{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:742EMNWMG2OMQEAWZYNICRNNLP","short_pith_number":"pith:742EMNWM","canonical_record":{"source":{"id":"q-bio/0703062","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-bio.PE","submitted_at":"2007-03-28T10:19:14Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"b93b2b241f66ded1bc8bd563d54eeb83620c56913ac538807dff39790060a093","abstract_canon_sha256":"29b8d20afad0fc4a444037c905d47bdb0b6066c592dc0e48e60c6a3bccb27f55"},"schema_version":"1.0"},"canonical_sha256":"ff344636cc369cc81016ce1a8145ad5be3c2a0280927fba6513fa00998c0ab61","source":{"kind":"arxiv","id":"q-bio/0703062","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-bio/0703062","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"q-bio/0703062v1","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-bio/0703062","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"742EMNWMG2OM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"742EMNWMG2OMQEAW","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"742EMNWM","created_at":"2026-05-18T12:25:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:742EMNWMG2OMQEAWZYNICRNNLP","target":"record","payload":{"canonical_record":{"source":{"id":"q-bio/0703062","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"q-bio.PE","submitted_at":"2007-03-28T10:19:14Z","cross_cats_sorted":["cond-mat.stat-mech"],"title_canon_sha256":"b93b2b241f66ded1bc8bd563d54eeb83620c56913ac538807dff39790060a093","abstract_canon_sha256":"29b8d20afad0fc4a444037c905d47bdb0b6066c592dc0e48e60c6a3bccb27f55"},"schema_version":"1.0"},"canonical_sha256":"ff344636cc369cc81016ce1a8145ad5be3c2a0280927fba6513fa00998c0ab61","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:22:17.640411Z","signature_b64":"EK/LKZfWDorQMAay2kcOhxntwK7GIs99rWsNohWj0HP/n4QKZ/bL1sPpICpYvbxGGkGyggUMHxTyoq2MZBywCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ff344636cc369cc81016ce1a8145ad5be3c2a0280927fba6513fa00998c0ab61","last_reissued_at":"2026-05-18T03:22:17.639787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:22:17.639787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"q-bio/0703062","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":"2026-05-18T03:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Vu6LrxDo5q6ddy02F352BFIz9ZCom5P1iiCkPD4+UG5s1IIoloyXnQByLOiYN220HN8PRcsSHM71B43UNgIaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:38:30.549949Z"},"content_sha256":"252128f57254983541c97ff9de5940a74a5425d134310636fc1e11bd0b57fc11","schema_version":"1.0","event_id":"sha256:252128f57254983541c97ff9de5940a74a5425d134310636fc1e11bd0b57fc11"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:742EMNWMG2OMQEAWZYNICRNNLP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolutionary game theory and population dynamics","license":"","headline":"","cross_cats":["cond-mat.stat-mech"],"primary_cat":"q-bio.PE","authors_text":"Jacek Miekisz","submitted_at":"2007-03-28T10:19:14Z","abstract_excerpt":"Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts of evolutionary game theory and review basic properties of deterministic replicator dynamics and stochastic dynamics of finite populations. We discuss stability of equilibria in deterministic dynamics with migration, time-delay, and in stochastic dynamics of well-mixed populations and spatial games with local interactions. We analyze the dependence of the lo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-bio/0703062","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":"2026-05-18T03:22:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"himePZCH/40r/mv/5SeXa7VBWQsojqcMIVjHTHOYu18noG3ugAtHQDYZHaLTyy/HEKCNwyc7rJLbdEuaZL48Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T15:38:30.550284Z"},"content_sha256":"a5cd7337164af8c5335cabad7eab3550eaa5716810f3f308c00194d6a8c73394","schema_version":"1.0","event_id":"sha256:a5cd7337164af8c5335cabad7eab3550eaa5716810f3f308c00194d6a8c73394"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/742EMNWMG2OMQEAWZYNICRNNLP/bundle.json","state_url":"https://pith.science/pith/742EMNWMG2