{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:SYYJNF7S6Q6E37CLPQ4G3EUO5F","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":"71850b9c718819b999115454d4e60fcab1deb25697f5cd57b0d4c564b70257f9","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-10-13T08:01:39Z","title_canon_sha256":"702f20584eeb6c43e42ba46f78926260d2db6a6f1e418a9185e315bd32ebbada"},"schema_version":"1.0","source":{"id":"math/0510269","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0510269","created_at":"2026-07-04T15:11:12Z"},{"alias_kind":"arxiv_version","alias_value":"math/0510269v2","created_at":"2026-07-04T15:11:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0510269","created_at":"2026-07-04T15:11:12Z"},{"alias_kind":"pith_short_12","alias_value":"SYYJNF7S6Q6E","created_at":"2026-07-04T15:11:12Z"},{"alias_kind":"pith_short_16","alias_value":"SYYJNF7S6Q6E37CL","created_at":"2026-07-04T15:11:12Z"},{"alias_kind":"pith_short_8","alias_value":"SYYJNF7S","created_at":"2026-07-04T15:11:12Z"}],"graph_snapshots":[{"event_id":"sha256:d39ccbb345c881a6dd156b6448d347dd9e00a40935e62810ab512044cbd74121","target":"graph","created_at":"2026-07-04T15:11:12Z","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/math/0510269/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We construct a locally geometric $\\infty$-stack $M_{Hod}(X,Perf)$ of perfect complexes with $\\lambda$-connection structure on a smooth projective variety $X$. This maps to $A ^1 / G_m$, so it can be considered as the Hodge filtration of its fiber over 1 which is $M_{DR}(X,Perf)$, parametrizing complexes of $D_X$-modules which are $O_X$-perfect. We apply the result of Toen-Vaquie that $Perf(X)$ is locally geometric. The proof of geometricity of the map $M_{Hod}(X,Perf) \\to Perf(X)$ uses a Hochschild-like notion of weak complexes of modules over a sheaf of rings of differential operators. We pro","authors_text":"Carlos T. Simpson (JAD)","cross_cats":[],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2005-10-13T08:01:39Z","title":"Geometricity of the Hodge filtration on the $\\infty$-stack of perfect complexes over $X_{DR}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0510269","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":"sha256:66ce7905eb1bcf5b710ed6d3689bf9783a5b39583ebf69d3d1a695a7b42925ce","target":"record","created_at":"2026-07-04T15:11:12Z","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":"71850b9c718819b999115454d4e60fcab1deb25697f5cd57b0d4c564b70257f9","cross_cats_sorted":[],"license":"","primary_cat":"math.AG","submitted_at":"2005-10-13T08:01:39Z","title_canon_sha256":"702f20584eeb6c43e42ba46f78926260d2db6a6f1e418a9185e315bd32ebbada"},"schema_version":"1.0","source":{"id":"math/0510269","kind":"arxiv","version":2}},"canonical_sha256":"96309697f2f43c4dfc4b7c386d928ee977f962cc452735d62551985eb574f085","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"96309697f2f43c4dfc4b7c386d928ee977f962cc452735d62551985eb574f085","first_computed_at":"2026-07-04T15:11:12.987094Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T15:11:12.987094Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WBXucmqmjkjaj2dhZUg434oiSqmgzF8VDoDQZU6fxVhytShuQv2hSoqkZ/12ZXuPCdsTCxpzip5b35A7rRfBAg==","signature_status":"signed_v1","signed_at":"2026-07-04T15:11:12.987470Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0510269","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:66ce7905eb1bcf5b710ed6d3689bf9783a5b39583ebf69d3d1a695a7b42925ce","sha256:d39ccbb345c881a6dd156b6448d347dd9e00a40935e62810ab512044cbd74121"],"state_sha256":"996717f569aeaea39ec9072ea00d8b097ed0f062362d5f73b398bc777fe542c0"}