{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2025:Q36C7HNGX4F4G4NIIHI3HIOI5A","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":"bef0b49868bd2830dedb6983aebf43f8bc19281e86f43c29c45c333ffd72b72b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-09-08T15:54:46Z","title_canon_sha256":"70b907673f153980add3feae7a9aacd1a79ec42f4cfdac6c8bbd12b083447138"},"schema_version":"1.0","source":{"id":"2509.06817","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2509.06817","created_at":"2026-07-05T12:06:53Z"},{"alias_kind":"arxiv_version","alias_value":"2509.06817v1","created_at":"2026-07-05T12:06:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2509.06817","created_at":"2026-07-05T12:06:53Z"},{"alias_kind":"pith_short_12","alias_value":"Q36C7HNGX4F4","created_at":"2026-07-05T12:06:53Z"},{"alias_kind":"pith_short_16","alias_value":"Q36C7HNGX4F4G4NI","created_at":"2026-07-05T12:06:53Z"},{"alias_kind":"pith_short_8","alias_value":"Q36C7HNG","created_at":"2026-07-05T12:06:53Z"}],"graph_snapshots":[{"event_id":"sha256:5e31d04e7dfcbfec43aee00981522ab5cb840b867a3bb79b908544f08720bb34","target":"graph","created_at":"2026-07-05T12:06:53Z","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/2509.06817/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"A well known conjecture asserts that a cubic fourfold X is rational if it has a cohomologically associated K3 surface. G.Ouchi proved that if X admits a finite group G of symplectic automorphisms, whose order is different from 2, then X has an associated K3 surface S in the derived sense.This is equivalent to have a cohomologically associated K3 surface and therefore X is conjecturally rational. In this note we prove that cubic fourfolds with a cyclic group of symplectic automorphisms whose order is not a power of 2, are rational and belong to the Hassett divisor C_d, with d = 14, 42. We also ","authors_text":"Claudio Pedrini","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-09-08T15:54:46Z","title":"Rational cubic fourfolds with a symplectic group of automorphisms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.06817","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":"sha256:9b701c5496df1aed5a72f4a529dd9ec1b7ba1df14e1f009300ee0d6e9d56a070","target":"record","created_at":"2026-07-05T12:06:53Z","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":"bef0b49868bd2830dedb6983aebf43f8bc19281e86f43c29c45c333ffd72b72b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2025-09-08T15:54:46Z","title_canon_sha256":"70b907673f153980add3feae7a9aacd1a79ec42f4cfdac6c8bbd12b083447138"},"schema_version":"1.0","source":{"id":"2509.06817","kind":"arxiv","version":1}},"canonical_sha256":"86fc2f9da6bf0bc371a841d1b3a1c8e81520087ae833d04bf01504d8810e9524","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86fc2f9da6bf0bc371a841d1b3a1c8e81520087ae833d04bf01504d8810e9524","first_computed_at":"2026-07-05T12:06:53.453835Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T12:06:53.453835Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CQyhSeY+R9zzMMpBN1M8I3IxMyMEQ6RKgK1LYujCTXtz0S7l6nJWEvvfJrca3VD0C1Mq46Vx8TxqX70HaBONAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T12:06:53.454436Z","signed_message":"canonical_sha256_bytes"},"source_id":"2509.06817","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9b701c5496df1aed5a72f4a529dd9ec1b7ba1df14e1f009300ee0d6e9d56a070","sha256:5e31d04e7dfcbfec43aee00981522ab5cb840b867a3bb79b908544f08720bb34"],"state_sha256":"133c97e9d307aebe3e7ae6febaed3a12f5d2bc1a03f86fb9e4dd6284d88e4676"}