{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:BJMAXNH7F33NEGBBEZEPVZF2RV","short_pith_number":"pith:BJMAXNH7","canonical_record":{"source":{"id":"0906.5535","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:12:21Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"8d6a8031ec022406465b856a8bcbc4e1139225d79795644b7beb95122418cef7","abstract_canon_sha256":"4fbbbfdb913496a1ffd7c03a00a87f3d51d8c5af96c1e70246af48f75c8a2b1e"},"schema_version":"1.0"},"canonical_sha256":"0a580bb4ff2ef6d218212648fae4ba8d7c8b13543317ef96b87baae7400b838c","source":{"kind":"arxiv","id":"0906.5535","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5535","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5535v3","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5535","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"BJMAXNH7F33N","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BJMAXNH7F33NEGBB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BJMAXNH7","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:BJMAXNH7F33NEGBBEZEPVZF2RV","target":"record","payload":{"canonical_record":{"source":{"id":"0906.5535","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:12:21Z","cross_cats_sorted":["q-bio.QM"],"title_canon_sha256":"8d6a8031ec022406465b856a8bcbc4e1139225d79795644b7beb95122418cef7","abstract_canon_sha256":"4fbbbfdb913496a1ffd7c03a00a87f3d51d8c5af96c1e70246af48f75c8a2b1e"},"schema_version":"1.0"},"canonical_sha256":"0a580bb4ff2ef6d218212648fae4ba8d7c8b13543317ef96b87baae7400b838c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:13:11.745824Z","signature_b64":"f3iJOIxsiFsn+3BbOyHTS5scXGIH5G9yMPdNJmaaGtU4Aj/q+3Ntr/g2uJz0uvni73F3wn3qdDkmVyU2nliaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a580bb4ff2ef6d218212648fae4ba8d7c8b13543317ef96b87baae7400b838c","last_reissued_at":"2026-05-18T02:13:11.745386Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:13:11.745386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0906.5535","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VyRzy4XnJAZuF/4pd+RIFKrg8k2pBw6u4YD5fKm/HJEt7Rypr+SprZAGZle5AooW6bgWW4yfbdsJMmC06YEBCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:00:56.162206Z"},"content_sha256":"b8c11f3e8e8aa43e9cdd98630d78959d1a41e432cd89f1bb665a29ee23f99bc8","schema_version":"1.0","event_id":"sha256:b8c11f3e8e8aa43e9cdd98630d78959d1a41e432cd89f1bb665a29ee23f99bc8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:BJMAXNH7F33NEGBBEZEPVZF2RV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Robust ecological pattern formation induced by demographic noise","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.QM"],"primary_cat":"q-bio.PE","authors_text":"Nigel Goldenfeld, Thomas Butler","submitted_at":"2009-06-30T14:12:21Z","abstract_excerpt":"We demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing instability in mean field theory, demographic noise greatly enlarges the region of parameter space where pattern formation occurs. To distinguish between patterns generated by fluctuations and those present at the mean field level in real ecosystems, we calculate the power spectrum in the noise-driven case and predict the presence of fat tails not present in the mea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5535","kind":"arxiv","version":3},"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":"2026-05-18T02:13:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QLFNyIhq2tULpFNyG400bcL8G/2Uo50ND3ZbEhsFVtMezza2LR72chhiuISt1WIzt690zQEJ6lQaDVQuIy8TAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T15:00:56.163258Z"},"content_sha256":"b01c5dd1b7af984be7315df5f59f09849ffbf72c46341ddd3da82df70b4f39a0","schema_version":"1.0","event_id":"sha256:b01c5dd1b7af984be7315df5f59f09849ffbf72c46341ddd3da82df70b4f39a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BJMAXNH7F33NEGBBEZEPVZF2RV/bundle.json","state_url":"https://pith.science/pith/BJMAXNH7F33NEGBBEZEPVZF2RV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BJMAXNH7F33NEGBBEZEPVZF2RV/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