{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2020:4YCWXXNYF255LMVR5T6WTI7HXC","short_pith_number":"pith:4YCWXXNY","canonical_record":{"source":{"id":"2009.07640","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T12:40:36Z","cross_cats_sorted":["math.AP","math.MP","math.PR"],"title_canon_sha256":"89482fe0652492c85d5268ca7fe5c2788a4fe6f080ddd7a83b9bc0ebc074b599","abstract_canon_sha256":"3cb82f9d6e40e48f82bb5f031d377146d6412670fb67ee9aa87e3925d351d90e"},"schema_version":"1.0"},"canonical_sha256":"e6056bddb82ebbd5b2b1ecfd69a3e7b897d8f39a87c4e2166b0f61c86346d9d6","source":{"kind":"arxiv","id":"2009.07640","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07640","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07640v4","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07640","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"4YCWXXNYF255","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"pith_short_16","alias_value":"4YCWXXNYF255LMVR","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"pith_short_8","alias_value":"4YCWXXNY","created_at":"2026-07-05T03:30:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2020:4YCWXXNYF255LMVR5T6WTI7HXC","target":"record","payload":{"canonical_record":{"source":{"id":"2009.07640","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T12:40:36Z","cross_cats_sorted":["math.AP","math.MP","math.PR"],"title_canon_sha256":"89482fe0652492c85d5268ca7fe5c2788a4fe6f080ddd7a83b9bc0ebc074b599","abstract_canon_sha256":"3cb82f9d6e40e48f82bb5f031d377146d6412670fb67ee9aa87e3925d351d90e"},"schema_version":"1.0"},"canonical_sha256":"e6056bddb82ebbd5b2b1ecfd69a3e7b897d8f39a87c4e2166b0f61c86346d9d6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T03:30:50.265278Z","signature_b64":"N8OuiXFLl0jhvtXAQd/jxsuRhyLPBZItTaDnD9rYASGBz+tgYl6W5/a3f/iZrcDOPZXxpYlAU7VSUUVvt653DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e6056bddb82ebbd5b2b1ecfd69a3e7b897d8f39a87c4e2166b0f61c86346d9d6","last_reissued_at":"2026-07-05T03:30:50.264733Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T03:30:50.264733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2009.07640","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T03:30:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HcjVNa2RyctEaHNTsGrm0wbyMHTOr/AWFYKL7tKkJcCSsUX1fh1nKaPpHgv/kkRU1/z7f4d3IZhEbZVKZSMiDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T07:34:49.243309Z"},"content_sha256":"641eff2e897b55979fd0d1ac508fc92b300c3adac4e29602f8a21959b3091b98","schema_version":"1.0","event_id":"sha256:641eff2e897b55979fd0d1ac508fc92b300c3adac4e29602f8a21959b3091b98"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2020:4YCWXXNYF255LMVR5T6WTI7HXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Microlocal Approach to Renormalization in Stochastic PDEs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Claudio Dappiaggi, Lorenzo Zambotti, Nicol\\`o Drago, Paolo Rinaldi","submitted_at":"2020-09-16T12:40:36Z","abstract_excerpt":"We present a novel framework for the study of a large class of non-linear stochastic PDEs, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedomw without resorting to any regularization scheme and to the subtraction of infinities. As an example of the effectiveness of the approach we apply it to the perturbative analysis of the stochastic $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07640","kind":"arxiv","version":4},"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/2009.07640/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":"2026-07-05T03:30:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cdXpPp83BMpJtAI1p6vmjMLH90Gu974Tlru6V+5c+oGqJxFT2eRdZrdVZMiJbIV5Lnxw8MNrN3gzuo88e4ppCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T07:34:49.243859Z"},"content_sha256":"e419030ac8933a485192b44c740af4e73a81928b5f9950d4adaa258204d5c38f","schema_version":"1.0","event_id":"sha256:e419030ac8933a485192b44c740af4e73a81928b5f9950d4adaa258204d5c38f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4YCWXXNYF255LMVR5T6WTI7HXC/bundle.json","state_url":"https://pith.science/pith/4YCWXXNYF255LMVR5T6WTI7HXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4YCWXXNYF255LMVR5T6WTI7HXC/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