{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:DTF5BQYAPJXNHNVUIE57CS3X5Y","short_pith_number":"pith:DTF5BQYA","canonical_record":{"source":{"id":"2010.06025","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T20:58:36Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"31ac6869d7f1b60c2e36dcc99fed21bb3341658941320f5a3e030f19e5259b0f","abstract_canon_sha256":"8473543ac33f61761042204355dea0820d2abb245a669ccd8e12490c7409ace9"},"schema_version":"1.0"},"canonical_sha256":"1ccbd0c3007a6ed3b6b4413bf14b77ee353583fb6647ff450ad25f0b330b8a9e","source":{"kind":"arxiv","id":"2010.06025","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.06025","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"2010.06025v3","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.06025","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"DTF5BQYAPJXN","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"DTF5BQYAPJXNHNVU","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"DTF5BQYA","created_at":"2026-07-05T02:06:15Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:DTF5BQYAPJXNHNVUIE57CS3X5Y","target":"record","payload":{"canonical_record":{"source":{"id":"2010.06025","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T20:58:36Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"31ac6869d7f1b60c2e36dcc99fed21bb3341658941320f5a3e030f19e5259b0f","abstract_canon_sha256":"8473543ac33f61761042204355dea0820d2abb245a669ccd8e12490c7409ace9"},"schema_version":"1.0"},"canonical_sha256":"1ccbd0c3007a6ed3b6b4413bf14b77ee353583fb6647ff450ad25f0b330b8a9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:06:15.130001Z","signature_b64":"GNhEk3QVDm+/IvKfgKUbuBkYdnrnX0wD/1eShv2ChyI7YoU6uNZRBYR0pR8KY6Jr7pwR+tGg5RW8HVdwCqpEDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1ccbd0c3007a6ed3b6b4413bf14b77ee353583fb6647ff450ad25f0b330b8a9e","last_reissued_at":"2026-07-05T02:06:15.129587Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:06:15.129587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2010.06025","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9ZDQ2s6cdgyVSzGr63/MWsgk+gQzXOko1XTyo/ZbuugzoQSyYf7mM81RSo90rAGubPwkAAVYN56NNV+tJt+wCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:30:28.841043Z"},"content_sha256":"2936f02138fe7be426cf9cc7a001fe31ae8c0ae710eed4546d3da5efdbbb81d7","schema_version":"1.0","event_id":"sha256:2936f02138fe7be426cf9cc7a001fe31ae8c0ae710eed4546d3da5efdbbb81d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:DTF5BQYAPJXNHNVUIE57CS3X5Y","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The replicator equation in stochastic spatial evolutionary games","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Yu-Ting Chen","submitted_at":"2020-10-12T20:58:36Z","abstract_excerpt":"We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\\to \\infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths satisfying $1/N\\ll w\\ll 1$. Under appropriate conditions on the space, the limiting density processes of strategy are proven to obey the replicator equation, and the normalized fluctuations converge to a Gaussian process with the Wright-Fisher covariance function in the limiting densities. As an application, we resolve in the positive a conjecture from the bi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06025","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2010.06025/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T02:06:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QSKYmbpuQAMRUB7g/C6vpzBni/IvuMzg6KaTInWXq2NWWJUNMnQOY4NYEgzL7cObHGlyFQsmGrc8iwjQ9gSsDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-05T16:30:28.842623Z"},"content_sha256":"adc39cc6151029f5c574aa82a6d08c9f530974d99e8871eec8d811dbc3b8f841","schema_version":"1.0","event_id":"sha256:adc39cc6151029f5c574aa82a6d08c9f530974d99e8871eec8d811dbc3b8f841"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DTF5BQYAPJXNHNVUIE57CS3X5Y/bundle.json","state_url":"https://pith.science/pith/DTF5BQYAPJXNHNVUIE57CS3X5Y/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DTF5BQYAPJXNHNVUIE57CS3X5Y/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":"2026-08-05T16:30:28Z","links":{"resolver":"https://pith.science/pith/DTF5BQYAPJXNHNVUIE57CS3X5Y","bundle":"https://pith.science/pith/DTF5BQYAPJXNHNVUIE57CS3X5Y/bundle.json","state":"https://pith.science/pith/DTF5BQYAPJXNHNVUIE57CS3X5Y/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DTF5BQYAPJXNHNVUIE57CS3X5Y/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:DTF5BQYAPJXNHNVUIE57CS3X5Y","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":"8473543ac33f61761042204355dea0820d2abb245a669ccd8e12490c7409ace9","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T20:58:36Z","title_canon_sha256":"31ac6869d7f1b60c2e36dcc99fed21bb3341658941320f5a3e030f19e5259b0f"},"schema_version":"1.0","source":{"id":"2010.06025","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2010.06025","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"arxiv_version","alias_value":"2010.06025v3","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2010.06025","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"pith_short_12","alias_value":"DTF5BQYAPJXN","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"pith_short_16","alias_value":"DTF5BQYAPJXNHNVU","created_at":"2026-07-05T02:06:15Z"},{"alias_kind":"pith_short_8","alias_value":"DTF5BQYA","created_at":"2026-07-05T02:06:15Z"}],"graph_snapshots":[{"event_id":"sha256:adc39cc6151029f5c574aa82a6d08c9f530974d99e8871eec8d811dbc3b8f841","target":"graph","created_at":"2026-07-05T02:06:15Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2010.06025/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the multi-strategy stochastic evolutionary game with death-birth updating in expanding spatial populations of size $N\\to \\infty$. The model is a voter model perturbation. For typical populations, we require perturbation strengths satisfying $1/N\\ll w\\ll 1$. Under appropriate conditions on the space, the limiting density processes of strategy are proven to obey the replicator equation, and the normalized fluctuations converge to a Gaussian process with the Wright-Fisher covariance function in the limiting densities. As an application, we resolve in the positive a conjecture from the bi","authors_text":"Yu-Ting Chen","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T20:58:36Z","title":"The replicator equation in stochastic spatial evolutionary games"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2010.06025","kind":"arxiv","version":3},"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":"sha256:2936f02138fe7be426cf9cc7a001fe31ae8c0ae710eed4546d3da5efdbbb81d7","target":"record","created_at":"2026-07-05T02:06:15Z","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":"8473543ac33f61761042204355dea0820d2abb245a669ccd8e12490c7409ace9","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2020-10-12T20:58:36Z","title_canon_sha256":"31ac6869d7f1b60c2e36dcc99fed21bb3341658941320f5a3e030f19e5259b0f"},"schema_version":"1.0","source":{"id":"2010.06025","kind":"arxiv","version":3}},"canonical_sha256":"1ccbd0c3007a6ed3b6b4413bf14b77ee353583fb6647ff450ad25f0b330b8a9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1ccbd0c3007a6ed3b6b4413bf14b77ee353583fb6647ff450ad25f0b330b8a9e","first_computed_at":"2026-07-05T02:06:15.129587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:06:15.129587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GNhEk3QVDm+/IvKfgKUbuBkYdnrnX0wD/1eShv2ChyI7YoU6uNZRBYR0pR8KY6Jr7pwR+tGg5RW8HVdwCqpEDw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:06:15.130001Z","signed_message":"canonical_sha256_bytes"},"source_id":"2010.06025","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2936f02138fe7be426cf9cc7a001fe31ae8c0ae710eed4546d3da5efdbbb81d7","sha256:adc39cc6151029f5c574aa82a6d08c9f530974d99e8871eec8d811dbc3b8f841"],"state_sha256":"95018727940f1016548b4052c1730affa3be02081a1fa08da8f9b92553fd1d1e"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xzrVm08GTdG27z6jZSJKAMo/NT1YOkS5hKwT9R/X3sKUPog5xWCddP19LIUL9fN0AFIOGV6m9TX9bQc0Z7VCBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-05T16:30:28.850858Z","bundle_sha256":"003a00d4f18b1d1f23bae35ca3a19dcd5a2df3da15fa3d1e7ac6e3b2147caa8b"}}