{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:FLUCHF5GIGXIKC4OTCXHFW6ZOE","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":"60152287738944610fd63dfe9229db11f071bd2eb5f9eb9c7e4e95c7b3262b27","cross_cats_sorted":["math.AT","math.DS","math.MP","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T05:17:38Z","title_canon_sha256":"9d63f6c558eb6ddb2ffb97f1124d74520935a4005d1cad10e07607a27ca49c44"},"schema_version":"1.0","source":{"id":"1511.03393","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.03393","created_at":"2026-05-17T23:47:36Z"},{"alias_kind":"arxiv_version","alias_value":"1511.03393v4","created_at":"2026-05-17T23:47:36Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.03393","created_at":"2026-05-17T23:47:36Z"},{"alias_kind":"pith_short_12","alias_value":"FLUCHF5GIGXI","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_16","alias_value":"FLUCHF5GIGXIKC4O","created_at":"2026-05-18T12:29:19Z"},{"alias_kind":"pith_short_8","alias_value":"FLUCHF5G","created_at":"2026-05-18T12:29:19Z"}],"graph_snapshots":[{"event_id":"sha256:811ee47b723f42f0c64315b593a74f0df2e2b131d083d4d41e7f85e1c9e7f34b","target":"graph","created_at":"2026-05-17T23:47:36Z","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":"Many natural and engineered dynamical systems, including all living objects, exhibit signatures of what can be called spontaneous dynamical long-range order (DLRO). This order's omnipresence has long been recognized by the scientific community, as evidenced by a myriad of related concepts, theoretical and phenomenological frameworks, and experimental phenomena such as turbulence, $1/f$ noise, dynamical complexity, chaos and the butterfly effect, the Richter scale for earthquakes and the scale-free statistics of other sudden processes, self-organization and pattern formation, self-organized cri","authors_text":"Igor V. Ovchinnikov","cross_cats":["math.AT","math.DS","math.MP","nlin.AO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T05:17:38Z","title":"Introduction to Supersymmetric Theory of Stochastics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.03393","kind":"arxiv","version":4},"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":"sha256:7822dac5b42243e4509ad6332c68a6b08a42129429dc462d7851e9ede3f9094c","target":"record","created_at":"2026-05-17T23:47:36Z","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":"60152287738944610fd63dfe9229db11f071bd2eb5f9eb9c7e4e95c7b3262b27","cross_cats_sorted":["math.AT","math.DS","math.MP","nlin.AO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2015-11-11T05:17:38Z","title_canon_sha256":"9d63f6c558eb6ddb2ffb97f1124d74520935a4005d1cad10e07607a27ca49c44"},"schema_version":"1.0","source":{"id":"1511.03393","kind":"arxiv","version":4}},"canonical_sha256":"2ae82397a641ae850b8e98ae72dbd9712fbb18b4f441e521f41fcd1512e7a0ac","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ae82397a641ae850b8e98ae72dbd9712fbb18b4f441e521f41fcd1512e7a0ac","first_computed_at":"2026-05-17T23:47:36.647698Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:47:36.647698Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2Ln1n3Cri1O+nDmyeusqWBSdw2bCgSkIAPqdExdGLxSmDkKiDrnypTsYcuyFesENFre05KBkyZVgEEOF+T6mDg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:47:36.648179Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.03393","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7822dac5b42243e4509ad6332c68a6b08a42129429dc462d7851e9ede3f9094c","sha256:811ee47b723f42f0c64315b593a74f0df2e2b131d083d4d41e7f85e1c9e7f34b"],"state_sha256":"9e7262eb3084f2553462e740da5643a5f46a5768c1749d24e7383f8dd54ad9d1"}