{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:NRIVSQA2PUMX6F5J4NTW2A7JGG","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":"0ce9e6b3cfbbca951d159781ce8836f3a808116ecca4bfd9400a222333d9e76d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T12:02:33Z","title_canon_sha256":"ac45de047c8168429628bac3dbe4b7d97b9a38138e3b91b583d64e63beb70804"},"schema_version":"1.0","source":{"id":"2605.22371","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.22371","created_at":"2026-05-22T01:04:40Z"},{"alias_kind":"arxiv_version","alias_value":"2605.22371v1","created_at":"2026-05-22T01:04:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.22371","created_at":"2026-05-22T01:04:40Z"},{"alias_kind":"pith_short_12","alias_value":"NRIVSQA2PUMX","created_at":"2026-05-22T01:04:40Z"},{"alias_kind":"pith_short_16","alias_value":"NRIVSQA2PUMX6F5J","created_at":"2026-05-22T01:04:40Z"},{"alias_kind":"pith_short_8","alias_value":"NRIVSQA2","created_at":"2026-05-22T01:04:40Z"}],"graph_snapshots":[{"event_id":"sha256:d3cf1604e2b58fe22bfac324b7ab8ec8b80b135a82d06d0b4a83554a01543007","target":"graph","created_at":"2026-05-22T01:04:40Z","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/2605.22371/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $k$ be a positive integer and let $X_k$ be the cubic hypersurface defined by the equation $x^3-(y_1^2+\\cdots+y_{4k}^2)z=0$. In this paper, we give an asymptotic formula for the counting function of semi-integral points on $X_k$. We also prove that this asymptotic formula agrees with Manin's conjecture for $\\mathcal{M}$-points \\cite[Conjecture~1.4]{Moe26a} on the $a$-invariant and the $b$-invariant.","authors_text":"Haruki Ito","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T12:02:33Z","title":"The distribution of semi-integral points on a class of singular cubic hypersurfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22371","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":"sha256:7d6c308211865b52305fddfa9ec928eef9898b2cdc4c51e90c00f43ffae3b290","target":"record","created_at":"2026-05-22T01:04:40Z","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":"0ce9e6b3cfbbca951d159781ce8836f3a808116ecca4bfd9400a222333d9e76d","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T12:02:33Z","title_canon_sha256":"ac45de047c8168429628bac3dbe4b7d97b9a38138e3b91b583d64e63beb70804"},"schema_version":"1.0","source":{"id":"2605.22371","kind":"arxiv","version":1}},"canonical_sha256":"6c5159401a7d197f17a9e3676d03e9319cb5c404a8723d5841e4cb1a7b5cd3fe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6c5159401a7d197f17a9e3676d03e9319cb5c404a8723d5841e4cb1a7b5cd3fe","first_computed_at":"2026-05-22T01:04:40.352549Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-22T01:04:40.352549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fUjcnLi0UWHKWx00C7w5RFnlhHMx5Dp+/M9Y2T1az4aTrJHDg4jVviGZBKZOVF2mR/EPwpg6pfeR3zCJR7mICw==","signature_status":"signed_v1","signed_at":"2026-05-22T01:04:40.353365Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.22371","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7d6c308211865b52305fddfa9ec928eef9898b2cdc4c51e90c00f43ffae3b290","sha256:d3cf1604e2b58fe22bfac324b7ab8ec8b80b135a82d06d0b4a83554a01543007"],"state_sha256":"62f9c7e671d5755ec962136c73cf0aa0b6c4229acf16d2f7e92fa667e8ab5b0e"}