OMQEAWZYNICRNNLP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/742EMNWMG2OMQEAWZYNICRNNLP/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":"2026-06-23T15:38:30Z","links":{"resolver":"https://pith.science/pith/742EMNWMG2OMQEAWZYNICRNNLP","bundle":"https://pith.science/pith/742EMNWMG2OMQEAWZYNICRNNLP/bundle.json","state":"https://pith.science/pith/742EMNWMG2OMQEAWZYNICRNNLP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/742EMNWMG2OMQEAWZYNICRNNLP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:742EMNWMG2OMQEAWZYNICRNNLP","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":"29b8d20afad0fc4a444037c905d47bdb0b6066c592dc0e48e60c6a3bccb27f55","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"q-bio.PE","submitted_at":"2007-03-28T10:19:14Z","title_canon_sha256":"b93b2b241f66ded1bc8bd563d54eeb83620c56913ac538807dff39790060a093"},"schema_version":"1.0","source":{"id":"q-bio/0703062","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"q-bio/0703062","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"arxiv_version","alias_value":"q-bio/0703062v1","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.q-bio/0703062","created_at":"2026-05-18T03:22:17Z"},{"alias_kind":"pith_short_12","alias_value":"742EMNWMG2OM","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"742EMNWMG2OMQEAW","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"742EMNWM","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:a5cd7337164af8c5335cabad7eab3550eaa5716810f3f308c00194d6a8c73394","target":"graph","created_at":"2026-05-18T03:22:17Z","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":"Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts of evolutionary game theory and review basic properties of deterministic replicator dynamics and stochastic dynamics of finite populations. We discuss stability of equilibria in deterministic dynamics with migration, time-delay, and in stochastic dynamics of well-mixed populations and spatial games with local interactions. We analyze the dependence of the lo","authors_text":"Jacek Miekisz","cross_cats":["cond-mat.stat-mech"],"headline":"","license":"","primary_cat":"q-bio.PE","submitted_at":"2007-03-28T10:19:14Z","title":"Evolutionary game theory and population dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"q-bio/0703062","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":"sha256:252128f57254983541c97ff9de5940a74a5425d134310636fc1e11bd0b57fc11","target":"record","created_at":"2026-05-18T03:22:17Z","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":"29b8d20afad0fc4a444037c905d47bdb0b6066c592dc0e48e60c6a3bccb27f55","cross_cats_sorted":["cond-mat.stat-mech"],"license":"","primary_cat":"q-bio.PE","submitted_at":"2007-03-28T10:19:14Z","title_canon_sha256":"b93b2b241f66ded1bc8bd563d54eeb83620c56913ac538807dff39790060a093"},"schema_version":"1.0","source":{"id":"q-bio/0703062","kind":"arxiv","version":1}},"canonical_sha256":"ff344636cc369cc81016ce1a8145ad5be3c2a0280927fba6513fa00998c0ab61","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ff344636cc369cc81016ce1a8145ad5be3c2a0280927fba6513fa00998c0ab61","first_computed_at":"2026-05-18T03:22:17.639787Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:17.639787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EK/LKZfWDorQMAay2kcOhxntwK7GIs99rWsNohWj0HP/n4QKZ/bL1sPpICpYvbxGGkGyggUMHxTyoq2MZBywCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:17.640411Z","signed_message":"canonical_sha256_bytes"},"source_id":"q-bio/0703062","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:252128f57254983541c97ff9de5940a74a5425d134310636fc1e11bd0b57fc11","sha256:a5cd7337164af8c5335cabad7eab3550eaa5716810f3f308c00194d6a8c73394"],"state_sha256":"23b1cbd461e38e265870d56e31f4a1eeec9333f1cb4084981b641a4c628aca42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R9BKPZBV+dDHLet0psZEis3nWS2yWtJqMdkJGs6hsmN1iDUj51PlOqOxO8lnRoifBAJ+Iz67r2qh/vtRyLdpAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T15:38:30.552190Z","bundle_sha256":"1699c498172e6aa06a5981470c67371a78bb9ce26378cc63e6df83006cccd366"}}