{"paper":{"title":"Local newforms for generic representations of $p$-adic ${\\rm SO}_{2n+1}$: Reduction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Non-vanishing of newform spaces for supercuspidals implies the same for all generic representations of p-adic SO(2n+1).","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Yao Cheng","submitted_at":"2026-05-15T07:00:01Z","abstract_excerpt":"We prove that if the space of newforms is non-zero for every irreducible generic supercuspidal representation of ${\\rm SO}_{2n+1}$ then it is also non-zero for all irreducible generic representations of ${\\rm SO}_{2n+1}$."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We prove that if the space of newforms is non-zero for every irreducible generic supercuspidal representation of SO_{2n+1} then it is also non-zero for all irreducible generic representations of SO_{2n+1}.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The definitions and standard properties of newforms and generic representations for p-adic SO(2n+1) as used in the reduction steps, which are invoked to extend the supercuspidal case to the general case.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Proves that if newform spaces are non-zero for all irreducible generic supercuspidal representations of SO(2n+1), then they are non-zero for all irreducible generic representations.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Non-vanishing of newform spaces for supercuspidals implies the same for all generic representations of p-adic SO(2n+1).","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"54e117340244fa93a86fc7479576d884df57544d2ec9239bdfdc44841110a10c"},"source":{"id":"2605.15678","kind":"arxiv","version":1},"verdict":{"id":"3c0d5431-5770-4dbd-af72-dac7172cc39b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-19T19:56:46.114057Z","strongest_claim":"We prove that if the space of newforms is non-zero for every irreducible generic supercuspidal representation of SO_{2n+1} then it is also non-zero for all irreducible generic representations of SO_{2n+1}.","one_line_summary":"Proves that if newform spaces are non-zero for all irreducible generic supercuspidal representations of SO(2n+1), then they are non-zero for all irreducible generic representations.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The definitions and standard properties of newforms and generic representations for p-adic SO(2n+1) as used in the reduction steps, which are invoked to extend the supercuspidal case to the general case.","pith_extraction_headline":"Non-vanishing of newform spaces for supercuspidals implies the same for all generic representations of p-adic SO(2n+1)."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.15678/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"doi_title_agreement","ran_at":"2026-05-19T20:31:19.224386Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:10:49.232150Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:33:29.859804Z","status":"skipped","version":"1.0.0","findings_count":0},{"name":"claim_evidence","ran_at":"2026-05-19T17:21:56.055958Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"cedaae6a107f3c56d40118b00f91015ba220072335cb545c6e75e240b1029d63"},"references":{"count":51,"sample":[{"doi":"","year":2013,"title":"J. 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