{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:X5IIU2RRG2VFCPQKVW2T4BDKZT","short_pith_number":"pith:X5IIU2RR","canonical_record":{"source":{"id":"1204.3703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-04-17T05:16:58Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"08b8b3687c73960893626640ba7c95dd893233a0f835edcdfc930092f56d86e8","abstract_canon_sha256":"b9319c6a4be877c06b290fc485bba33839b2ef4e2a0ab76467bbdad66c8ddfc9"},"schema_version":"1.0"},"canonical_sha256":"bf508a6a3136aa513e0aadb53e046accf0f4ad7269a6c58805c310cf403f98dd","source":{"kind":"arxiv","id":"1204.3703","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3703","created_at":"2026-05-18T01:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3703v1","created_at":"2026-05-18T01:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3703","created_at":"2026-05-18T01:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"X5IIU2RRG2VF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X5IIU2RRG2VFCPQK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X5IIU2RR","created_at":"2026-05-18T12:27:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:X5IIU2RRG2VFCPQKVW2T4BDKZT","target":"record","payload":{"canonical_record":{"source":{"id":"1204.3703","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-04-17T05:16:58Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"08b8b3687c73960893626640ba7c95dd893233a0f835edcdfc930092f56d86e8","abstract_canon_sha256":"b9319c6a4be877c06b290fc485bba33839b2ef4e2a0ab76467bbdad66c8ddfc9"},"schema_version":"1.0"},"canonical_sha256":"bf508a6a3136aa513e0aadb53e046accf0f4ad7269a6c58805c310cf403f98dd","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:57:51.676223Z","signature_b64":"sy7CYOUHGOugH6io3SnKRySWx6njdn5kHW8LMKicbhxnuQ6AkoqNQDYrAfhC+6ovnrGSgDCzTo6bm07foVcjAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bf508a6a3136aa513e0aadb53e046accf0f4ad7269a6c58805c310cf403f98dd","last_reissued_at":"2026-05-18T01:57:51.675674Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:57:51.675674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.3703","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":"2026-05-18T01:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5ZZhFC7iA3nb3B9/jjpJGZlTzP5rQr7+JP4th0seSc9+9ijJ1eqMEEAvKPTat4uuU8H/MnTKFCmWN8dAXHe+BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:18:21.290440Z"},"content_sha256":"90620da0322803d4b318ecdfbbad4eefc8514e6ac8194b4199a774b7cc3f708a","schema_version":"1.0","event_id":"sha256:90620da0322803d4b318ecdfbbad4eefc8514e6ac8194b4199a774b7cc3f708a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:X5IIU2RRG2VFCPQKVW2T4BDKZT","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fast migration and emergent population dynamics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"physics.bio-ph","authors_text":"Evgeniy Khain, Leonard M. Sander, Michael Khasin","submitted_at":"2012-04-17T05:16:58Z","abstract_excerpt":"We consider population dynamics on a network of patches, each of which has a the same local dynamics, with different population scales (carrying capacities). It is reasonable to assume that if the patches are coupled by very fast migration the whole system will look like an individual patch with a large effective carrying capacity. This is called a \"well-mixed\" system. We show that, in general, it is not true that the well-mixed system has the same dynamics as each local patch. Different global dynamics can emerge from coupling, and usually must be figured out for each individual case. We give"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3703","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":"2026-05-18T01:57:51Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b1h/i/I7euA687gpu4Yzv2/7GYdXzpv+OA7BeTrScN5ou3c7tvr7Q+N50fm7mSFDuTrhO3paoqER33CcRa0yBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T03:18:21.290787Z"},"content_sha256":"ddb02d76e51cb0e7136b79a280813c0ef9db59fd78e56d8ff483b6753837d443","schema_version":"1.0","event_id":"sha256:ddb02d76e51cb0e7136b79a280813c0ef9db59fd78e56d8ff483b6753837d443"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/X5IIU2RRG2VFCPQKVW2T4BDKZT/bundle.json","state_url":"https://