{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:HBOG3SL3JVEXGRJTK2D4JM4CGV","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":"e12f6c87f04ef6da0cbbbe2db744071f239c1db089b0ecba448472dc4104305f","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.AG","submitted_at":"2007-05-09T06:32:58Z","title_canon_sha256":"8b66f2d78a2f14b559d4b2898505da70dc539417c89cfb653aba969ab9811880"},"schema_version":"1.0","source":{"id":"0705.1210","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0705.1210","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"arxiv_version","alias_value":"0705.1210v3","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0705.1210","created_at":"2026-05-18T04:28:30Z"},{"alias_kind":"pith_short_12","alias_value":"HBOG3SL3JVEX","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_16","alias_value":"HBOG3SL3JVEXGRJT","created_at":"2026-05-18T12:25:55Z"},{"alias_kind":"pith_short_8","alias_value":"HBOG3SL3","created_at":"2026-05-18T12:25:55Z"}],"graph_snapshots":[{"event_id":"sha256:4a7e8a06f6c351beaf34e6ebf7cdec5d00bfd8fd55bfc12c7919a6aab412d380","target":"graph","created_at":"2026-05-18T04:28:30Z","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":"We continue our study of F-thresholds begun in math/0607660 by an in depth analysis of the hypersurface case. We use the D--module theoretic description of generalized test ideals which allows us to show that in any F--finite regular ring the F-thresholds of hypersurfaces are discrete and rational (in math/0607660 the finite type over a field case was shown for arbitrary ideals). Furthermore we show that any limit of F-pure thresholds of principal ideals in bouneded dimension is again an F-pure-threshold, hence in particular the limit is rational. The study of the set of F-pure-thresholds lead","authors_text":"Karen Smith, Manuel Blickle, Mircea Musta\\c{t}\\v{a}","cross_cats":["math.AC"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2007-05-09T06:32:58Z","title":"F-thresholds of hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0705.1210","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:f12eb01cc729a9bf9fb2bef543eb822a3e4d9b9e3aa87078ef0982f873c93661","target":"record","created_at":"2026-05-18T04:28:30Z","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":"e12f6c87f04ef6da0cbbbe2db744071f239c1db089b0ecba448472dc4104305f","cross_cats_sorted":["math.AC"],"license":"","primary_cat":"math.AG","submitted_at":"2007-05-09T06:32:58Z","title_canon_sha256":"8b66f2d78a2f14b559d4b2898505da70dc539417c89cfb653aba969ab9811880"},"schema_version":"1.0","source":{"id":"0705.1210","kind":"arxiv","version":3}},"canonical_sha256":"385c6dc97b4d497345335687c4b3823551d0db312f5e1814e315315a77ba3490","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"385c6dc97b4d497345335687c4b3823551d0db312f5e1814e315315a77ba3490","first_computed_at":"2026-05-18T04:28:30.286510Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:28:30.286510Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v2i67SaQ6qEBaB7fQ/kxPoyTLlF4wsnwe1B/h0726onSVxiQcKBywhUQ/V0Z0nVqBdnP8RfTsDFL6zDntdeVCA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:28:30.286885Z","signed_message":"canonical_sha256_bytes"},"source_id":"0705.1210","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f12eb01cc729a9bf9fb2bef543eb822a3e4d9b9e3aa87078ef0982f873c93661","sha256:4a7e8a06f6c351beaf34e6ebf7cdec5d00bfd8fd55bfc12c7919a6aab412d380"],"state_sha256":"e1b3465cc14947934d371c0f6f645eaa23282748f3056e82f866b54dc6804773"}