{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:VG6XQB3BYEWNT6XR5EHGOVMDX3","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":"a8eb7131292a792dd0657e9e9aedc3d877d3ccc2e2e2b0bce3ab49c626bbb0b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-05-11T03:04:56Z","title_canon_sha256":"6fca430c5a20ff1d9c02930abaeb847f7e43bbaa2aa8832407c568171bb07750"},"schema_version":"1.0","source":{"id":"1805.04233","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.04233","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"arxiv_version","alias_value":"1805.04233v2","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.04233","created_at":"2026-05-18T00:05:56Z"},{"alias_kind":"pith_short_12","alias_value":"VG6XQB3BYEWN","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_16","alias_value":"VG6XQB3BYEWNT6XR","created_at":"2026-05-18T12:32:59Z"},{"alias_kind":"pith_short_8","alias_value":"VG6XQB3B","created_at":"2026-05-18T12:32:59Z"}],"graph_snapshots":[{"event_id":"sha256:5c0223a0994a492cb0492b3ff839d8c644b653a7381ef1b6c824194c271549c0","target":"graph","created_at":"2026-05-18T00:05:56Z","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":"One-dimensional formal groups over an algebraically closed field of positive characteristic are classified by their height. In the case of $K3$ surfaces, the height of their formal groups takes integer values between $1$ and $10$, or $\\infty$. For Calabi-Yau threefolds, the height is bounded by $h^{1,2}+1$ if it is finite, where $h^{1,2}$ is a Hodge number. At present, there are only a limited number of concrete examples for explicit values or the distribution of the height. In this paper, we consider Calabi-Yau threefolds arising from weighted Delsarte threefolds in positive characteristic. W","authors_text":"Yasuhiro Goto","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-05-11T03:04:56Z","title":"A Note on the Formal Groups of Weighted Delsarte Threefolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04233","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":"sha256:2c466fdbe36527d3322aa528800406b3593754d67df030e551cb2091515d7fce","target":"record","created_at":"2026-05-18T00:05:56Z","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":"a8eb7131292a792dd0657e9e9aedc3d877d3ccc2e2e2b0bce3ab49c626bbb0b5","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-sa/4.0/","primary_cat":"math.NT","submitted_at":"2018-05-11T03:04:56Z","title_canon_sha256":"6fca430c5a20ff1d9c02930abaeb847f7e43bbaa2aa8832407c568171bb07750"},"schema_version":"1.0","source":{"id":"1805.04233","kind":"arxiv","version":2}},"canonical_sha256":"a9bd780761c12cd9faf1e90e675583bedb60052262d98bd6680fac7da572dea9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9bd780761c12cd9faf1e90e675583bedb60052262d98bd6680fac7da572dea9","first_computed_at":"2026-05-18T00:05:56.097264Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:05:56.097264Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"YP8Y3Ua4hwAxGLwXEQP3ATOGRqhm5fraIXIAMrq+ndnm7WBvYIB6saJNimj+4dJW2cGhFj+HEIAvEyPm7xfiBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:05:56.097953Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.04233","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2c466fdbe36527d3322aa528800406b3593754d67df030e551cb2091515d7fce","sha256:5c0223a0994a492cb0492b3ff839d8c644b653a7381ef1b6c824194c271549c0"],"state_sha256":"04bb46fef09a7475c506970f2efac736e9c6e4797ba8cabdfe959a402a3a8295"}