{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:KMO5KROSECTCQHHSWUPIKWQBPH","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":"efdead033333e53a6789f12e2e653314218ddbe3110a4bc0c89b2442a5df1fb2","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2011-04-21T20:38:35Z","title_canon_sha256":"c85ddf4814b540957663841d9f4a395b0c32b85769e345ab5d265367259e0212"},"schema_version":"1.0","source":{"id":"1104.4355","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1104.4355","created_at":"2026-05-18T02:22:01Z"},{"alias_kind":"arxiv_version","alias_value":"1104.4355v2","created_at":"2026-05-18T02:22:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1104.4355","created_at":"2026-05-18T02:22:01Z"},{"alias_kind":"pith_short_12","alias_value":"KMO5KROSECTC","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_16","alias_value":"KMO5KROSECTCQHHS","created_at":"2026-05-18T12:26:32Z"},{"alias_kind":"pith_short_8","alias_value":"KMO5KROS","created_at":"2026-05-18T12:26:32Z"}],"graph_snapshots":[{"event_id":"sha256:6f2927c90758c4077eec8e58692ad3c1ee631b7b7f9b84eedbad34d6d5aaf44b","target":"graph","created_at":"2026-05-18T02:22:01Z","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":"The paradox of enrichment was observed by M. Rosenzweig in a class of predator-prey models. Two of the parameters in the models are crucial for the paradox. These two parameters are the prey's carrying capacity and prey's half-saturation for predation. Intuitively, increasing the carrying capacity due to enrichment of the prey's environment should lead to a more stable predator-prey system. Analytically, it turns out that increasing the carrying capacity always leads to an unstable predator-prey system that is susceptible to extinction from environmental random perturbations. This is the so-ca","authors_text":"Y. Charles Li, Z. C. Feng","cross_cats":["math-ph","math.AP","math.DS","math.MP","nlin.CD"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2011-04-21T20:38:35Z","title":"A Resolution of the Paradox of Enrichment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4355","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":"sha256:70b0e5cb8944554328bf724b5e6166823d6b11db69b6c3a0e5ac56beb09887dd","target":"record","created_at":"2026-05-18T02:22:01Z","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":"efdead033333e53a6789f12e2e653314218ddbe3110a4bc0c89b2442a5df1fb2","cross_cats_sorted":["math-ph","math.AP","math.DS","math.MP","nlin.CD"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2011-04-21T20:38:35Z","title_canon_sha256":"c85ddf4814b540957663841d9f4a395b0c32b85769e345ab5d265367259e0212"},"schema_version":"1.0","source":{"id":"1104.4355","kind":"arxiv","version":2}},"canonical_sha256":"531dd545d220a6281cf2b51e855a0179c9da6443c8eefab649f04a48e34f1a52","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"531dd545d220a6281cf2b51e855a0179c9da6443c8eefab649f04a48e34f1a52","first_computed_at":"2026-05-18T02:22:01.381517Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:22:01.381517Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7BKl3XJLoC7jIiaya9/ZntsEXkcXC1pyoDrF1KdiCNTj1Wm1IaPa/i35upfaUIrYUTPSRwSPfO1g+gAywMpsDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:22:01.382109Z","signed_message":"canonical_sha256_bytes"},"source_id":"1104.4355","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:70b0e5cb8944554328bf724b5e6166823d6b11db69b6c3a0e5ac56beb09887dd","sha256:6f2927c90758c4077eec8e58692ad3c1ee631b7b7f9b84eedbad34d6d5aaf44b"],"state_sha256":"b582d9f2bece1b2057805bc2bf497fdb5309695fab3fe1ed20e776ed4c79785c"}