{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:NEU6JYYHNFR5BFC4TPGJNVTECT","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":"082aa61ca03079fae263c6c1664e58efef94d729480b507410d0fd398b09ad9b","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-07T11:38:46Z","title_canon_sha256":"6d7eaa98685a6a2db161eb4f1ed93ff88cb4edfd04fd84581f226bf13c94770e"},"schema_version":"1.0","source":{"id":"1606.02102","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.02102","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"arxiv_version","alias_value":"1606.02102v2","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.02102","created_at":"2026-05-18T00:45:49Z"},{"alias_kind":"pith_short_12","alias_value":"NEU6JYYHNFR5","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"NEU6JYYHNFR5BFC4","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"NEU6JYYH","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:2d8104a92e50fcc8fb62681240ed1d5210c59053ac67448151c76b45a86f3fae","target":"graph","created_at":"2026-05-18T00:45:49Z","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":"In this paper we study the stochastic quantization problem on the two dimensional torus and establish ergodicity for the solutions. Furthermore, we prove a characterization of the $\\Phi^4_2$ quantum field on the torus in terms of its density under translation. We also deduce that the $\\Phi^4_2$ quantum field on the torus is an extreme point in the set of all $L$-symmetrizing measures, where $L$ is the corresponding generator.","authors_text":"Michael Rockner, Rongchan Zhu, Xiangchan Zhu","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-07T11:38:46Z","title":"Ergodicity for the stochastic quantization problems on the 2D-torus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.02102","kind":"arxiv","version":2},"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:ede846011aa10a45947085bf0ee2820a75efa037f7a357146d2f6912fcef62e7","target":"record","created_at":"2026-05-18T00:45:49Z","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":"082aa61ca03079fae263c6c1664e58efef94d729480b507410d0fd398b09ad9b","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-06-07T11:38:46Z","title_canon_sha256":"6d7eaa98685a6a2db161eb4f1ed93ff88cb4edfd04fd84581f226bf13c94770e"},"schema_version":"1.0","source":{"id":"1606.02102","kind":"arxiv","version":2}},"canonical_sha256":"6929e4e3076963d0945c9bcc96d66414fd8d7300a2667e862eda0833d230b0d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6929e4e3076963d0945c9bcc96d66414fd8d7300a2667e862eda0833d230b0d7","first_computed_at":"2026-05-18T00:45:49.301239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:45:49.301239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nz03rMMPPI5iIKYWpAoM26z7KUKU9Gt5kPsp2/vmDTdtyKK7gi7biGnKy3ZAaSXFppKG8zhT8P49p7noLzHcBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:45:49.301784Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.02102","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ede846011aa10a45947085bf0ee2820a75efa037f7a357146d2f6912fcef62e7","sha256:2d8104a92e50fcc8fb62681240ed1d5210c59053ac67448151c76b45a86f3fae"],"state_sha256":"039af049dc5147ec28556432b4de9668bc8a832f0088e102e7d240498631f588"}