{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:TD2WYWJWSZKV72RDQX7Z4RBXS7","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":"aa13fd36bad040c5b104c308d51373ca3b5f529dc941e156116c1b3e5d351cf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-23T03:33:26Z","title_canon_sha256":"a3d555246182eaa6f9a94a6e22dcf75f492290c078d174b01131cc2854aaf075"},"schema_version":"1.0","source":{"id":"2606.24103","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2606.24103","created_at":"2026-06-24T01:14:41Z"},{"alias_kind":"arxiv_version","alias_value":"2606.24103v1","created_at":"2026-06-24T01:14:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.24103","created_at":"2026-06-24T01:14:41Z"},{"alias_kind":"pith_short_12","alias_value":"TD2WYWJWSZKV","created_at":"2026-06-24T01:14:41Z"},{"alias_kind":"pith_short_16","alias_value":"TD2WYWJWSZKV72RD","created_at":"2026-06-24T01:14:41Z"},{"alias_kind":"pith_short_8","alias_value":"TD2WYWJW","created_at":"2026-06-24T01:14:41Z"}],"graph_snapshots":[{"event_id":"sha256:5b58157acee3151400d8cfcc0c259e545b69148444a4233dd64d5be8b9e1d459","target":"graph","created_at":"2026-06-24T01:14:41Z","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/2606.24103/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $f: X \\to X$ be a polarized endomorphism of a smooth projective surface which is birationally ruled. We answer a question of Koll\\'ar and Zhuang, in the affirmative, on the incompressibility of $f$, under the assumption that $f$ is Galois and an explicit lower bound of deg$(f)$ depending only on $X$. We also give examples showing the optimality of such a lower bound.","authors_text":"De-Qi Zhang, Qianli Fang, Yujie Luo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-23T03:33:26Z","title":"Essential dimensions of polarized endomorphisms of certain algebraic surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.24103","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":"sha256:6cdce1c38684553a402da678124942bfd20840326a2d25b0a0510e29d557baff","target":"record","created_at":"2026-06-24T01:14:41Z","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":"aa13fd36bad040c5b104c308d51373ca3b5f529dc941e156116c1b3e5d351cf6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-23T03:33:26Z","title_canon_sha256":"a3d555246182eaa6f9a94a6e22dcf75f492290c078d174b01131cc2854aaf075"},"schema_version":"1.0","source":{"id":"2606.24103","kind":"arxiv","version":1}},"canonical_sha256":"98f56c593696555fea2385ff9e443797f1fcbe31a407fb9a81feab41f136179c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"98f56c593696555fea2385ff9e443797f1fcbe31a407fb9a81feab41f136179c","first_computed_at":"2026-06-24T01:14:41.158304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-24T01:14:41.158304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mugYpJhe0BnOSvGwZD5VgDauqA7WrSx5CEM4W7NSXjSUWPNjge+J8CkelfDLjYgNl3VRYUXSaWMkFJKu/QRiBg==","signature_status":"signed_v1","signed_at":"2026-06-24T01:14:41.158715Z","signed_message":"canonical_sha256_bytes"},"source_id":"2606.24103","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6cdce1c38684553a402da678124942bfd20840326a2d25b0a0510e29d557baff","sha256:5b58157acee3151400d8cfcc0c259e545b69148444a4233dd64d5be8b9e1d459"],"state_sha256":"c1fe6e0812af21cf7a3c3e9a5bc601174d14609e6d573c7bd528ff703b20a050"}