{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:PF3OQESMEA4FGQP3OYUJUGEBVB","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":"86cd7ddd5333a0ac00bb195a2765ab8a5ef8200e76182775b3977890cefaabc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-09T12:10:10Z","title_canon_sha256":"f4d2cee8a160553854240e1b2e68094506ac128d6e8447d9eb76b80948dde1d2"},"schema_version":"1.0","source":{"id":"1708.02797","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1708.02797","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"arxiv_version","alias_value":"1708.02797v2","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1708.02797","created_at":"2026-05-17T23:43:56Z"},{"alias_kind":"pith_short_12","alias_value":"PF3OQESMEA4F","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"PF3OQESMEA4FGQP3","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"PF3OQESM","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:f339ee02a64efada525e8238b4d82211002b366cefb6e9aa7431c84b0c0412b4","target":"graph","created_at":"2026-05-17T23:43:56Z","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":"Given a surjective morphism $\\pi\\colon X\\to Y$ of normal varieties satisfying some regularity hypotheses we prove how to recover a Cox ring of the generic fiber of $\\pi$ from the Cox ring of $X$. As a corollary we show that in some cases it is also possible to recover the Cox ring of a very general fiber, and finally we give an application in the case of the blowing-up of a toric fiber space.","authors_text":"Antonio Laface, Luca Ugaglia","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-09T12:10:10Z","title":"Cox ring of the generic fiber"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.02797","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:bb5a42f203923dcddba928c455b734756f95ffc50c29e21267517ee420c25d48","target":"record","created_at":"2026-05-17T23:43:56Z","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":"86cd7ddd5333a0ac00bb195a2765ab8a5ef8200e76182775b3977890cefaabc5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2017-08-09T12:10:10Z","title_canon_sha256":"f4d2cee8a160553854240e1b2e68094506ac128d6e8447d9eb76b80948dde1d2"},"schema_version":"1.0","source":{"id":"1708.02797","kind":"arxiv","version":2}},"canonical_sha256":"7976e8124c20385341fb76289a1881a86ff725804fb33508cacc684d45043537","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7976e8124c20385341fb76289a1881a86ff725804fb33508cacc684d45043537","first_computed_at":"2026-05-17T23:43:56.903621Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:43:56.903621Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TN/5PdSotKGjy6RkAFDDnn7kGI1CQHoRMQCWviKuVkP/nrOQOP5VENuhsILWeMVC7Xtldz8ON5vJzKNDqN6mBw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:43:56.904305Z","signed_message":"canonical_sha256_bytes"},"source_id":"1708.02797","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb5a42f203923dcddba928c455b734756f95ffc50c29e21267517ee420c25d48","sha256:f339ee02a64efada525e8238b4d82211002b366cefb6e9aa7431c84b0c0412b4"],"state_sha256":"0310f4bc1eee16297a4b0c5793932eaac9e043725b24bd744d9613d5f9d4d9f5"}