{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:VMQU7ZP5QDB5POO4IRO27R7DWJ","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":"309de35f3f279d3dcd5514aeb3ce032763b5e35202300ab2bfa75277b7304d50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-04-27T01:49:28Z","title_canon_sha256":"2018c2fc6a62384b88e3209c395760bdcd30de9a6554cce728f3202698cd6338"},"schema_version":"1.0","source":{"id":"2606.18253","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.18253","created_at":"2026-06-19T16:10:56Z"},{"alias_kind":"arxiv_version","alias_value":"2606.18253v1","created_at":"2026-06-19T16:10:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.18253","created_at":"2026-06-19T16:10:56Z"},{"alias_kind":"pith_short_12","alias_value":"VMQU7ZP5QDB5","created_at":"2026-06-19T16:10:56Z"},{"alias_kind":"pith_short_16","alias_value":"VMQU7ZP5QDB5POO4","created_at":"2026-06-19T16:10:56Z"},{"alias_kind":"pith_short_8","alias_value":"VMQU7ZP5","created_at":"2026-06-19T16:10:56Z"}],"graph_snapshots":[{"event_id":"sha256:dfdb9b458ed773eaf310822f161c56f1b9e98fadcd593d452bfd01b2f1eee00d","target":"graph","created_at":"2026-06-19T16:10:56Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2606.18253/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Huybrechts proved the finiteness of constant cycle curves of fixed order in any linear system $|L|$ on a K3 surface. In this paper, we study constant cycle surfaces on the Fano variety of lines $F(X)$ of a smooth cubic fourfold $X$. Fano surfaces $F(Y) \\subset F(X)$ of hyperplane sections $Y \\subset X$ are higher-dimensional analogues of curves on K3 surfaces. We prove that there are at most finitely many constant cycle surfaces of the form $F(Y)$ of any fixed order on $F(X)$.","authors_text":"Jiexiang Huang","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-04-27T01:49:28Z","title":"Constant cycle surfaces on Fano varieties of cubic fourfolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18253","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":"sha256:20fdcc12c257ba93cb8f84cc97b4ae1a3c6f0686672c7bd8966f9456fe654621","target":"record","created_at":"2026-06-19T16:10:56Z","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":"309de35f3f279d3dcd5514aeb3ce032763b5e35202300ab2bfa75277b7304d50","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-04-27T01:49:28Z","title_canon_sha256":"2018c2fc6a62384b88e3209c395760bdcd30de9a6554cce728f3202698cd6338"},"schema_version":"1.0","source":{"id":"2606.18253","kind":"arxiv","version":1}},"canonical_sha256":"ab214fe5fd80c3d7b9dc445dafc7e3b278c81e2811ac96a359ed399ece778330","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ab214fe5fd80c3d7b9dc445dafc7e3b278c81e2811ac96a359ed399ece778330","first_computed_at":"2026-06-19T16:10:56.149623Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-19T16:10:56.149623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"f6PUnDjjPHLblxXb+wPTlOiDa6Guudx9CrfM5NaYyAIQ69yxSW9O+TtA0qQG/2RJpZRCrKaNnseSxlnoSKV+Aw==","signature_status":"signed_v1","signed_at":"2026-06-19T16:10:56.149963Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.18253","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:20fdcc12c257ba93cb8f84cc97b4ae1a3c6f0686672c7bd8966f9456fe654621","sha256:dfdb9b458ed773eaf310822f161c56f1b9e98fadcd593d452bfd01b2f1eee00d"],"state_sha256":"465b2b2bf9c86eae69d471bcd9a3cb7e8d5e64b05d769fe341d180c55c5d4b9d"}