{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FS2UEGWPS2AOETEDEUT235RI3R","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":"6e1c4c8a6238a9c14a7c70928d4ef06dc6837b0137df5c8e9da7358cef6efe9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-23T10:00:42Z","title_canon_sha256":"f4d0b1f8d16ddc22a49b9fbc237bb47c41e61dbad8d06fd413cb89a803b9fcf2"},"schema_version":"1.0","source":{"id":"1305.5366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.5366","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"arxiv_version","alias_value":"1305.5366v1","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.5366","created_at":"2026-05-18T03:25:04Z"},{"alias_kind":"pith_short_12","alias_value":"FS2UEGWPS2AO","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FS2UEGWPS2AOETED","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FS2UEGWP","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:254a569d9132ac16febfbc9e0fea93159cd20fe89f3aaaa25139c2531bb1fd0b","target":"graph","created_at":"2026-05-18T03:25:04Z","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"},"paper":{"abstract_excerpt":"A smooth family $\\varphi:\\mathcal V\\to S$ of surfaces will be called {\\em completable} if there is a logarithmic deformation $(\\bar {\\mathcal V},{\\mathcal D})$ over $S$ so that ${\\mathcal V}=\\bar{\\mathcal V}\\backslash {\\mathcal D}$. Two smooth surfaces $V$ and $V'$ are said to be deformations of each other if there is a completable flat family ${\\mathcal V}\\to S$ of smooth surfaces over a connected base so that $V$ and $V'$ are fibers over suitable points $s,s'\\in S$. This relation generates an equivalence relation called {\\em deformation equivalence}. In this paper we give a complete combinat","authors_text":"Hubert Flenner, Mikhail Zaidenberg, Shulim Kaliman","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-23T10:00:42Z","title":"Deformation equivalence of affine ruled surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.5366","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:d53c460dfa63c0e7de773072c0e6382af83a868b2f57cf525e0c3a144d925cf9","target":"record","created_at":"2026-05-18T03:25:04Z","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":"6e1c4c8a6238a9c14a7c70928d4ef06dc6837b0137df5c8e9da7358cef6efe9e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2013-05-23T10:00:42Z","title_canon_sha256":"f4d0b1f8d16ddc22a49b9fbc237bb47c41e61dbad8d06fd413cb89a803b9fcf2"},"schema_version":"1.0","source":{"id":"1305.5366","kind":"arxiv","version":1}},"canonical_sha256":"2cb5421acf9680e24c832527adf628dc4eb7ed2f34b342aede11bcc1eae6ab50","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2cb5421acf9680e24c832527adf628dc4eb7ed2f34b342aede11bcc1eae6ab50","first_computed_at":"2026-05-18T03:25:04.987985Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:25:04.987985Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"m5pNTqK4rT22jW6O2+/agJPPHY8JBWS6/NAUX9eYBfRtFBsYcjX6q2U7KOuWeh6DjnS/Kxr8SaqVQ+AjR5rmCA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:25:04.988583Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.5366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d53c460dfa63c0e7de773072c0e6382af83a868b2f57cf525e0c3a144d925cf9","sha256:254a569d9132ac16febfbc9e0fea93159cd20fe89f3aaaa25139c2531bb1fd0b"],"state_sha256":"89d50b7367b6153723ecb150dd995577c8bb8f55f9a2cbf2332d1f11e29c3aa2"}