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For F=Q this gives rise to dimension formulas regarding certain subspaces of the inner cohomology of the genus two Shimura variety corresponding to the principal congruence subgroup level N=2. We prove the conjectures made by Bergstr\\\"om, Faber and van der Geer in a recent paper."},"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":"1310.2552","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2013-10-09T17:29:07Z","cross_cats_sorted":[],"title_canon_sha256":"ad0bc79a3acab250ec48eab3b262cd906b239762cbbc5bbb5b81f4c6cfe1326e","abstract_canon_sha256":"a8dd8b6838d750a0bda272d47330c87292094e28b325f091f4bafdc0e91f9a20"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:56.081479Z","signature_b64":"lHgxmdCRjvowEBscyQA3ZbF7uLUonyLWyvK9qZbk8dDBw9bmfENN4oi+NvM0tN7d63VKapeJh0aNTMkL3Ex8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a548e8d14d3b81810882dcdc73c7cb528b14261fa87075491a94a0e079e1e3e","last_reissued_at":"2026-05-18T02:54:56.080987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:56.080987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Invariant Vectors for Weak Endoscopic and Saito-Kurokawa Lifts to GSp(4)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Mirko R\\\"osner","submitted_at":"2013-10-09T17:29:07Z","abstract_excerpt":"Let A be the adele ring over a totally real number field F. 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