{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:DMGO4BGGYN4U6F3KUGXP4ZJ7P4","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":"5856c2e480d143e193e3e6535be1ed4c224c647ad06860ae4eeaed35bf3af5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-09T17:41:28Z","title_canon_sha256":"75b51c44df1a12489c6eba53f67226a61ff864d3c00a2bee140f9c72cb24c44a"},"schema_version":"1.0","source":{"id":"1611.03023","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1611.03023","created_at":"2026-05-18T00:59:42Z"},{"alias_kind":"arxiv_version","alias_value":"1611.03023v1","created_at":"2026-05-18T00:59:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.03023","created_at":"2026-05-18T00:59:42Z"},{"alias_kind":"pith_short_12","alias_value":"DMGO4BGGYN4U","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_16","alias_value":"DMGO4BGGYN4U6F3K","created_at":"2026-05-18T12:30:12Z"},{"alias_kind":"pith_short_8","alias_value":"DMGO4BGG","created_at":"2026-05-18T12:30:12Z"}],"graph_snapshots":[{"event_id":"sha256:a771d1f75da46bb5dbc6f6969f24f258c93e2a31298cda64374e53a4bb90b115","target":"graph","created_at":"2026-05-18T00:59:42Z","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 provide conditions for the existence of measurable solutions to the equation $\\xi(T\\omega)=f(\\omega,\\xi(\\omega))$, where $T:\\Omega \\rightarrow\\Omega$ is an automorphism of the probability space $\\Omega$ and $f(\\omega,\\cdot)$ is a strictly non-expansive mapping. We use results of this kind to establish a stochastic nonlinear analogue of the Perron-Frobenius theorem on eigenvalues and eigenvectors of a positive matrix. We consider a random mapping $D(\\omega)$ of a random closed cone $K(\\omega)$ in a finite-dimensional linear space into the cone $K(T\\omega)$. Under assumptions of monotonicity ","authors_text":"E. Babaei, I.V. Evstigneev, S.A. Pirogov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-09T17:41:28Z","title":"Stochastic Fixed Points and Nonlinear Perron-Frobenius Theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03023","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":"sha256:4b1d33828d349aec041382cc1ffb3d688139f99e2314fd22620a28016f154b2c","target":"record","created_at":"2026-05-18T00:59:42Z","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":"5856c2e480d143e193e3e6535be1ed4c224c647ad06860ae4eeaed35bf3af5a1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2016-11-09T17:41:28Z","title_canon_sha256":"75b51c44df1a12489c6eba53f67226a61ff864d3c00a2bee140f9c72cb24c44a"},"schema_version":"1.0","source":{"id":"1611.03023","kind":"arxiv","version":1}},"canonical_sha256":"1b0cee04c6c3794f176aa1aefe653f7f334d05534e00edccf65104b4cfd7c382","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b0cee04c6c3794f176aa1aefe653f7f334d05534e00edccf65104b4cfd7c382","first_computed_at":"2026-05-18T00:59:42.826233Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:42.826233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HH5Urul1lASxZJoEDNaUP7dRtYQF/G5x8dmKhl5qFKECWODixtmmLkrT8de149Yi5uIPT29FyBHCaBpDSnWUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:42.826964Z","signed_message":"canonical_sha256_bytes"},"source_id":"1611.03023","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4b1d33828d349aec041382cc1ffb3d688139f99e2314fd22620a28016f154b2c","sha256:a771d1f75da46bb5dbc6f6969f24f258c93e2a31298cda64374e53a4bb90b115"],"state_sha256":"7deef65b7c2318b7d98a6f38d6a6bf23cb191fb7e4c67c61cc57c9f275fd110d"}