{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:GYOTGC5JMLJ6NSQLRS7IUMYI5E","short_pith_number":"pith:GYOTGC5J","canonical_record":{"source":{"id":"1806.05079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-13T14:22:08Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"94231c943456275b1fd48373d9b46add02ed610d23f391293db65a89a5a472a6","abstract_canon_sha256":"f8484cfa2643f3027ecd459c737cffd2f728d1236532d81b63ffe1d6bb09b812"},"schema_version":"1.0"},"canonical_sha256":"361d330ba962d3e6ca0b8cbe8a3308e908a512ec18db5570d191ae3e2a0d39e7","source":{"kind":"arxiv","id":"1806.05079","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05079","created_at":"2026-05-18T00:03:05Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05079v1","created_at":"2026-05-18T00:03:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05079","created_at":"2026-05-18T00:03:05Z"},{"alias_kind":"pith_short_12","alias_value":"GYOTGC5JMLJ6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GYOTGC5JMLJ6NSQL","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GYOTGC5J","created_at":"2026-05-18T12:32:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:GYOTGC5JMLJ6NSQLRS7IUMYI5E","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05079","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-13T14:22:08Z","cross_cats_sorted":["q-bio.PE"],"title_canon_sha256":"94231c943456275b1fd48373d9b46add02ed610d23f391293db65a89a5a472a6","abstract_canon_sha256":"f8484cfa2643f3027ecd459c737cffd2f728d1236532d81b63ffe1d6bb09b812"},"schema_version":"1.0"},"canonical_sha256":"361d330ba962d3e6ca0b8cbe8a3308e908a512ec18db5570d191ae3e2a0d39e7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:05.295077Z","signature_b64":"m/lCmbov9+6zXRtsGZIHWGHnGq2te5eb27CIg3SimCDWtQDyacOSp9YpM7TRAFPyhWAQVourWlJiVXxG4HgGAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"361d330ba962d3e6ca0b8cbe8a3308e908a512ec18db5570d191ae3e2a0d39e7","last_reissued_at":"2026-05-18T00:03:05.294682Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:05.294682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05079","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:03:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3rLX87pYHRHdXP+JMUdNWEJz0Pr1hTHEh+S0yO6YmgCxagKTJlakKPHHzNjyQaB6rtJFcfc7V6wLhjYawkOzBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:59:57.452298Z"},"content_sha256":"cabae716a0838924e9e6f4dc3f4f7c9cff96bdc741c8b8c0370e253b264cdd77","schema_version":"1.0","event_id":"sha256:cabae716a0838924e9e6f4dc3f4f7c9cff96bdc741c8b8c0370e253b264cdd77"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:GYOTGC5JMLJ6NSQLRS7IUMYI5E","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Giant fluctuations in logistic growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.PE"],"primary_cat":"physics.bio-ph","authors_text":"Bahram Houchmandzadeh","submitted_at":"2018-06-13T14:22:08Z","abstract_excerpt":"We analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying capacity, the number of each species is subject to giant fluctuations (variance $\\sim$ mean 2) if the two species have similar growth rate. We show that the deterministic logistic equation can be used only when the growth rates are significantly different, otherwise such growth has to be investigated by stochastic processes tools. These results generalize to a wide"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05079","kind":"arxiv","version":1},"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":"2026-05-18T00:03:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5jflYZEoMPttcwF2mDa15bcstPHkVRlBldsHpZp9mhxkyzSM4qSzYKH2fTPc3yOGPNq0+GJF5+lszbdXKICXCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-04T10:59:57.452670Z"},"content_sha256":"f998f6b746f4657607949aaa93b526f7f7b34ff7f0f0a92dea64fdb4d7613879","schema_version":"1.0","event_id":"sha256:f998f6b746f4657607949aaa93b526f7f7b34ff7f0f0a92dea64fdb4d7613879"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GYOTGC5JMLJ6NSQLRS7IUMYI5E/bundle.json","state_url":"https://pith.science/pith/GYOTGC5JMLJ6NSQLRS7IUMYI5E/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GYOTGC5JMLJ6NSQLRS7IUMYI5E/