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For every $\\la=(t_1,O_1,\\ppp,t_n,O_n)\\in\\Lambda$ and every $x=(x^1,\\ppp,x^n)\\in\\R^{m_1}\\times\\ppp\\times\\R^{m_n}$ we define $\\pi_\\la(x)=\\pi(t_1O_1x^1,\\ppp,t_nO_nx^n)$. Suppose that $\\pi$ is surjective and set $$\\mathfrak{m}:=\\min\\set{\\sum_{i\\in I}\\dim_H(K_i) + \\dim\\pi(\\bigoplus_{i\\in I^c}\\R^{m_i}), I\\subset\\set{1,\\ppp,n}, I\\ne\\emptyset}.$$ Then","authors_text":"Carlos Gustavo Moreira, Jorge Erick L\\'opez Vel\\'azquez","cross_cats":["math.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-28T19:42:26Z","title":"A variant of Marstrand's theorem for projections of cartesian products"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5776","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:c6025d197f847b145616ebbeaa29d2af266642144017ac33de685770425b2c37","target":"record","created_at":"2026-05-18T04:19:11Z","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":"e6b8e462131bf2c266fb52eaebfd30f2a8af47d45b67cb22a1718d480267939b","cross_cats_sorted":["math.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-28T19:42:26Z","title_canon_sha256":"0104a788a0f3bea825a7d1bcb4ec58f969d8ff7c8923cc1159e6521ebfac3aeb"},"schema_version":"1.0","source":{"id":"1106.5776","kind":"arxiv","version":2}},"canonical_sha256":"4fe4e39a46239fd5abc9752ceeecf0ef75f42142a12f04826c49d3e685bc2589","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4fe4e39a46239fd5abc9752ceeecf0ef75f42142a12f04826c49d3e685bc2589","first_computed_at":"2026-05-18T04:19:11.726970Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:19:11.726970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8staFAdoCC+tiMjbuHaK19wyiXeN2Y9hFADo1ITFApIEupoQGoXXoojUpi4RSsSfo7se3er2v0kvRCIo7uK6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:19:11.727604Z","signed_message":"canonical_sha256_bytes"},"source_id":"1106.5776","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c6025d197f847b145616ebbeaa29d2af266642144017ac33de685770425b2c37","sha256:9705bfe0e7bdb416acc0784e3f3a65c6f01dc9715710a5db158ed6bcd834ce82"],"state_sha256":"a7a7710ec8fe54cad4b98c92661067a0ef6e6166830deac5fa5165fc04551da6"}