":"2026-05-30T15:00:56Z","links":{"resolver":"https://pith.science/pith/BJMAXNH7F33NEGBBEZEPVZF2RV","bundle":"https://pith.science/pith/BJMAXNH7F33NEGBBEZEPVZF2RV/bundle.json","state":"https://pith.science/pith/BJMAXNH7F33NEGBBEZEPVZF2RV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BJMAXNH7F33NEGBBEZEPVZF2RV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:BJMAXNH7F33NEGBBEZEPVZF2RV","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":"4fbbbfdb913496a1ffd7c03a00a87f3d51d8c5af96c1e70246af48f75c8a2b1e","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:12:21Z","title_canon_sha256":"8d6a8031ec022406465b856a8bcbc4e1139225d79795644b7beb95122418cef7"},"schema_version":"1.0","source":{"id":"0906.5535","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0906.5535","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"arxiv_version","alias_value":"0906.5535v3","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0906.5535","created_at":"2026-05-18T02:13:11Z"},{"alias_kind":"pith_short_12","alias_value":"BJMAXNH7F33N","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"BJMAXNH7F33NEGBB","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"BJMAXNH7","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:b01c5dd1b7af984be7315df5f59f09849ffbf72c46341ddd3da82df70b4f39a0","target":"graph","created_at":"2026-05-18T02:13:11Z","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 demonstrate that demographic noise can induce persistent spatial pattern formation and temporal oscillations in the Levin-Segel predator-prey model for plankton-herbivore population dynamics. Although the model exhibits a Turing instability in mean field theory, demographic noise greatly enlarges the region of parameter space where pattern formation occurs. To distinguish between patterns generated by fluctuations and those present at the mean field level in real ecosystems, we calculate the power spectrum in the noise-driven case and predict the presence of fat tails not present in the mea","authors_text":"Nigel Goldenfeld, Thomas Butler","cross_cats":["q-bio.QM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:12:21Z","title":"Robust ecological pattern formation induced by demographic noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0906.5535","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:b8c11f3e8e8aa43e9cdd98630d78959d1a41e432cd89f1bb665a29ee23f99bc8","target":"record","created_at":"2026-05-18T02:13:11Z","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":"4fbbbfdb913496a1ffd7c03a00a87f3d51d8c5af96c1e70246af48f75c8a2b1e","cross_cats_sorted":["q-bio.QM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"q-bio.PE","submitted_at":"2009-06-30T14:12:21Z","title_canon_sha256":"8d6a8031ec022406465b856a8bcbc4e1139225d79795644b7beb95122418cef7"},"schema_version":"1.0","source":{"id":"0906.5535","kind":"arxiv","version":3}},"canonical_sha256":"0a580bb4ff2ef6d218212648fae4ba8d7c8b13543317ef96b87baae7400b838c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0a580bb4ff2ef6d218212648fae4ba8d7c8b13543317ef96b87baae7400b838c","first_computed_at":"2026-05-18T02:13:11.745386Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:13:11.745386Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f3iJOIxsiFsn+3BbOyHTS5scXGIH5G9yMPdNJmaaGtU4Aj/q+3Ntr/g2uJz0uvni73F3wn3qdDkmVyU2nliaBA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:13:11.745824Z","signed_message":"canonical_sha256_bytes"},"source_id":"0906.5535","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b8c11f3e8e8aa43e9cdd98630d78959d1a41e432cd89f1bb665a29ee23f99bc8","sha256:b01c5dd1b7af984be7315df5f59f09849ffbf72c46341ddd3da82df70b4f39a0"],"state_sha256":"7f0ad4956b1ef5ca432656db28329f4c7dc626cc6cb9717170aa332fee485880"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UHedOf++l3tHwv9bnKIJVa/9E5T+DAA0TQ1EnLvuHyzYny7wt0haRDX204YQcRz+2l0S1Ky5t/Tpt19A/DVnDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T15:00:56.169081Z","bundle_sha256":"4a0edd610f2f1828688abb7a1b8eff8007af9dc536a1f2dc48ab1bbe4ca1b465"}}