{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:6CXQBVNXAMWAR4E67ZPBQIG6LH","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":"72c66c4c1c96cd92a83d12ee56b66de811a50172fc77b1eaf2f865595eed331a","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-16T20:54:40Z","title_canon_sha256":"bb56844f1d4cfce50041346d259c645a2cde06cb8677670b61f07aa05b7beeea"},"schema_version":"1.0","source":{"id":"1102.3426","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.3426","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"arxiv_version","alias_value":"1102.3426v3","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.3426","created_at":"2026-05-18T03:52:54Z"},{"alias_kind":"pith_short_12","alias_value":"6CXQBVNXAMWA","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"6CXQBVNXAMWAR4E6","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"6CXQBVNX","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:8bfc7c1362fa7a83325ac47cfb51677c58418aab218a660e49bb749a2976f41f","target":"graph","created_at":"2026-05-18T03:52:54Z","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":"Evolutionary dynamics have been traditionally studied in the context of homogeneous populations, mainly described my the Moran process. Recently, this approach has been generalized in \\cite{LHN} by arranging individuals on the nodes of a network. Undirected networks seem to have a smoother behavior than directed ones, and thus it is more challenging to find suppressors/amplifiers of selection. In this paper we present the first class of undirected graphs which act as suppressors of selection, by achieving a fixation probability that is at most one half of that of the complete graph, as the num","authors_text":"Christoforos Raptopoulos, George B. Mertzios, Paul G. Spirakis, Sotiris Nikoletseas","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-16T20:54:40Z","title":"Natural Models for Evolution on Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.3426","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:c8ad95706f1aac8584dd89433f511d2ef3ba2b736ec67106d13577c711075e9c","target":"record","created_at":"2026-05-18T03:52:54Z","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":"72c66c4c1c96cd92a83d12ee56b66de811a50172fc77b1eaf2f865595eed331a","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2011-02-16T20:54:40Z","title_canon_sha256":"bb56844f1d4cfce50041346d259c645a2cde06cb8677670b61f07aa05b7beeea"},"schema_version":"1.0","source":{"id":"1102.3426","kind":"arxiv","version":3}},"canonical_sha256":"f0af00d5b7032c08f09efe5e1820de59eb173cf24b4ba1d3717971315e4d3997","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0af00d5b7032c08f09efe5e1820de59eb173cf24b4ba1d3717971315e4d3997","first_computed_at":"2026-05-18T03:52:54.916788Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:52:54.916788Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"15V7KSPghBKJWcB8lXPgFH9QpC58w5VvOreOAqLRTZ1qwPw9hG6WvSeFLTOiKtAMEVQ7H+4Krglry+Tx0fcyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:52:54.917536Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.3426","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8ad95706f1aac8584dd89433f511d2ef3ba2b736ec67106d13577c711075e9c","sha256:8bfc7c1362fa7a83325ac47cfb51677c58418aab218a660e49bb749a2976f41f"],"state_sha256":"b76fecb833e60b2136da5f939ed0015d14958f6b94bd6fe468ef16d8761b45c8"}