":"2026-08-10T07:34:49Z","links":{"resolver":"https://pith.science/pith/4YCWXXNYF255LMVR5T6WTI7HXC","bundle":"https://pith.science/pith/4YCWXXNYF255LMVR5T6WTI7HXC/bundle.json","state":"https://pith.science/pith/4YCWXXNYF255LMVR5T6WTI7HXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4YCWXXNYF255LMVR5T6WTI7HXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:4YCWXXNYF255LMVR5T6WTI7HXC","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":"3cb82f9d6e40e48f82bb5f031d377146d6412670fb67ee9aa87e3925d351d90e","cross_cats_sorted":["math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T12:40:36Z","title_canon_sha256":"89482fe0652492c85d5268ca7fe5c2788a4fe6f080ddd7a83b9bc0ebc074b599"},"schema_version":"1.0","source":{"id":"2009.07640","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2009.07640","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"arxiv_version","alias_value":"2009.07640v4","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2009.07640","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"pith_short_12","alias_value":"4YCWXXNYF255","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"pith_short_16","alias_value":"4YCWXXNYF255LMVR","created_at":"2026-07-05T03:30:50Z"},{"alias_kind":"pith_short_8","alias_value":"4YCWXXNY","created_at":"2026-07-05T03:30:50Z"}],"graph_snapshots":[{"event_id":"sha256:e419030ac8933a485192b44c740af4e73a81928b5f9950d4adaa258204d5c38f","target":"graph","created_at":"2026-07-05T03:30:50Z","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/2009.07640/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a novel framework for the study of a large class of non-linear stochastic PDEs, which is inspired by the algebraic approach to quantum field theory. The main merit is that, by realizing random fields within a suitable algebra of functional-valued distributions, we are able to use techniques proper of microlocal analysis which allow us to discuss renormalization and its associated freedomw without resorting to any regularization scheme and to the subtraction of infinities. As an example of the effectiveness of the approach we apply it to the perturbative analysis of the stochastic $\\","authors_text":"Claudio Dappiaggi, Lorenzo Zambotti, Nicol\\`o Drago, Paolo Rinaldi","cross_cats":["math.AP","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T12:40:36Z","title":"A Microlocal Approach to Renormalization in Stochastic PDEs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2009.07640","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":"sha256:641eff2e897b55979fd0d1ac508fc92b300c3adac4e29602f8a21959b3091b98","target":"record","created_at":"2026-07-05T03:30:50Z","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":"3cb82f9d6e40e48f82bb5f031d377146d6412670fb67ee9aa87e3925d351d90e","cross_cats_sorted":["math.AP","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2020-09-16T12:40:36Z","title_canon_sha256":"89482fe0652492c85d5268ca7fe5c2788a4fe6f080ddd7a83b9bc0ebc074b599"},"schema_version":"1.0","source":{"id":"2009.07640","kind":"arxiv","version":4}},"canonical_sha256":"e6056bddb82ebbd5b2b1ecfd69a3e7b897d8f39a87c4e2166b0f61c86346d9d6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e6056bddb82ebbd5b2b1ecfd69a3e7b897d8f39a87c4e2166b0f61c86346d9d6","first_computed_at":"2026-07-05T03:30:50.264733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T03:30:50.264733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"N8OuiXFLl0jhvtXAQd/jxsuRhyLPBZItTaDnD9rYASGBz+tgYl6W5/a3f/iZrcDOPZXxpYlAU7VSUUVvt653DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T03:30:50.265278Z","signed_message":"canonical_sha256_bytes"},"source_id":"2009.07640","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:641eff2e897b55979fd0d1ac508fc92b300c3adac4e29602f8a21959b3091b98","sha256:e419030ac8933a485192b44c740af4e73a81928b5f9950d4adaa258204d5c38f"],"state_sha256":"94de87d448e9ded02dec9f89b324e1139f158a378c919ba4603e404740d76364"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aXoddmYkSZbpmd1whXmFqmzpuYwy9RjxZrJxyTK4PnGhGQzdBwA/f/yLqZndVDuUzO4omsqOWdiYPsIjfHvxAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T07:34:49.250695Z","bundle_sha256":"92c8a317f4cd07a92a60fdd36c75a9329764331a2e1641431b664e1b192e73b0"}}