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As an application, we give a complete description of the fibers of the face map $|\\Delta|^f$ defined by Pappas-Rapoport and prove that the face map is surjective."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"As an application, we give a complete description of the fibers of the face map |Δ|^f defined by Pappas-Rapoport and prove that the face map is surjective.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The subsets Adm(μ)_F associated to each face F of the coweight polytope P_μ are well-defined, disjoint or overlapping in a controlled way, and their union exhausts Adm(μ) to form a decomposition.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper introduces a face decomposition of the μ-admissible set and proves surjectivity of the Pappas-Rapoport face map |Δ|^f with a complete description of its fibers.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The mu-admissible set decomposes into faces indexed by those of the coweight polytope, proving the face map is surjective.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f307dfeb37f6df56d9ee58800844a0048b5187ad0d579e94e1b72c748b5ac0c2"},"source":{"id":"2605.15657","kind":"arxiv","version":1},"verdict":{"id":"c8f3b5c9-d090-4166-b347-f4d209cf69e4","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T22:10:50.177651Z","strongest_claim":"As an application, we give a complete description of the fibers of the face map |Δ|^f defined by Pappas-Rapoport and prove that the face map is surjective.","one_line_summary":"The paper introduces a face decomposition of the μ-admissible set and proves surjectivity of the Pappas-Rapoport face map |Δ|^f with a complete description of its fibers.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The subsets Adm(μ)_F associated to each face F of the coweight polytope P_μ are well-defined, disjoint or overlapping in a controlled way, and their union exhausts Adm(μ) to form a decomposition.","pith_extraction_headline":"The mu-admissible set decomposes into faces indexed by those of the coweight polytope, proving the face map is surjective."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15657/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T22:31:19.661952Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T22:21:50.303600Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:35.313235Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:56.078942Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"6b8f38328c96be9710ab53b8d284588125ccc7faa79a5638254153aee60b074f"},"references":{"count":21,"sample":[{"doi":"","year":2022,"title":"J. 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