{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:I4L2YLHYSX2IPUCSMT75UNFCAZ","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":"e111016fd9f72a658e801e12ef8e611d5f28a1fcd0c2abc1378182eefb70c1c2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-26T16:09:50Z","title_canon_sha256":"11cc25d0831d2f73917390d9db9f46dec948de755bd29dfa1443063cc3e48c46"},"schema_version":"1.0","source":{"id":"1906.11187","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1906.11187","created_at":"2026-07-05T01:23:54Z"},{"alias_kind":"arxiv_version","alias_value":"1906.11187v4","created_at":"2026-07-05T01:23:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1906.11187","created_at":"2026-07-05T01:23:54Z"},{"alias_kind":"pith_short_12","alias_value":"I4L2YLHYSX2I","created_at":"2026-07-05T01:23:54Z"},{"alias_kind":"pith_short_16","alias_value":"I4L2YLHYSX2IPUCS","created_at":"2026-07-05T01:23:54Z"},{"alias_kind":"pith_short_8","alias_value":"I4L2YLHY","created_at":"2026-07-05T01:23:54Z"}],"graph_snapshots":[{"event_id":"sha256:ee136e65529c3a447094f099be3a3cb2cd0bad3d0dc6084c1822c97faf12162a","target":"graph","created_at":"2026-07-05T01:23:54Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1906.11187/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study a class of elliptic SPDEs with additive Gaussian noise on $\\mathbb{R}^2 \\times M$, with $M$ a $d$-dimensional manifold equipped with a positive Radon measure, and a real-valued non linearity given by the derivative of a smooth potential $V$, convex at infinity and growing at most exponentially. For quite general coefficients and a suitable regularity of the noise we obtain, via the dimensional reduction principle discussed in our previous paper on the topic, the identity between the law of the solution to the SPDE evaluated at the origin with a Gibbs type measure on the abstract Wiene","authors_text":"Francesco C. De Vecchi, Massimiliano Gubinelli, Sergio Albeverio","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-26T16:09:50Z","title":"The elliptic stochastic quantization of some two dimensional Euclidean QFTs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.11187","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:b2b3f30ada6868285ce1600e777dc5d26b6f1c60b435d2fe336954146971ec42","target":"record","created_at":"2026-07-05T01:23:54Z","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":"e111016fd9f72a658e801e12ef8e611d5f28a1fcd0c2abc1378182eefb70c1c2","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2019-06-26T16:09:50Z","title_canon_sha256":"11cc25d0831d2f73917390d9db9f46dec948de755bd29dfa1443063cc3e48c46"},"schema_version":"1.0","source":{"id":"1906.11187","kind":"arxiv","version":4}},"canonical_sha256":"4717ac2cf895f487d05264ffda34a206486e25bbc19bc88c7a6ef5851219198b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4717ac2cf895f487d05264ffda34a206486e25bbc19bc88c7a6ef5851219198b","first_computed_at":"2026-07-05T01:23:54.328406Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T01:23:54.328406Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fW1V31D1sNgvtLpAzzNJAGfXQ4MHqs+3blgPUqiuAOP7iaz5jSAJJeV+sUOLVy5aV3ieaTfa8VijwTdkgLb5CA==","signature_status":"signed_v1","signed_at":"2026-07-05T01:23:54.328870Z","signed_message":"canonical_sha256_bytes"},"source_id":"1906.11187","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2b3f30ada6868285ce1600e777dc5d26b6f1c60b435d2fe336954146971ec42","sha256:ee136e65529c3a447094f099be3a3cb2cd0bad3d0dc6084c1822c97faf12162a"],"state_sha256":"5373a9786c3657bcd9677f0552863cfb25e3ffca5fa0f0f340158a073b3a137c"}