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Moreover, we study relations between quasiregular mappings, averaged derivatives, BMO spaces and Carleson measures on B^n and the role of the multiplicity of a map.","weakest_assumption":"The quasiregular mappings satisfy the appropriate growth and multiplicity conditions required for the Harnack estimates and characterizations to hold."}},"verdict_id":"b920cced-e882-43c0-b5fe-7c4056b2c1c2"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:7bc0022c0b975579fd0db71089c154796ab7b483bcd0b0b2f37345ec8c1ab8ed","target":"record","created_at":"2026-05-18T02:44:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f681f85d1048ab5fca614480f2ef04599b460ca359a9d633daaa98adf5e93f9c","cross_cats_sorted":["math.FA"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CV","submitted_at":"2026-05-13T15:14:49Z","title_canon_sha256":"ff49800bebcdb3f1ca5be97efa1c8addd2b554b612b9c2f46d51965c9c4792cd"},"schema_version":"1.0","source":{"id":"2605.13655","kind":"arxiv","version":1}},"canonical_sha256":"e91b64609562427c293d1054e9ed0fe8d286c9ab3dd5490881b0ab1eb64ec576","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e91b64609562427c293d1054e9ed0fe8d286c9ab3dd5490881b0ab1eb64ec576","first_computed_at":"2026-05-18T02:44:17.399628Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:17.399628Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RGK0v7re1g1pYkAr9756/EiCbzcJn4cLxdbMPA/8GQMaD2QOYJtgkWcfNR9jfNP1FPoRBbnJwUvJNGwVRIr8Cw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:17.400127Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.13655","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7bc0022c0b975579fd0db71089c154796ab7b483bcd0b0b2f37345ec8c1ab8ed","sha256:a9f3813e8472e58ab7576e2a0725b5874d2d6bb1eb5a6dcd847f3b359ef510a3"],"state_sha256":"c2c185439033a57fbeae05038f8507fdf7b390905851744479775d2d401c81be"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Q30uIIsn4yqbLeRRF9Lny/YzBMDKVAKPx+zNclcR1sEPaXEQWsMMWdPXZMZA85hnotW0AuJH/ODT1P+9kqZXAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T22:57:26.272557Z","bundle_sha256":"e00a502f9a957feb8a77ab2cda6357807b23303fd1c79de8ad7851b9739aff31"}}