{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:AXNLPCFC2JC4NDPJNSLDOBNINX","short_pith_number":"pith:AXNLPCFC","schema_version":"1.0","canonical_sha256":"05dab788a2d245c68de96c963705a86def054a97a04959c1664d4697351ac1b9","source":{"kind":"arxiv","id":"1003.2326","version":5},"attestation_state":"computed","paper":{"title":"Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Harald Grobner","submitted_at":"2010-03-11T13:01:31Z","abstract_excerpt":"In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree 1. The latter ones turn out to be CAP-representations, though $G$ satisfies Strong Multiplicity One. A non-vanishing result on intertwining operators of induced representations will serve as a starting point for further investigations concerning rationality of critical $L$-values."},"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":"1003.2326","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2010-03-11T13:01:31Z","cross_cats_sorted":[],"title_canon_sha256":"090f10732441eaad528c0986e6822a82bb0c98865aa9f1aad387abe37eb8ce88","abstract_canon_sha256":"67bb3b546998897e3eaa1d1a7b7845896b9fafcffcdf029ccdb9f93bd33fbf6f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:12:18.747099Z","signature_b64":"2Nbeti8HFOQJGUxxZDaFX97seAXQ2pUcy5cjdU8q6LH9mGvRvW+GoOhRubCtEsuaMRMUvS/tXx7uwDPqka7PAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"05dab788a2d245c68de96c963705a86def054a97a04959c1664d4697351ac1b9","last_reissued_at":"2026-05-18T04:12:18.746557Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:12:18.746557Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Automorphic Forms, Cohomology and CAP Representations. The Case $GL_2$ over a definite quaternion algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Harald Grobner","submitted_at":"2010-03-11T13:01:31Z","abstract_excerpt":"In this paper we fully describe the cuspidal and the Eisenstein cohomology of the group $G=GL_2$ over a definite quaternion algebra $D/\\Q$. Functoriality is used to show the existence of residual and cuspidal automorphic forms, having cohomology in degree 1. The latter ones turn out to be CAP-representations, though $G$ satisfies Strong Multiplicity One. A non-vanishing result on intertwining operators of induced representations will serve as a starting point for further investigations concerning rationality of critical $L$-values."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.2326","kind":"arxiv","version":5},"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":"1003.2326","created_at":"2026-05-18T04:12:18.746651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.2326v5","created_at":"2026-05-18T04:12:18.746651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.2326","created_at":"2026-05-18T04:12:18.746651+00:00"},{"alias_kind":"pith_short_12","alias_value":"AXNLPCFC2JC4","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_16","alias_value":"AXNLPCFC2JC4NDPJ","created_at":"2026-05-18T12:26:05.355336+00:00"},{"alias_kind":"pith_short_8","alias_value":"AXNLPCFC","created_at":"2026-05-18T12:26:05.355336+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/AXNLPCFC2JC4NDPJNSLDOBNINX","json":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX.json","graph_json":"https://pith.science/api/pith-number/AXNLPCFC2JC4NDPJNSLDOBNINX/graph.json","events_json":"https://pith.science/api/pith-number/AXNLPCFC2JC4NDPJNSLDOBNINX/events.json","paper":"https://pith.science/paper/AXNLPCFC"},"agent_actions":{"view_html":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX","download_json":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX.json","view_paper":"https://pith.science/paper/AXNLPCFC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.2326&json=true","fetch_graph":"https://pith.science/api/pith-number/AXNLPCFC2JC4NDPJNSLDOBNINX/graph.json","fetch_events":"https://pith.science/api/pith-number/AXNLPCFC2JC4NDPJNSLDOBNINX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX/action/storage_attestation","attest_author":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX/action/author_attestation","sign_citation":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX/action/citation_signature","submit_replication":"https://pith.science/pith/AXNLPCFC2JC4NDPJNSLDOBNINX/action/replication_record"}},"created_at":"2026-05-18T04:12:18.746651+00:00","updated_at":"2026-05-18T04:12:18.746651+00:00"}