{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:HHPWMEHKNZQO6ODR6HCX6XUPAZ","short_pith_number":"pith:HHPWMEHK","canonical_record":{"source":{"id":"1312.6333","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-22T02:48:40Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"66611150f58d2b79a3d4458d0840e6cde7d4ccd4a06a5d76c76eea04196554c6","abstract_canon_sha256":"3db9d1a49a3ae77fe4d19ffa9078e72d387448c71ddb39980805e6a7d097f021"},"schema_version":"1.0"},"canonical_sha256":"39df6610ea6e60ef3871f1c57f5e8f064146ceef1e2f7dace394e4f1a4e26f72","source":{"kind":"arxiv","id":"1312.6333","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6333","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6333v2","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6333","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"HHPWMEHKNZQO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HHPWMEHKNZQO6ODR","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HHPWMEHK","created_at":"2026-05-18T12:27:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:HHPWMEHKNZQO6ODR6HCX6XUPAZ","target":"record","payload":{"canonical_record":{"source":{"id":"1312.6333","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-22T02:48:40Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"66611150f58d2b79a3d4458d0840e6cde7d4ccd4a06a5d76c76eea04196554c6","abstract_canon_sha256":"3db9d1a49a3ae77fe4d19ffa9078e72d387448c71ddb39980805e6a7d097f021"},"schema_version":"1.0"},"canonical_sha256":"39df6610ea6e60ef3871f1c57f5e8f064146ceef1e2f7dace394e4f1a4e26f72","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:31.753750Z","signature_b64":"ewYLyp6G3eflgXt4jBI5IhhU2IR4VbYXnKSz2peB5G7nS9NQFw6CjOAgLXd8AsxGprhrx6zj4vdWtTxxOR5QCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"39df6610ea6e60ef3871f1c57f5e8f064146ceef1e2f7dace394e4f1a4e26f72","last_reissued_at":"2026-05-18T02:45:31.753099Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:31.753099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1312.6333","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":"2026-05-18T02:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/G2FNeyGgAtzHOc/NH+fMrYaL4ZwQ7fvulNMQQY5By90rkTvD6zfa1Ouc5E1lOmfBM67rO6K/VhO3EM5vuC2AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:50:12.790611Z"},"content_sha256":"c93459756db5e873f819d0389a679bbc5b4940886d03e29038c7263a2e220abe","schema_version":"1.0","event_id":"sha256:c93459756db5e873f819d0389a679bbc5b4940886d03e29038c7263a2e220abe"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:HHPWMEHKNZQO6ODR6HCX6XUPAZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fixation probabilities on superstars, revisited and revised","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"math.PR","authors_text":"Alastair Jamieson-Lane, Christoph Hauert","submitted_at":"2013-12-22T02:48:40Z","abstract_excerpt":"Population structures can be crucial determinants of evolutionary processes. For the Moran process on graphs certain structures suppress selective pressure, while others amplify it (Lieberman et al. 2005 Nature 433 312-316). Evolutionary amplifiers suppress random drift and enhance selection. Recently, some results for the most powerful known evolutionary amplifier, the superstar, have been invalidated by a counter example (D\\'iaz et al. 2013 Proc. R. Soc. A 469 20130193). Here we correct the original proof and derive improved upper and lower bounds, which indicate that the fixation probabilit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6333","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":"2026-05-18T02:45:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fxdOY6aV0PelY68gyFGXUnFbcKOPl4+mz5KDcXnAPLtfb56Vi96EHA9rRwSG0oMu+De3U+7buzjeee2GQQg5AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T17:50:12.790942Z"},"content_sha256":"be9c115e9701f33223de4e6f8e676cc6b367d84fa966efa91149329312302db7","schema_version":"1.0","event_id":"sha256:be9c115e9701f33223de4e6f8e676cc6b367d84fa966efa91149329312302db7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HHPWMEHKNZQO6ODR6HCX6XUPAZ/bundle.json","state_url":"https://pith.science/pith/HHPWMEHKNZQO6ODR6HCX6XUPAZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HHPWMEHKNZQO6ODR6HCX6XUPAZ/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":"2026-06-25T17:50:12Z","links":{"resolver":"https://pith.science/pith/HHPWMEHKNZQO6ODR6HCX6XUPAZ","bundle":"https://pith.science/pith/HHPWMEHKNZQO6ODR6HCX6XUPAZ/bundle.json","state":"https://pith.science/pith/HHPWMEHKNZQO6ODR6HCX6XUPAZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HHPWMEHKNZQO6ODR6HCX6XUPAZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:HHPWMEHKNZQO6ODR6HCX6XUPAZ","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":"3db9d1a49a3ae77fe4d19ffa9078e72d387448c71ddb39980805e6a7d097f021","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-22T02:48:40Z","title_canon_sha256":"66611150f58d2b79a3d4458d0840e6cde7d4ccd4a06a5d76c76eea04196554c6"},"schema_version":"1.0","source":{"id":"1312.6333","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1312.6333","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"arxiv_version","alias_value":"1312.6333v2","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.6333","created_at":"2026-05-18T02:45:31Z"},{"alias_kind":"pith_short_12","alias_value":"HHPWMEHKNZQO","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_16","alias_value":"HHPWMEHKNZQO6ODR","created_at":"2026-05-18T12:27:46Z"},{"alias_kind":"pith_short_8","alias_value":"HHPWMEHK","created_at":"2026-05-18T12:27:46Z"}],"graph_snapshots":[{"event_id":"sha256:be9c115e9701f33223de4e6f8e676cc6b367d84fa966efa91149329312302db7","target":"graph","created_at":"2026-05-18T02:45:31Z","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":"Population structures can be crucial determinants of evolutionary processes. For the Moran process on graphs certain structures suppress selective pressure, while others amplify it (Lieberman et al. 2005 Nature 433 312-316). Evolutionary amplifiers suppress random drift and enhance selection. Recently, some results for the most powerful known evolutionary amplifier, the superstar, have been invalidated by a counter example (D\\'iaz et al. 2013 Proc. R. Soc. A 469 20130193). Here we correct the original proof and derive improved upper and lower bounds, which indicate that the fixation probabilit","authors_text":"Alastair Jamieson-Lane, Christoph Hauert","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-22T02:48:40Z","title":"Fixation probabilities on superstars, revisited and revised"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.6333","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:c93459756db5e873f819d0389a679bbc5b4940886d03e29038c7263a2e220abe","target":"record","created_at":"2026-05-18T02:45:31Z","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":"3db9d1a49a3ae77fe4d19ffa9078e72d387448c71ddb39980805e6a7d097f021","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-22T02:48:40Z","title_canon_sha256":"66611150f58d2b79a3d4458d0840e6cde7d4ccd4a06a5d76c76eea04196554c6"},"schema_version":"1.0","source":{"id":"1312.6333","kind":"arxiv","version":2}},"canonical_sha256":"39df6610ea6e60ef3871f1c57f5e8f064146ceef1e2f7dace394e4f1a4e26f72","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"39df6610ea6e60ef3871f1c57f5e8f064146ceef1e2f7dace394e4f1a4e26f72","first_computed_at":"2026-05-18T02:45:31.753099Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:31.753099Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ewYLyp6G3eflgXt4jBI5IhhU2IR4VbYXnKSz2peB5G7nS9NQFw6CjOAgLXd8AsxGprhrx6zj4vdWtTxxOR5QCA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:31.753750Z","signed_message":"canonical_sha256_bytes"},"source_id":"1312.6333","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c93459756db5e873f819d0389a679bbc5b4940886d03e29038c7263a2e220abe","sha256:be9c115e9701f33223de4e6f8e676cc6b367d84fa966efa91149329312302db7"],"state_sha256":"47913d507aecb484c16d5423d4e0e1acfa02f4f20d7b85750d87ffe558e36232"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"bWL4LlDzBZ0RMJcJZIRg7Nvgd1ayssXEKQTBuZuc2RwdU3gWHuvpCy6mmOQJCVTQs94/by5gX+BJGtHbdAwwBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T17:50:12.792764Z","bundle_sha256":"6aa7305abd8006e0fe7fb9ed0d3b7bef181880af2791667c071a20f1ce9bf87d"}}