{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:OGBKW2VEERL7A5EOVOIXRWC36G","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":"77d36a567828e698228ca0a40d68187881f7ca6ef1fc35117eae83d368632879","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-06T20:19:16Z","title_canon_sha256":"92d4f69d13e405ff06c9b8805dd075584d620fd82ed37a2863e6732d21438036"},"schema_version":"1.0","source":{"id":"1606.01928","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.01928","created_at":"2026-05-18T01:12:44Z"},{"alias_kind":"arxiv_version","alias_value":"1606.01928v1","created_at":"2026-05-18T01:12:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.01928","created_at":"2026-05-18T01:12:44Z"},{"alias_kind":"pith_short_12","alias_value":"OGBKW2VEERL7","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_16","alias_value":"OGBKW2VEERL7A5EO","created_at":"2026-05-18T12:30:36Z"},{"alias_kind":"pith_short_8","alias_value":"OGBKW2VE","created_at":"2026-05-18T12:30:36Z"}],"graph_snapshots":[{"event_id":"sha256:a2bbee32af8039c11757124e086887e294499cd632d9d7cea9f456386e43c2e4","target":"graph","created_at":"2026-05-18T01:12:44Z","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":"For a truncated stochastically perturbed equation $x_{n+1}=\\max\\{ f(x_n)+l\\chi_{n+1}, 0 \\}$ with $f(x)<x$ on $(0,m)$, which corresponds to the Allee effect, we observe that for very small perturbation amplitude $l$, the eventual behavior is similar to a non-perturbed case: there is extinction for small initial values in $(0,m-\\varepsilon)$ and persistence for $x_0 \\in (m+\\delta, H]$ for some $H$ satisfying $H>f(H)>m$. As the amplitude grows, an interval $(m-\\varepsilon, m+\\delta)$ of initial values arises and expands, such that with a certain probability, $x_n$ sustains in $[m, H]$, and possib","authors_text":"Alexandra Rodkina, Elena Braverman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-06T20:19:16Z","title":"Stochastic difference equations with the Allee effect"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.01928","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":"sha256:26ef8349c115bae835b3369c7aea9edbd729fae1f87a9ef1cc97533207340089","target":"record","created_at":"2026-05-18T01:12:44Z","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":"77d36a567828e698228ca0a40d68187881f7ca6ef1fc35117eae83d368632879","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-06-06T20:19:16Z","title_canon_sha256":"92d4f69d13e405ff06c9b8805dd075584d620fd82ed37a2863e6732d21438036"},"schema_version":"1.0","source":{"id":"1606.01928","kind":"arxiv","version":1}},"canonical_sha256":"7182ab6aa42457f0748eab9178d85bf18b7fab3788a34952bd1f8f1e9472991c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7182ab6aa42457f0748eab9178d85bf18b7fab3788a34952bd1f8f1e9472991c","first_computed_at":"2026-05-18T01:12:44.987364Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:44.987364Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O5GSXK84UNdJEZ3oEmHzbLCmbokgiaBlwzm3ihTIfKhkl0guSpOJ7bZ5G32lSTDUqS9TwQSNhTLY0HomV2gsAw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:44.987822Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.01928","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26ef8349c115bae835b3369c7aea9edbd729fae1f87a9ef1cc97533207340089","sha256:a2bbee32af8039c11757124e086887e294499cd632d9d7cea9f456386e43c2e4"],"state_sha256":"ddaa9e199c4f58654b0a63fde99703353ef12ea80c4ce3e210ccfe87f1d32de1"}