{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:6HHTDH4C4MDU5R2ZDGKDLWOTNZ","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":"085143392c595b9f6245b810423dbeed895df1d819ea48702a35a4deaa3b9677","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-11T12:31:29Z","title_canon_sha256":"bc93678a48dc3c76f91dc04422c06fd3401105ece834bbcc2b603b94f87c6115"},"schema_version":"1.0","source":{"id":"1004.1803","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1004.1803","created_at":"2026-05-18T04:26:43Z"},{"alias_kind":"arxiv_version","alias_value":"1004.1803v2","created_at":"2026-05-18T04:26:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1004.1803","created_at":"2026-05-18T04:26:43Z"},{"alias_kind":"pith_short_12","alias_value":"6HHTDH4C4MDU","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"6HHTDH4C4MDU5R2Z","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"6HHTDH4C","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:2af8d20a2d8a24a9ad031dcd6d4013026d10cec8770ac0e7c4c09dfa3c6d1efa","target":"graph","created_at":"2026-05-18T04:26:43Z","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":"The problem of resolution of singularities in positive characteristic can be reformulated as follows: Fix a hypersurface $X$, embedded in a smooth scheme, with points of multiplicity at most $n$. Let an $n$-sequence of transformations of $X$ be a finite composition of monoidal transformations with centers included in the $n$-fold points of $X$, and of its successive strict transforms. The open problem (in positive characteristic) is to prove that there is an $n$-sequence such that the final strict transform of $X$ has no points of multiplicity $n$ (no $n$-fold points).\n  In characteristic zero","authors_text":"Ang\\'elica Benito, Orlando E. Villamayor","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-11T12:31:29Z","title":"Monoidal transforms and invariants of singularities in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.1803","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":"sha256:46a40780b6098b60b76b441e78c1d3e4a035e0c381760ad5b5a255f3a1193cf3","target":"record","created_at":"2026-05-18T04:26:43Z","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":"085143392c595b9f6245b810423dbeed895df1d819ea48702a35a4deaa3b9677","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2010-04-11T12:31:29Z","title_canon_sha256":"bc93678a48dc3c76f91dc04422c06fd3401105ece834bbcc2b603b94f87c6115"},"schema_version":"1.0","source":{"id":"1004.1803","kind":"arxiv","version":2}},"canonical_sha256":"f1cf319f82e3074ec759199435d9d36e5d16dfad63e08b19ad84e518139e61d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f1cf319f82e3074ec759199435d9d36e5d16dfad63e08b19ad84e518139e61d7","first_computed_at":"2026-05-18T04:26:43.641002Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:26:43.641002Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YeSBhLh3as7q3jd3Xp0x4rdHZqxonnaFRXloNPROHqQePTZ7C6Iqo0oNMqhdDdgMxQlkUQ9Eh5JpiLO+VMR6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:26:43.641823Z","signed_message":"canonical_sha256_bytes"},"source_id":"1004.1803","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:46a40780b6098b60b76b441e78c1d3e4a035e0c381760ad5b5a255f3a1193cf3","sha256:2af8d20a2d8a24a9ad031dcd6d4013026d10cec8770ac0e7c4c09dfa3c6d1efa"],"state_sha256":"c7acef103c2b0f2adf4d0273541de731a1429b1af2488053d050a1b46c5ccb59"}