{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:WSTSM4FRSSLQJKXSGGHHGQFM7W","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":"3459a473867143c997aa6e838e770f072e592f91393ccdae67750ac8c05ba5b0","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-11-13T13:48:56Z","title_canon_sha256":"2a22ab087aa7a3cf4b3e94257e375e830f452c9abf2732abc90fd75e1b8e8f9c"},"schema_version":"1.0","source":{"id":"2511.10312","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2511.10312","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"arxiv_version","alias_value":"2511.10312v1","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2511.10312","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"pith_short_12","alias_value":"WSTSM4FRSSLQ","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"pith_short_16","alias_value":"WSTSM4FRSSLQJKXS","created_at":"2026-06-23T03:13:51Z"},{"alias_kind":"pith_short_8","alias_value":"WSTSM4FR","created_at":"2026-06-23T03:13:51Z"}],"graph_snapshots":[{"event_id":"sha256:277a2a7c0ceefd254952768b34f476488459153bad0a67169365926a75d1bb5e","target":"graph","created_at":"2026-06-23T03:13:51Z","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/2511.10312/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We develop the deformation-obstruction calculus for morphisms of complexes with a fixed lift of the codomain, to derived categories of flat nilpotent deformations of abelian categories. As an application, we give an alternative proof that semiorthogonal decompositions deform uniquely in smooth proper families of schemes.","authors_text":"Andrea T. Ricolfi, Pieter Belmans, Shinnosuke Okawa, Wendy Lowen","cross_cats":["math.CT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-11-13T13:48:56Z","title":"Deformation theory for a morphism in the derived category with fixed lift of the codomain"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2511.10312","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":"sha256:6ebbdf09b05e8d9e02d1cdfc5ca998bf48f201057fe315e3e90c5ae42bdd7ae7","target":"record","created_at":"2026-06-23T03:13:51Z","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":"3459a473867143c997aa6e838e770f072e592f91393ccdae67750ac8c05ba5b0","cross_cats_sorted":["math.CT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-11-13T13:48:56Z","title_canon_sha256":"2a22ab087aa7a3cf4b3e94257e375e830f452c9abf2732abc90fd75e1b8e8f9c"},"schema_version":"1.0","source":{"id":"2511.10312","kind":"arxiv","version":1}},"canonical_sha256":"b4a72670b1949704aaf2318e7340acfda4a5b0ec5325fd1bb92553a2ad3de3f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4a72670b1949704aaf2318e7340acfda4a5b0ec5325fd1bb92553a2ad3de3f3","first_computed_at":"2026-06-23T03:13:51.239043Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-23T03:13:51.239043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IZwRlPyV44TuPPqDIRoPTFgFDdXvaLmxtrvorlmaII2Op0JYOL9R9XpyVbXFO60LjNXo0ybNqqQ7NWcTRO2iAg==","signature_status":"signed_v1","signed_at":"2026-06-23T03:13:51.239508Z","signed_message":"canonical_sha256_bytes"},"source_id":"2511.10312","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6ebbdf09b05e8d9e02d1cdfc5ca998bf48f201057fe315e3e90c5ae42bdd7ae7","sha256:277a2a7c0ceefd254952768b34f476488459153bad0a67169365926a75d1bb5e"],"state_sha256":"9d4e5a873bae41046de55011ae7221b9c9d7edc8e58efbe5cea957207fb798b4"}