f9b352901553482532725d8c2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3CzZAUPGjPAj4XyimuivVk3GtK5KrXCF7BnCCAIv33ICK6C8EmxU3NE1QK2+IVwoAY3Lbj7edw/H4EHURd7MBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T19:12:38.993787Z","bundle_sha256":"8719a6fa79aa818fd9e381a4d1fc0decb86a9e0423da18bb7d7a7994499ebe42"}}