{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:Z7MDY2LVYVTZYQZ2HEELCTDXFR","short_pith_number":"pith:Z7MDY2LV","schema_version":"1.0","canonical_sha256":"cfd83c6975c5679c433a3908b14c772c513ea8dcc83eb224fd492a82bc465785","source":{"kind":"arxiv","id":"1612.08725","version":2},"attestation_state":"computed","paper":{"title":"Minimal weights of Hilbert modular forms in characteristic p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fred Diamond, Payman Kassaei","submitted_at":"2016-12-27T20:22:08Z","abstract_excerpt":"We consider mod p Hilbert modular forms associated to a totally real field of degree d in which p is unramified. We prove that every such form arises by multiplication by partial Hasse invariants from one whose weight (a d-tuple of integers) lies in a certain cone contained in the set of non-negative weights, answering a question of Andreatta and Goren. The proof is based on properties of the Goren-Oort stratification on mod p Hilbert modular varieties established by Goren and Oort, and Tian and Xiao."},"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":"1612.08725","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2016-12-27T20:22:08Z","cross_cats_sorted":[],"title_canon_sha256":"64ef8a70d6f303b372611e551c11a17ce468b6240ac88d9aeceb4ac8ef0e3ce1","abstract_canon_sha256":"9c48c85827c1936aedb13f048ce3c438d958d1cde6c9e8ad0145e7b22d2f6302"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:12.901475Z","signature_b64":"pZ06u6vanFNJBFafqCjk/C8tNxP+VaXvnObpt19LsJnpJl3x3z53MBQoE6DfDvZAX7YTtceNyU/1MxqvD33WAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfd83c6975c5679c433a3908b14c772c513ea8dcc83eb224fd492a82bc465785","last_reissued_at":"2026-05-17T23:53:12.900710Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:12.900710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal weights of Hilbert modular forms in characteristic p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Fred Diamond, Payman Kassaei","submitted_at":"2016-12-27T20:22:08Z","abstract_excerpt":"We consider mod p Hilbert modular forms associated to a totally real field of degree d in which p is unramified. We prove that every such form arises by multiplication by partial Hasse invariants from one whose weight (a d-tuple of integers) lies in a certain cone contained in the set of non-negative weights, answering a question of Andreatta and Goren. The proof is based on properties of the Goren-Oort stratification on mod p Hilbert modular varieties established by Goren and Oort, and Tian and Xiao."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.08725","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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":"1612.08725","created_at":"2026-05-17T23:53:12.900816+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.08725v2","created_at":"2026-05-17T23:53:12.900816+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.08725","created_at":"2026-05-17T23:53:12.900816+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z7MDY2LVYVTZ","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z7MDY2LVYVTZYQZ2","created_at":"2026-05-18T12:30:53.716459+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z7MDY2LV","created_at":"2026-05-18T12:30:53.716459+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/Z7MDY2LVYVTZYQZ2HEELCTDXFR","json":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR.json","graph_json":"https://pith.science/api/pith-number/Z7MDY2LVYVTZYQZ2HEELCTDXFR/graph.json","events_json":"https://pith.science/api/pith-number/Z7MDY2LVYVTZYQZ2HEELCTDXFR/events.json","paper":"https://pith.science/paper/Z7MDY2LV"},"agent_actions":{"view_html":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR","download_json":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR.json","view_paper":"https://pith.science/paper/Z7MDY2LV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.08725&json=true","fetch_graph":"https://pith.science/api/pith-number/Z7MDY2LVYVTZYQZ2HEELCTDXFR/graph.json","fetch_events":"https://pith.science/api/pith-number/Z7MDY2LVYVTZYQZ2HEELCTDXFR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR/action/storage_attestation","attest_author":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR/action/author_attestation","sign_citation":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR/action/citation_signature","submit_replication":"https://pith.science/pith/Z7MDY2LVYVTZYQZ2HEELCTDXFR/action/replication_record"}},"created_at":"2026-05-17T23:53:12.900816+00:00","updated_at":"2026-05-17T23:53:12.900816+00:00"}