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Let $G=\\operatorname{GO}_{2n}$ denote the split orthogonal similitude group over $F$. For any parahoric level structure, we prove that the associated spin local model for $G$ is a flat $\\mathcal{O}$-scheme with reduced special fiber. This confirms a conjecture of Pappas and Rapoport in the split case. As a corollary, we construct a flat (integral) moduli space of PEL-type D."},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2512.16704","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2025-12-18T16:08:21Z","cross_cats_sorted":[],"title_canon_sha256":"51eb1052c26ea82535a94c6e9f2469adc3983c0216d75e484b2e5f7c6ba51b24","abstract_canon_sha256":"60acf13c69e87fa4835d11f1a6e1cf28f405dc619a386d287074d68e79504f41"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:00.470913Z","signature_b64":"EbqcrmZI1w84eQzxePxkB1h0wS5mTqFjS6VTpmeLSNusNWd9P8g8Cwy+8JpVilNJIGlvZaVolXqPN0kluZ0pBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"36790ebb3f5acb548ba95532d1ba685f5163a7c0be15c915dbe5f06b38c14229","last_reissued_at":"2026-05-17T23:39:00.470135Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:00.470135Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the flatness of spin local models for split even orthogonal groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Spin local models for the split orthogonal similitude group GO_{2n} are flat O-schemes with reduced special fibers for any parahoric level structure.","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jie Yang","submitted_at":"2025-12-18T16:08:21Z","abstract_excerpt":"Let $F$ be a complete discretely valued field with ring of integers $\\mathcal{O}$ and residue field of characteristic $p>2$. Let $G=\\operatorname{GO}_{2n}$ denote the split orthogonal similitude group over $F$. For any parahoric level structure, we prove that the associated spin local model for $G$ is a flat $\\mathcal{O}$-scheme with reduced special fiber. This confirms a conjecture of Pappas and Rapoport in the split case. As a corollary, we construct a flat (integral) moduli space of PEL-type D."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"For any parahoric level structure, the associated spin local model for G=GO_{2n} is a flat O-scheme with reduced special fiber.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The orthogonal similitude group G is split over the complete discretely valued field F with residue characteristic p>2.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Spin local models for split GO_{2n} are flat O-schemes with reduced special fiber, confirming the Pappas-Rapoport conjecture in the split case.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Spin local models for the split orthogonal similitude group GO_{2n} are flat O-schemes with reduced special fibers for any parahoric level structure.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f8e11e3bdf12a192e469a33d63f761588de59d1eb3da1bb3aa52d9af1c2fd4c9"},"source":{"id":"2512.16704","kind":"arxiv","version":2},"verdict":{"id":"326561bc-400f-4b1d-b750-a32bb2278ab8","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-16T21:16:22.024093Z","strongest_claim":"For any parahoric level structure, the associated spin local model for G=GO_{2n} is a flat O-scheme with reduced special fiber.","one_line_summary":"Spin local models for split GO_{2n} are flat O-schemes with reduced special fiber, confirming the Pappas-Rapoport conjecture in the split case.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The orthogonal similitude group G is split over the complete discretely valued field F with residue characteristic p>2.","pith_extraction_headline":"Spin local models for the split orthogonal similitude group GO_{2n} are flat O-schemes with reduced special fibers for any parahoric level structure."},"references":{"count":23,"sample":[{"doi":"","year":2008,"title":"G. 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