{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:ORFABZWOY6USEDBLWYRRBYOG2M","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":"56c62cd276553a652bfb0bcb7a453e10766a4fb985b36f3d1d5156d4cd0ee33a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-05-29T14:33:16Z","title_canon_sha256":"ca1c56f7075c8f3c4fdaeb55ce133371ce22fd896c4338ba0c5a3c400cd8b735"},"schema_version":"1.0","source":{"id":"2405.19127","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2405.19127","created_at":"2026-07-05T08:24:48Z"},{"alias_kind":"arxiv_version","alias_value":"2405.19127v1","created_at":"2026-07-05T08:24:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2405.19127","created_at":"2026-07-05T08:24:48Z"},{"alias_kind":"pith_short_12","alias_value":"ORFABZWOY6US","created_at":"2026-07-05T08:24:48Z"},{"alias_kind":"pith_short_16","alias_value":"ORFABZWOY6USEDBL","created_at":"2026-07-05T08:24:48Z"},{"alias_kind":"pith_short_8","alias_value":"ORFABZWO","created_at":"2026-07-05T08:24:48Z"}],"graph_snapshots":[{"event_id":"sha256:0c4ecc2a7e9f81a92a7f21db3b037cb49e783822e10b8b8eee071506a8f710c6","target":"graph","created_at":"2026-07-05T08:24:48Z","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/2405.19127/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We give a generalization to bi-filtered $\\mathcal D$-modules underlying mixed Hodge modules of the relation between microlocalization along $f_1,...,f_r \\in \\mathcal O_X(X)$ and vanishing cycles along $g = \\sum_{i=1}^r y_i f_i$. This leads to an interesting isomorphism between localization triangles. As an application, we use these results to compare the $k$-plane Radon transform and the Fourier-Laplace transform for mixed Hodge modules. This is then applied to the Hodge module structure of certain GKZ systems.","authors_text":"Bradley Dirks","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-05-29T14:33:16Z","title":"Fourier transform and Radon transform for mixed Hodge modules"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.19127","kind":"arxiv","version":1},"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:d7aee0b3c201735538de411aa90d4311f4e4b895287e1a138329a289bd2d47bb","target":"record","created_at":"2026-07-05T08:24:48Z","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":"56c62cd276553a652bfb0bcb7a453e10766a4fb985b36f3d1d5156d4cd0ee33a","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.AG","submitted_at":"2024-05-29T14:33:16Z","title_canon_sha256":"ca1c56f7075c8f3c4fdaeb55ce133371ce22fd896c4338ba0c5a3c400cd8b735"},"schema_version":"1.0","source":{"id":"2405.19127","kind":"arxiv","version":1}},"canonical_sha256":"744a00e6cec7a9220c2bb62310e1c6d30bef6395b97a473d39ec79a9d1741903","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"744a00e6cec7a9220c2bb62310e1c6d30bef6395b97a473d39ec79a9d1741903","first_computed_at":"2026-07-05T08:24:48.292571Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:24:48.292571Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PtNo67JvEJdGCG3d1mjcDYV+GRWG3jOIDdPN5v20DzoiBVy6/OMSH9yTsMhlpRTAuVGm/NhmLeUutcU94zOPCw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:24:48.293028Z","signed_message":"canonical_sha256_bytes"},"source_id":"2405.19127","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d7aee0b3c201735538de411aa90d4311f4e4b895287e1a138329a289bd2d47bb","sha256:0c4ecc2a7e9f81a92a7f21db3b037cb49e783822e10b8b8eee071506a8f710c6"],"state_sha256":"669d271ae546c12a5c5967b7e21b921142d53a0b9e524f88c2d4647505974935"}