{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:GPYGMJ2PADWE5JAYJ3HTRSMLCS","short_pith_number":"pith:GPYGMJ2P","canonical_record":{"source":{"id":"1605.06530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-05-20T20:23:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dfe01a1f1c07362c4520210fe33970ea005e17adcbc04c32c318d9b5b104ce29","abstract_canon_sha256":"9077c16c0b546cacbe6d5c089dce31443098d2550ac05584e2ed1edbc6a2d7bb"},"schema_version":"1.0"},"canonical_sha256":"33f066274f00ec4ea4184ecf38c98b14a7a24f5fd8aa484a78c7d226bc8cef63","source":{"kind":"arxiv","id":"1605.06530","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06530","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06530v2","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06530","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"GPYGMJ2PADWE","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GPYGMJ2PADWE5JAY","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GPYGMJ2P","created_at":"2026-05-18T12:30:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:GPYGMJ2PADWE5JAYJ3HTRSMLCS","target":"record","payload":{"canonical_record":{"source":{"id":"1605.06530","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-05-20T20:23:06Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"dfe01a1f1c07362c4520210fe33970ea005e17adcbc04c32c318d9b5b104ce29","abstract_canon_sha256":"9077c16c0b546cacbe6d5c089dce31443098d2550ac05584e2ed1edbc6a2d7bb"},"schema_version":"1.0"},"canonical_sha256":"33f066274f00ec4ea4184ecf38c98b14a7a24f5fd8aa484a78c7d226bc8cef63","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:04.419674Z","signature_b64":"ZtJYz8rab1QKj6RjiI2eguRy5EvP+P38jKoXu4zryaGjNn4xqml5U0EXVgD1K++G30RxqebsnpF5akKisBTLBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33f066274f00ec4ea4184ecf38c98b14a7a24f5fd8aa484a78c7d226bc8cef63","last_reissued_at":"2026-05-18T00:38:04.419014Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:04.419014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.06530","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":"2026-05-18T00:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oceUKY6Gq+aR95I3orq0vIyxMFE3hjJsfjzWXoWHUVGtXrE4aZfOQaIZCcMbQyYLpyzYP8/0xaeVbo6aGMHkAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:17:48.272805Z"},"content_sha256":"50374bebb19b8308563eecaedf1cf4ba15cf1b942feb301c72a6a7cb995062a9","schema_version":"1.0","event_id":"sha256:50374bebb19b8308563eecaedf1cf4ba15cf1b942feb301c72a6a7cb995062a9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:GPYGMJ2PADWE5JAYJ3HTRSMLCS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Evolutionary dynamics on any population structure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"q-bio.PE","authors_text":"Babak Fotouhi, Benjamin Allen, Gabor Lippner, Martin A. Nowak, Naghmeh Momeni, Shing-Tung Yau, Yu-Ting Chen","submitted_at":"2016-05-20T20:23:06Z","abstract_excerpt":"Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been absent for a long time, but have recently emerged for special structures where all individuals have the same number of neighbors. But the problem of determining which trait is favored by selection in the natural case where the number of neighbors can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06530","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":"2026-05-18T00:38:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iLum6SoaOF1XISDi2I+xc4ohWnm1fnksISUAu/tDkFv4RAW6IBf5EbCkBTS6Kx/SVnZefsi76ZLw/7UngyzwDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T02:17:48.273495Z"},"content_sha256":"1dae62b4b86b0ca53d6fc9089f73ea6dc31d3e904265425489dd8608727051ab","schema_version":"1.0","event_id":"sha256:1dae62b4b86b0ca53d6fc9089f73ea6dc31d3e904265425489dd8608727051ab"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GPYGMJ2PADWE5JAYJ3HTRSMLCS/bundle.json","state_url":"https://pith.science/pith/GPYGMJ2PADWE5JAYJ3HTRSMLCS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GPYGMJ2PADWE5JAYJ3HTRSMLCS/