{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:6YRZ7KBHAGWQB5IZVUI7H57OEX","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":"59781c34f45988712dacd6f62744a681b48c493fb2dd5a788a19728107beb976","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-02-13T18:42:28Z","title_canon_sha256":"6d5af517b023be894b5616e1b8393462dc2a15a00c6e584247257200c9fd3203"},"schema_version":"1.0","source":{"id":"2402.08660","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2402.08660","created_at":"2026-07-05T08:28:38Z"},{"alias_kind":"arxiv_version","alias_value":"2402.08660v3","created_at":"2026-07-05T08:28:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2402.08660","created_at":"2026-07-05T08:28:38Z"},{"alias_kind":"pith_short_12","alias_value":"6YRZ7KBHAGWQ","created_at":"2026-07-05T08:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"6YRZ7KBHAGWQB5IZ","created_at":"2026-07-05T08:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"6YRZ7KBH","created_at":"2026-07-05T08:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:fae03726cf02b06695e71749c0351e1c053da632686c00c40cda1eeade2ac6aa","target":"graph","created_at":"2026-07-05T08:28:38Z","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/2402.08660/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We propose a solution to the \"curvature problem\" from arXiv:1505.03698 and arXiv:0905.3845 for infinitesimal deformations. Let $k$ be a field, $A$ a dg algebra over $k$ and $A_n = A[t]/(t^{n+1})$ a cdg algebra over $R_n = k[t]/(t^{n+1})$, $n \\geq 0$, with reduction $A_n/tA_n = A$. We define the $n$-derived category $D^n(A_n)$ as the quotient of the homotopy category by the modules for which all quotients appearing in the associated graded object are acyclic. We prove this to be a compactly generated triangulated category with a semiorthogonal decomposition by $n + 1$ copies of $D(A)$, in which","authors_text":"Alessandro Lehmann, Wendy Lowen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-02-13T18:42:28Z","title":"Filtered derived categories of curved deformations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.08660","kind":"arxiv","version":3},"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":"sha256:34ef52ddd6a00712b9c4b06666bfc7f7711ff7bac4e4a54b8955202d565e348f","target":"record","created_at":"2026-07-05T08:28:38Z","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":"59781c34f45988712dacd6f62744a681b48c493fb2dd5a788a19728107beb976","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.KT","submitted_at":"2024-02-13T18:42:28Z","title_canon_sha256":"6d5af517b023be894b5616e1b8393462dc2a15a00c6e584247257200c9fd3203"},"schema_version":"1.0","source":{"id":"2402.08660","kind":"arxiv","version":3}},"canonical_sha256":"f6239fa82701ad00f519ad11f3f7ee25d77919ddf5a00d5b0794a192f1affde3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6239fa82701ad00f519ad11f3f7ee25d77919ddf5a00d5b0794a192f1affde3","first_computed_at":"2026-07-05T08:28:38.058358Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:28:38.058358Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cM7Fxf4m16ekEGx+2wXmeMLuOQg7yhzvgvr7fF6ZaxdYvZkLKg7kWrixpDINl93xHqZHiu9XziMsbgjUVrpBAw==","signature_status":"signed_v1","signed_at":"2026-07-05T08:28:38.058818Z","signed_message":"canonical_sha256_bytes"},"source_id":"2402.08660","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:34ef52ddd6a00712b9c4b06666bfc7f7711ff7bac4e4a54b8955202d565e348f","sha256:fae03726cf02b06695e71749c0351e1c053da632686c00c40cda1eeade2ac6aa"],"state_sha256":"b607ea050a7d73eb6511d1de455ff458ceedff0e4077d9c773e6bc21f5f30d3a"}