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":"2026-07-04T10:59:57Z","links":{"resolver":"https://pith.science/pith/GYOTGC5JMLJ6NSQLRS7IUMYI5E","bundle":"https://pith.science/pith/GYOTGC5JMLJ6NSQLRS7IUMYI5E/bundle.json","state":"https://pith.science/pith/GYOTGC5JMLJ6NSQLRS7IUMYI5E/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GYOTGC5JMLJ6NSQLRS7IUMYI5E/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:GYOTGC5JMLJ6NSQLRS7IUMYI5E","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":"f8484cfa2643f3027ecd459c737cffd2f728d1236532d81b63ffe1d6bb09b812","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-13T14:22:08Z","title_canon_sha256":"94231c943456275b1fd48373d9b46add02ed610d23f391293db65a89a5a472a6"},"schema_version":"1.0","source":{"id":"1806.05079","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05079","created_at":"2026-05-18T00:03:05Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05079v1","created_at":"2026-05-18T00:03:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05079","created_at":"2026-05-18T00:03:05Z"},{"alias_kind":"pith_short_12","alias_value":"GYOTGC5JMLJ6","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_16","alias_value":"GYOTGC5JMLJ6NSQL","created_at":"2026-05-18T12:32:25Z"},{"alias_kind":"pith_short_8","alias_value":"GYOTGC5J","created_at":"2026-05-18T12:32:25Z"}],"graph_snapshots":[{"event_id":"sha256:f998f6b746f4657607949aaa93b526f7f7b34ff7f0f0a92dea64fdb4d7613879","target":"graph","created_at":"2026-05-18T00:03:05Z","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 analyze the fluctuation of the number of individuals when two competing species, beginning with a few initial individuals, are submitted to a logistic growth. We show that when the total number of individuals reaches the carrying capacity, the number of each species is subject to giant fluctuations (variance $\\sim$ mean 2) if the two species have similar growth rate. We show that the deterministic logistic equation can be used only when the growth rates are significantly different, otherwise such growth has to be investigated by stochastic processes tools. These results generalize to a wide","authors_text":"Bahram Houchmandzadeh","cross_cats":["q-bio.PE"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-13T14:22:08Z","title":"Giant fluctuations in logistic growth"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05079","kind":"arxiv","version":1},"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:cabae716a0838924e9e6f4dc3f4f7c9cff96bdc741c8b8c0370e253b264cdd77","target":"record","created_at":"2026-05-18T00:03:05Z","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":"f8484cfa2643f3027ecd459c737cffd2f728d1236532d81b63ffe1d6bb09b812","cross_cats_sorted":["q-bio.PE"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"physics.bio-ph","submitted_at":"2018-06-13T14:22:08Z","title_canon_sha256":"94231c943456275b1fd48373d9b46add02ed610d23f391293db65a89a5a472a6"},"schema_version":"1.0","source":{"id":"1806.05079","kind":"arxiv","version":1}},"canonical_sha256":"361d330ba962d3e6ca0b8cbe8a3308e908a512ec18db5570d191ae3e2a0d39e7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"361d330ba962d3e6ca0b8cbe8a3308e908a512ec18db5570d191ae3e2a0d39e7","first_computed_at":"2026-05-18T00:03:05.294682Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:03:05.294682Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m/lCmbov9+6zXRtsGZIHWGHnGq2te5eb27CIg3SimCDWtQDyacOSp9YpM7TRAFPyhWAQVourWlJiVXxG4HgGAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:03:05.295077Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05079","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cabae716a0838924e9e6f4dc3f4f7c9cff96bdc741c8b8c0370e253b264cdd77","sha256:f998f6b746f4657607949aaa93b526f7f7b34ff7f0f0a92dea64fdb4d7613879"],"state_sha256":"93fd72cf970dbf55ac2cbdbe547f51f342c3344b3ae18b54a84be6609f1842f9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"COq+K7lsEPuFQHcmQk0+tDrAXZ3AYs90lRVszKtv7IkvyG2v1Ir3d4lkkUJkEznFkvbwtiVRQH0WN6V9aKQZCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-04T10:59:57.454632Z","bundle_sha256":"d4cbb78f7934ae5c1f0a7434130fbbfccfd1e7b35125fedcb9340e757c5edb8b"}}