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":"2026-06-11T02:17:48Z","links":{"resolver":"https://pith.science/pith/GPYGMJ2PADWE5JAYJ3HTRSMLCS","bundle":"https://pith.science/pith/GPYGMJ2PADWE5JAYJ3HTRSMLCS/bundle.json","state":"https://pith.science/pith/GPYGMJ2PADWE5JAYJ3HTRSMLCS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GPYGMJ2PADWE5JAYJ3HTRSMLCS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GPYGMJ2PADWE5JAYJ3HTRSMLCS","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":"9077c16c0b546cacbe6d5c089dce31443098d2550ac05584e2ed1edbc6a2d7bb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-05-20T20:23:06Z","title_canon_sha256":"dfe01a1f1c07362c4520210fe33970ea005e17adcbc04c32c318d9b5b104ce29"},"schema_version":"1.0","source":{"id":"1605.06530","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.06530","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"arxiv_version","alias_value":"1605.06530v2","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.06530","created_at":"2026-05-18T00:38:04Z"},{"alias_kind":"pith_short_12","alias_value":"GPYGMJ2PADWE","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GPYGMJ2PADWE5JAY","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GPYGMJ2P","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:1dae62b4b86b0ca53d6fc9089f73ea6dc31d3e904265425489dd8608727051ab","target":"graph","created_at":"2026-05-18T00:38:04Z","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":"Evolution occurs in populations of reproducing individuals. The structure of a biological population affects which traits evolve. Understanding evolutionary game dynamics in structured populations is difficult. Precise results have been absent for a long time, but have recently emerged for special structures where all individuals have the same number of neighbors. But the problem of determining which trait is favored by selection in the natural case where the number of neighbors can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class w","authors_text":"Babak Fotouhi, Benjamin Allen, Gabor Lippner, Martin A. Nowak, Naghmeh Momeni, Shing-Tung Yau, Yu-Ting Chen","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-05-20T20:23:06Z","title":"Evolutionary dynamics on any population structure"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.06530","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":"sha256:50374bebb19b8308563eecaedf1cf4ba15cf1b942feb301c72a6a7cb995062a9","target":"record","created_at":"2026-05-18T00:38:04Z","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":"9077c16c0b546cacbe6d5c089dce31443098d2550ac05584e2ed1edbc6a2d7bb","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2016-05-20T20:23:06Z","title_canon_sha256":"dfe01a1f1c07362c4520210fe33970ea005e17adcbc04c32c318d9b5b104ce29"},"schema_version":"1.0","source":{"id":"1605.06530","kind":"arxiv","version":2}},"canonical_sha256":"33f066274f00ec4ea4184ecf38c98b14a7a24f5fd8aa484a78c7d226bc8cef63","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33f066274f00ec4ea4184ecf38c98b14a7a24f5fd8aa484a78c7d226bc8cef63","first_computed_at":"2026-05-18T00:38:04.419014Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:38:04.419014Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZtJYz8rab1QKj6RjiI2eguRy5EvP+P38jKoXu4zryaGjNn4xqml5U0EXVgD1K++G30RxqebsnpF5akKisBTLBA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:38:04.419674Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.06530","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:50374bebb19b8308563eecaedf1cf4ba15cf1b942feb301c72a6a7cb995062a9","sha256:1dae62b4b86b0ca53d6fc9089f73ea6dc31d3e904265425489dd8608727051ab"],"state_sha256":"66c178f65b2b881b36e3c23ff223d0b554318e4796e5225cee06637692823775"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F2akqksgNWz+KzIO8gWoP16PoBaaeflD7nKdopro6hx/OMSa9Xw5/r/GMddy1W9qj/0NTJ3myNJA3x9nu0ApAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T02:17:48.277104Z","bundle_sha256":"daed88e1f7c5c2a5acc9985aa772df9c82e8ac3a629439234af5e95eee1f0ca6"}}