{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:NRIVSQA2PUMX6F5J4NTW2A7JGG","short_pith_number":"pith:NRIVSQA2","canonical_record":{"source":{"id":"2605.22371","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T12:02:33Z","cross_cats_sorted":[],"title_canon_sha256":"ac45de047c8168429628bac3dbe4b7d97b9a38138e3b91b583d64e63beb70804","abstract_canon_sha256":"0ce9e6b3cfbbca951d159781ce8836f3a808116ecca4bfd9400a222333d9e76d"},"schema_version":"1.0"},"canonical_sha256":"6c5159401a7d197f17a9e3676d03e9319cb5c404a8723d5841e4cb1a7b5cd3fe","source":{"kind":"arxiv","id":"2605.22371","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:NRIVSQA2PUMX6F5J4NTW2A7JGG","target":"record","payload":{"canonical_record":{"source":{"id":"2605.22371","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","primary_cat":"math.NT","submitted_at":"2026-05-21T12:02:33Z","cross_cats_sorted":[],"title_canon_sha256":"ac45de047c8168429628bac3dbe4b7d97b9a38138e3b91b583d64e63beb70804","abstract_canon_sha256":"0ce9e6b3cfbbca951d159781ce8836f3a808116ecca4bfd9400a222333d9e76d"},"schema_version":"1.0"},"canonical_sha256":"6c5159401a7d197f17a9e3676d03e9319cb5c404a8723d5841e4cb1a7b5cd3fe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-22T01:04:40.353365Z","signature_b64":"fUjcnLi0UWHKWx00C7w5RFnlhHMx5Dp+/M9Y2T1az4aTrJHDg4jVviGZBKZOVF2mR/EPwpg6pfeR3zCJR7mICw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6c5159401a7d197f17a9e3676d03e9319cb5c404a8723d5841e4cb1a7b5cd3fe","last_reissued_at":"2026-05-22T01:04:40.352549Z","signature_status":"signed_v1","first_computed_at":"2026-05-22T01:04:40.352549Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2605.22371","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"w3m6FXeIGQ5gNWCUaIpwhco/6at1hMGtg9ai2bYfoVRxKZB33jrQI5PIXe0lZRbTAeO8e4NTkiU8jsVpF+4FBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:35:45.547503Z"},"content_sha256":"7d6c308211865b52305fddfa9ec928eef9898b2cdc4c51e90c00f43ffae3b290","schema_version":"1.0","event_id":"sha256:7d6c308211865b52305fddfa9ec928eef9898b2cdc4c51e90c00f43ffae3b290"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:NRIVSQA2PUMX6F5J4NTW2A7JGG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The distribution of semi-integral points on a class of singular cubic hypersurfaces","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Haruki Ito","submitted_at":"2026-05-21T12:02:33Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.22371","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.22371/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-22T01:04:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"788o3yPv0xBUxdjPrU3M8i6An7qJ4SQvFfYeblVqImDEHRXc0K6FJ5bZj7WS6C7m8/EJSzzq76Cvcyh0eeJZBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T13:35:45.548302Z"},"content_sha256":"d3cf1604e2b58fe22bfac324b7ab8ec8b80b135a82d06d0b4a83554a01543007","schema_version":"1.0","event_id":"sha256:d3cf1604e2b58fe22bfac324b7ab8ec8b80b135a82d06d0b4a83554a01543007"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NRIVSQA2PUMX6F5J4NTW2A7JGG/bundle.json","state_url":"https://pith.science/pith/NRIVSQA2PUMX6F5J4NTW2A7JGG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NRIVSQA2PUMX6F5J4NTW2A7JGG/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-10T13:35:45Z","links":{"resolver":"https://pith.science/pith/NRIVSQA2PUMX6F5J4NTW2A7JGG","bundle":"https://pith.science/pith/NRIVSQA2PUMX6F5J4NTW2A7JGG/bundle.json","state":"https://pith.science/pith/NRIVSQA2PUMX6F5J4NTW2A7JGG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NRIVSQA2PUMX6F5J4NTW2A7JGG/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"irCQRRdz31htrY7jvoAx+MtjolQJj/aF4FgnnZB2wM4hAbTE0Za5y5yMmQ3UjElUgZyhr9cSEiX2DU3THOgCCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T13:35:45.552478Z","bundle_sha256":"8b24c8a7ecbb3009ae2dfbff046d10625201c17e95aa2f29c86b7bda6057b285"}}