{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:LU2JB6HV6UYCL7WQDQGAFCZIJ2","short_pith_number":"pith:LU2JB6HV","schema_version":"1.0","canonical_sha256":"5d3490f8f5f53025fed01c0c028b284e9b2c5faf1f1087875543a3dce10ccc1e","source":{"kind":"arxiv","id":"2509.07948","version":2},"attestation_state":"computed","paper":{"title":"Noncommutative Regularity Structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"math.PR","authors_text":"Ajay Chandra, Martin Hairer, Martin Peev","submitted_at":"2025-09-09T17:38:24Z","abstract_excerpt":"We extend the theory of regularity structures [Hai14] to allow processes belonging to locally $m$-convex topological algebras. This extension includes processes in the locally $C^{*}$-algebras of [CHP25] used to localise singular stochastic partial differential equations involving fermions, as well as processes in Banach algebras such as infinite-dimensional semicircular\\circular Brownian motion, and more generally the $q$-Gaussians of [BS91, BKS97, Bo\\.z99].\n  A new challenge we encounter in the $q$-Gaussian setting with $q \\in (-1,1)$ are noncommutative renormalisation estimates where we mus"},"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":"2509.07948","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2025-09-09T17:38:24Z","cross_cats_sorted":["math-ph","math.MP","math.OA"],"title_canon_sha256":"7f1ef7e0354dcccdec25e8c43462d271e55ec245312c305242897c6b117a0693","abstract_canon_sha256":"4ed836497a914dec0d1492d84c2ed55c644f1e322f19469f5810f8ddb0293356"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:08:09.032955Z","signature_b64":"Ntv0qInkyCyXAEtkLnxi5vEc7XPHk48tmrBOWYbRPWMTpZVyyC/9rGI/Xu63YrmwXEbdbJuF6aIOYjYU3P+AAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5d3490f8f5f53025fed01c0c028b284e9b2c5faf1f1087875543a3dce10ccc1e","last_reissued_at":"2026-07-05T12:08:09.032421Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:08:09.032421Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Noncommutative Regularity Structures","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.MP","math.OA"],"primary_cat":"math.PR","authors_text":"Ajay Chandra, Martin Hairer, Martin Peev","submitted_at":"2025-09-09T17:38:24Z","abstract_excerpt":"We extend the theory of regularity structures [Hai14] to allow processes belonging to locally $m$-convex topological algebras. This extension includes processes in the locally $C^{*}$-algebras of [CHP25] used to localise singular stochastic partial differential equations involving fermions, as well as processes in Banach algebras such as infinite-dimensional semicircular\\circular Brownian motion, and more generally the $q$-Gaussians of [BS91, BKS97, Bo\\.z99].\n  A new challenge we encounter in the $q$-Gaussian setting with $q \\in (-1,1)$ are noncommutative renormalisation estimates where we mus"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.07948","kind":"arxiv","version":2},"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/2509.07948/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":"2509.07948","created_at":"2026-07-05T12:08:09.032482+00:00"},{"alias_kind":"arxiv_version","alias_value":"2509.07948v2","created_at":"2026-07-05T12:08:09.032482+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.07948","created_at":"2026-07-05T12:08:09.032482+00:00"},{"alias_kind":"pith_short_12","alias_value":"LU2JB6HV6UYC","created_at":"2026-07-05T12:08:09.032482+00:00"},{"alias_kind":"pith_short_16","alias_value":"LU2JB6HV6UYCL7WQ","created_at":"2026-07-05T12:08:09.032482+00:00"},{"alias_kind":"pith_short_8","alias_value":"LU2JB6HV","created_at":"2026-07-05T12:08:09.032482+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2","json":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2.json","graph_json":"https://pith.science/api/pith-number/LU2JB6HV6UYCL7WQDQGAFCZIJ2/graph.json","events_json":"https://pith.science/api/pith-number/LU2JB6HV6UYCL7WQDQGAFCZIJ2/events.json","paper":"https://pith.science/paper/LU2JB6HV"},"agent_actions":{"view_html":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2","download_json":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2.json","view_paper":"https://pith.science/paper/LU2JB6HV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2509.07948&json=true","fetch_graph":"https://pith.science/api/pith-number/LU2JB6HV6UYCL7WQDQGAFCZIJ2/graph.json","fetch_events":"https://pith.science/api/pith-number/LU2JB6HV6UYCL7WQDQGAFCZIJ2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2/action/storage_attestation","attest_author":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2/action/author_attestation","sign_citation":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2/action/citation_signature","submit_replication":"https://pith.science/pith/LU2JB6HV6UYCL7WQDQGAFCZIJ2/action/replication_record"}},"created_at":"2026-07-05T12:08:09.032482+00:00","updated_at":"2026-07-05T12:08:09.032482+00:00"}