{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2021:UAONRT4H54ACGAKY3PBCXDPQ77","short_pith_number":"pith:UAONRT4H","schema_version":"1.0","canonical_sha256":"a01cd8cf87ef00230158dbc22b8df0ffeb8f24d9edee904685f42da476188503","source":{"kind":"arxiv","id":"2108.12664","version":3},"attestation_state":"computed","paper":{"title":"Elliptic stochastic quantization of Sinh-Gordon QFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Francesco C. De Vecchi, Nikolay Barashkov","submitted_at":"2021-08-28T15:26:25Z","abstract_excerpt":"The (elliptic) stochastic quantization equation for the (massive) $\\cosh(\\beta \\varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $\\beta^2 < 4 \\pi$), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantizatio"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2108.12664","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2021-08-28T15:26:25Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"f4d75546c62b0f6607f7c902a6f7335bbaec0691d4b26f987649feac7ec8a30e","abstract_canon_sha256":"40290a87d71dfb597452bd408f00045b442922d23406635bd3686c4fb6a50ed8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:22:27.172861Z","signature_b64":"cJobQA0QrCvpUQKjzYJeeGMX2e9AHqoWuHe3AqPwHReWTZNG9IkQsduICeJYn9MWcxPZfyWFcPgJyXxKClf0Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a01cd8cf87ef00230158dbc22b8df0ffeb8f24d9edee904685f42da476188503","last_reissued_at":"2026-07-05T11:22:27.172275Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:22:27.172275Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Elliptic stochastic quantization of Sinh-Gordon QFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.PR","authors_text":"Francesco C. De Vecchi, Nikolay Barashkov","submitted_at":"2021-08-28T15:26:25Z","abstract_excerpt":"The (elliptic) stochastic quantization equation for the (massive) $\\cosh(\\beta \\varphi)_2$ model, for the charged parameter in the $L^2$ regime (i.e. $\\beta^2 < 4 \\pi$), is studied. We prove the existence, uniqueness and the properties of the invariant measure of the solution to this equation. The proof is obtained through a priori estimates and a lattice approximation of the equation. For implementing this strategy we generalize some properties of Besov spaces in the continuum to analogous results for Besov spaces on the lattice. As a final result we show how to use the stochastic quantizatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2108.12664","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2108.12664/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2108.12664","created_at":"2026-07-05T11:22:27.172359+00:00"},{"alias_kind":"arxiv_version","alias_value":"2108.12664v3","created_at":"2026-07-05T11:22:27.172359+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2108.12664","created_at":"2026-07-05T11:22:27.172359+00:00"},{"alias_kind":"pith_short_12","alias_value":"UAONRT4H54AC","created_at":"2026-07-05T11:22:27.172359+00:00"},{"alias_kind":"pith_short_16","alias_value":"UAONRT4H54ACGAKY","created_at":"2026-07-05T11:22:27.172359+00:00"},{"alias_kind":"pith_short_8","alias_value":"UAONRT4H","created_at":"2026-07-05T11:22:27.172359+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2507.09278","citing_title":"Discrete reaction-diffusion system with stochastic dynamical boundary conditions: convergence results","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77","json":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77.json","graph_json":"https://pith.science/api/pith-number/UAONRT4H54ACGAKY3PBCXDPQ77/graph.json","events_json":"https://pith.science/api/pith-number/UAONRT4H54ACGAKY3PBCXDPQ77/events.json","paper":"https://pith.science/paper/UAONRT4H"},"agent_actions":{"view_html":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77","download_json":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77.json","view_paper":"https://pith.science/paper/UAONRT4H","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2108.12664&json=true","fetch_graph":"https://pith.science/api/pith-number/UAONRT4H54ACGAKY3PBCXDPQ77/graph.json","fetch_events":"https://pith.science/api/pith-number/UAONRT4H54ACGAKY3PBCXDPQ77/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77/action/storage_attestation","attest_author":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77/action/author_attestation","sign_citation":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77/action/citation_signature","submit_replication":"https://pith.science/pith/UAONRT4H54ACGAKY3PBCXDPQ77/action/replication_record"}},"created_at":"2026-07-05T11:22:27.172359+00:00","updated_at":"2026-07-05T11:22:27.172359+00:00"}