{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:I5SCGT2SW6QVBCMRPZT2Q77MCD","short_pith_number":"pith:I5SCGT2S","canonical_record":{"source":{"id":"1811.06339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-15T13:31:01Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"34ed03a031fcc97bd4251e88471faa5939796e1bf7620f535f3836d8cfc8b574","abstract_canon_sha256":"4f4467c6b9637b7a65ca8b19852e2d7e8270740b8ee2757c76a1a6a24da99e16"},"schema_version":"1.0"},"canonical_sha256":"4764234f52b7a15089917e67a87fec10fb8ddccbe0176c566ca452742718a63c","source":{"kind":"arxiv","id":"1811.06339","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06339","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06339v2","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06339","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"I5SCGT2SW6QV","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"pith_short_16","alias_value":"I5SCGT2SW6QVBCMR","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"pith_short_8","alias_value":"I5SCGT2S","created_at":"2026-07-05T00:17:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:I5SCGT2SW6QVBCMRPZT2Q77MCD","target":"record","payload":{"canonical_record":{"source":{"id":"1811.06339","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-15T13:31:01Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"34ed03a031fcc97bd4251e88471faa5939796e1bf7620f535f3836d8cfc8b574","abstract_canon_sha256":"4f4467c6b9637b7a65ca8b19852e2d7e8270740b8ee2757c76a1a6a24da99e16"},"schema_version":"1.0"},"canonical_sha256":"4764234f52b7a15089917e67a87fec10fb8ddccbe0176c566ca452742718a63c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:17:48.887324Z","signature_b64":"o7ohfhWHXGxMlYvh79Kg4SFQxWH7Jw/MPQGJO0B05NgVY/VV8SCmu/s71sLGN70AgirRHIo+xFFqNrsyoha3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4764234f52b7a15089917e67a87fec10fb8ddccbe0176c566ca452742718a63c","last_reissued_at":"2026-07-05T00:17:48.886844Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:17:48.886844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.06339","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:17:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VaJC5xV1132g7RHOI+s5i7FH82VSXJkEzNbwWM+Zn++Bh4vTIrUfg4dD/ePDW1VLMhmXTByl0OFcNrnRuNCHCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:58:35.536573Z"},"content_sha256":"6b283be161d7abc6547e23644fbb757f56807cbdbbc159d588648b3dd32c8d38","schema_version":"1.0","event_id":"sha256:6b283be161d7abc6547e23644fbb757f56807cbdbbc159d588648b3dd32c8d38"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:I5SCGT2SW6QVBCMRPZT2Q77MCD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"H\\\"ormander's theorem for semilinear SPDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.PR","authors_text":"Andris Gerasimovics, Martin Hairer","submitted_at":"2018-11-15T13:31:01Z","abstract_excerpt":"We consider a broad class of semilinear SPDEs with multiplicative noise driven by a finite-dimensional Wiener process. We show that, provided that an infinite-dimensional analogue of H\\\"ormander's bracket condition holds, the Malliavin matrix of the solution is an operator with dense range. In particular, we show that the laws of finite-dimensional projections of such solutions admit smooth densities with respect to Lebesgue measure. The main idea is to develop a robust pathwise solution theory for such SPDEs using rough paths theory, which then allows us to use a pathwise version of Norris's "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06339","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/1811.06339/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T00:17:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"R9NieWb6JhDjst82znbEQCaEBWbJTgQ4uZPZM87moir21RSKmJxGVdtnqa7MOXWtVns64UTmeYpsoPBrfmNEBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T19:58:35.537219Z"},"content_sha256":"ada67f4aeb947c45e439b3ce178b412aad7e1686dffbda902755504ecce8fa70","schema_version":"1.0","event_id":"sha256:ada67f4aeb947c45e439b3ce178b412aad7e1686dffbda902755504ecce8fa70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I5SCGT2SW6QVBCMRPZT2Q77MCD/bundle.json","state_url":"https://pith.science/pith/I5SCGT2SW6QVBCMRPZT2Q77MCD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I5SCGT2SW6QVBCMRPZT2Q77MCD/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T19:58:35Z","links":{"resolver":"https://pith.science/pith/I5SCGT2SW6QVBCMRPZT2Q77MCD","bundle":"https://pith.science/pith/I5SCGT2SW6QVBCMRPZT2Q77MCD/bundle.json","state":"https://pith.science/pith/I5SCGT2SW6QVBCMRPZT2Q77MCD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I5SCGT2SW6QVBCMRPZT2Q77MCD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:I5SCGT2SW6QVBCMRPZT2Q77MCD","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":"4f4467c6b9637b7a65ca8b19852e2d7e8270740b8ee2757c76a1a6a24da99e16","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-15T13:31:01Z","title_canon_sha256":"34ed03a031fcc97bd4251e88471faa5939796e1bf7620f535f3836d8cfc8b574"},"schema_version":"1.0","source":{"id":"1811.06339","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.06339","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"arxiv_version","alias_value":"1811.06339v2","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.06339","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"pith_short_12","alias_value":"I5SCGT2SW6QV","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"pith_short_16","alias_value":"I5SCGT2SW6QVBCMR","created_at":"2026-07-05T00:17:48Z"},{"alias_kind":"pith_short_8","alias_value":"I5SCGT2S","created_at":"2026-07-05T00:17:48Z"}],"graph_snapshots":[{"event_id":"sha256:ada67f4aeb947c45e439b3ce178b412aad7e1686dffbda902755504ecce8fa70","target":"graph","created_at":"2026-07-05T00:17:48Z","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/1811.06339/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider a broad class of semilinear SPDEs with multiplicative noise driven by a finite-dimensional Wiener process. We show that, provided that an infinite-dimensional analogue of H\\\"ormander's bracket condition holds, the Malliavin matrix of the solution is an operator with dense range. In particular, we show that the laws of finite-dimensional projections of such solutions admit smooth densities with respect to Lebesgue measure. The main idea is to develop a robust pathwise solution theory for such SPDEs using rough paths theory, which then allows us to use a pathwise version of Norris's ","authors_text":"Andris Gerasimovics, Martin Hairer","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-15T13:31:01Z","title":"H\\\"ormander's theorem for semilinear SPDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.06339","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":"sha256:6b283be161d7abc6547e23644fbb757f56807cbdbbc159d588648b3dd32c8d38","target":"record","created_at":"2026-07-05T00:17:48Z","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":"4f4467c6b9637b7a65ca8b19852e2d7e8270740b8ee2757c76a1a6a24da99e16","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-15T13:31:01Z","title_canon_sha256":"34ed03a031fcc97bd4251e88471faa5939796e1bf7620f535f3836d8cfc8b574"},"schema_version":"1.0","source":{"id":"1811.06339","kind":"arxiv","version":2}},"canonical_sha256":"4764234f52b7a15089917e67a87fec10fb8ddccbe0176c566ca452742718a63c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4764234f52b7a15089917e67a87fec10fb8ddccbe0176c566ca452742718a63c","first_computed_at":"2026-07-05T00:17:48.886844Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:17:48.886844Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"o7ohfhWHXGxMlYvh79Kg4SFQxWH7Jw/MPQGJO0B05NgVY/VV8SCmu/s71sLGN70AgirRHIo+xFFqNrsyoha3Bg==","signature_status":"signed_v1","signed_at":"2026-07-05T00:17:48.887324Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.06339","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b283be161d7abc6547e23644fbb757f56807cbdbbc159d588648b3dd32c8d38","sha256:ada67f4aeb947c45e439b3ce178b412aad7e1686dffbda902755504ecce8fa70"],"state_sha256":"e5eb7c48b50e5ad67bbe1a3676312d7fcd1640b5c69a6e025600bf3ec7dd6460"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ifj9LKtBWm0Dk5LXVgdovzCH59EoqI4INd2UVALI4G+IjOxImZcWvH2HKFdwt2hewbn2rYYer/QNnLgG4/FYDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T19:58:35.541913Z","bundle_sha256":"0bffb3249a32120c4cc6b3cb2f3f0cee327017a176d89bfbadae054e791bc62a"}}