{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:GIQW4QZZIXRWRDMNYR3EKTUJJW","short_pith_number":"pith:GIQW4QZZ","schema_version":"1.0","canonical_sha256":"32216e433945e3688d8dc476454e894d8a22e140cbee3946db34c82fd317d0df","source":{"kind":"arxiv","id":"2606.31395","version":1},"attestation_state":"computed","paper":{"title":"Holomorphic differential forms on some orthogonal modular varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shouhei Ma, Shuji Horinaga","submitted_at":"2026-06-30T09:24:04Z","abstract_excerpt":"We construct holomorphic differential forms of many degrees, including the minimum possible one, on the modular varieties associated to the even lattices of signature $(2, n)$ with $n\\equiv 1, 3$ mod $8$ and discriminant $-2$ in the range $n\\geq 25$. This is the first example of holomorphic differential forms of non-top degree on orthogonal modular varieties. The proof uses the Arthur multiplicity formula in the theory of automorphic representations."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2606.31395","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2026-06-30T09:24:04Z","cross_cats_sorted":[],"title_canon_sha256":"91b375b6d9b117964fe8f8095f5e79d300ee1d7fb30d256893da4ab7efc3ec0b","abstract_canon_sha256":"1cd28ecd008e25068a5d3aa9fb026e24ab35cf0f9f68ba4bb03d3c73f7d9f83b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-01T01:18:01.798351Z","signature_b64":"UeiDRnzKCnrQ+hTGkiYwNl+pZ+wPGmbL5YkBS2esH2R4iOHH5yXRHD6vlhojEPlp30QOwywEPWarAmKm4Q7dCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32216e433945e3688d8dc476454e894d8a22e140cbee3946db34c82fd317d0df","last_reissued_at":"2026-07-01T01:18:01.797855Z","signature_status":"signed_v1","first_computed_at":"2026-07-01T01:18:01.797855Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Holomorphic differential forms on some orthogonal modular varieties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Shouhei Ma, Shuji Horinaga","submitted_at":"2026-06-30T09:24:04Z","abstract_excerpt":"We construct holomorphic differential forms of many degrees, including the minimum possible one, on the modular varieties associated to the even lattices of signature $(2, n)$ with $n\\equiv 1, 3$ mod $8$ and discriminant $-2$ in the range $n\\geq 25$. This is the first example of holomorphic differential forms of non-top degree on orthogonal modular varieties. The proof uses the Arthur multiplicity formula in the theory of automorphic representations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31395","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/2606.31395/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"},"aliases":[{"alias_kind":"arxiv","alias_value":"2606.31395","created_at":"2026-07-01T01:18:01.797933+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.31395v1","created_at":"2026-07-01T01:18:01.797933+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.31395","created_at":"2026-07-01T01:18:01.797933+00:00"},{"alias_kind":"pith_short_12","alias_value":"GIQW4QZZIXRW","created_at":"2026-07-01T01:18:01.797933+00:00"},{"alias_kind":"pith_short_16","alias_value":"GIQW4QZZIXRWRDMN","created_at":"2026-07-01T01:18:01.797933+00:00"},{"alias_kind":"pith_short_8","alias_value":"GIQW4QZZ","created_at":"2026-07-01T01:18:01.797933+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW","json":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW.json","graph_json":"https://pith.science/api/pith-number/GIQW4QZZIXRWRDMNYR3EKTUJJW/graph.json","events_json":"https://pith.science/api/pith-number/GIQW4QZZIXRWRDMNYR3EKTUJJW/events.json","paper":"https://pith.science/paper/GIQW4QZZ"},"agent_actions":{"view_html":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW","download_json":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW.json","view_paper":"https://pith.science/paper/GIQW4QZZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.31395&json=true","fetch_graph":"https://pith.science/api/pith-number/GIQW4QZZIXRWRDMNYR3EKTUJJW/graph.json","fetch_events":"https://pith.science/api/pith-number/GIQW4QZZIXRWRDMNYR3EKTUJJW/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW/action/storage_attestation","attest_author":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW/action/author_attestation","sign_citation":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW/action/citation_signature","submit_replication":"https://pith.science/pith/GIQW4QZZIXRWRDMNYR3EKTUJJW/action/replication_record"}},"created_at":"2026-07-01T01:18:01.797933+00:00","updated_at":"2026-07-01T01:18:01.797933+00:00"}