pith.science/pith/X5IIU2RRG2VFCPQKVW2T4BDKZT/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/X5IIU2RRG2VFCPQKVW2T4BDKZT/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":"2026-05-27T03:18:21Z","links":{"resolver":"https://pith.science/pith/X5IIU2RRG2VFCPQKVW2T4BDKZT","bundle":"https://pith.science/pith/X5IIU2RRG2VFCPQKVW2T4BDKZT/bundle.json","state":"https://pith.science/pith/X5IIU2RRG2VFCPQKVW2T4BDKZT/state.json","well_known_bundle":"https://pith.science/.well-known/pith/X5IIU2RRG2VFCPQKVW2T4BDKZT/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:X5IIU2RRG2VFCPQKVW2T4BDKZT","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":"b9319c6a4be877c06b290fc485bba33839b2ef4e2a0ab76467bbdad66c8ddfc9","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-04-17T05:16:58Z","title_canon_sha256":"08b8b3687c73960893626640ba7c95dd893233a0f835edcdfc930092f56d86e8"},"schema_version":"1.0","source":{"id":"1204.3703","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.3703","created_at":"2026-05-18T01:57:51Z"},{"alias_kind":"arxiv_version","alias_value":"1204.3703v1","created_at":"2026-05-18T01:57:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.3703","created_at":"2026-05-18T01:57:51Z"},{"alias_kind":"pith_short_12","alias_value":"X5IIU2RRG2VF","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"X5IIU2RRG2VFCPQK","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"X5IIU2RR","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:ddb02d76e51cb0e7136b79a280813c0ef9db59fd78e56d8ff483b6753837d443","target":"graph","created_at":"2026-05-18T01:57:51Z","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":"We consider population dynamics on a network of patches, each of which has a the same local dynamics, with different population scales (carrying capacities). It is reasonable to assume that if the patches are coupled by very fast migration the whole system will look like an individual patch with a large effective carrying capacity. This is called a \"well-mixed\" system. We show that, in general, it is not true that the well-mixed system has the same dynamics as each local patch. Different global dynamics can emerge from coupling, and usually must be figured out for each individual case. We give","authors_text":"Evgeniy Khain, Leonard M. Sander, Michael Khasin","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-04-17T05:16:58Z","title":"Fast migration and emergent population dynamics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.3703","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":"sha256:90620da0322803d4b318ecdfbbad4eefc8514e6ac8194b4199a774b7cc3f708a","target":"record","created_at":"2026-05-18T01:57:51Z","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":"b9319c6a4be877c06b290fc485bba33839b2ef4e2a0ab76467bbdad66c8ddfc9","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2012-04-17T05:16:58Z","title_canon_sha256":"08b8b3687c73960893626640ba7c95dd893233a0f835edcdfc930092f56d86e8"},"schema_version":"1.0","source":{"id":"1204.3703","kind":"arxiv","version":1}},"canonical_sha256":"bf508a6a3136aa513e0aadb53e046accf0f4ad7269a6c58805c310cf403f98dd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bf508a6a3136aa513e0aadb53e046accf0f4ad7269a6c58805c310cf403f98dd","first_computed_at":"2026-05-18T01:57:51.675674Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:57:51.675674Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sy7CYOUHGOugH6io3SnKRySWx6njdn5kHW8LMKicbhxnuQ6AkoqNQDYrAfhC+6ovnrGSgDCzTo6bm07foVcjAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:57:51.676223Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.3703","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90620da0322803d4b318ecdfbbad4eefc8514e6ac8194b4199a774b7cc3f708a","sha256:ddb02d76e51cb0e7136b79a280813c0ef9db59fd78e56d8ff483b6753837d443"],"state_sha256":"f81442d5300b94f3c428e66c76d048a2c1a6595a6cedec15547995029810cd1c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Kctc8OfuYuyPicJ57OZlZ5hOeDntvX1V/KWpfNP59AZqqCpxUY8w/CdMMS4AhPye1k65Hw8E74kUu8T89h9UBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T03:18:21.293190Z","bundle_sha256":"3cee4401528fbc8fb5c8292c798aae2bca25952581ee8808d4563fd9eb1f8f91"}}