{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:J7SOHGSGEOP5LK6JOUWO53HQ55","short_pith_number":"pith:J7SOHGSG","schema_version":"1.0","canonical_sha256":"4fe4e39a46239fd5abc9752ceeecf0ef75f42142a12f04826c49d3e685bc2589","source":{"kind":"arxiv","id":"1106.5776","version":2},"attestation_state":"computed","paper":{"title":"A variant of Marstrand's theorem for projections of cartesian products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Carlos Gustavo Moreira, Jorge Erick L\\'opez Vel\\'azquez","submitted_at":"2011-06-28T19:42:26Z","abstract_excerpt":"We prove the following variant of Marstrand's theorem about projections of cartesian products of sets:\n  Consider the space $\\Lambda_m=\\set{(t,O), t\\in\\R, O\\in SO(m)}$ with the natural measure and set $\\Lambda=\\Lambda_{m_1}\\times\\ppp\\times\\Lambda_{m_n}$. 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"},"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":"1106.5776","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-06-28T19:42:26Z","cross_cats_sorted":["math.DS"],"title_canon_sha256":"0104a788a0f3bea825a7d1bcb4ec58f969d8ff7c8923cc1159e6521ebfac3aeb","abstract_canon_sha256":"e6b8e462131bf2c266fb52eaebfd30f2a8af47d45b67cb22a1718d480267939b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:11.727604Z","signature_b64":"8staFAdoCC+tiMjbuHaK19wyiXeN2Y9hFADo1ITFApIEupoQGoXXoojUpi4RSsSfo7se3er2v0kvRCIo7uK6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4fe4e39a46239fd5abc9752ceeecf0ef75f42142a12f04826c49d3e685bc2589","last_reissued_at":"2026-05-18T04:19:11.726970Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:11.726970Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A variant of Marstrand's theorem for projections of cartesian products","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.CA","authors_text":"Carlos Gustavo Moreira, Jorge Erick L\\'opez Vel\\'azquez","submitted_at":"2011-06-28T19:42:26Z","abstract_excerpt":"We prove the following variant of Marstrand's theorem about projections of cartesian products of sets:\n  Consider the space $\\Lambda_m=\\set{(t,O), t\\in\\R, O\\in SO(m)}$ with the natural measure and set $\\Lambda=\\Lambda_{m_1}\\times\\ppp\\times\\Lambda_{m_n}$. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.5776","kind":"arxiv","version":2},"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":"1106.5776","created_at":"2026-05-18T04:19:11.727061+00:00"},{"alias_kind":"arxiv_version","alias_value":"1106.5776v2","created_at":"2026-05-18T04:19:11.727061+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1106.5776","created_at":"2026-05-18T04:19:11.727061+00:00"},{"alias_kind":"pith_short_12","alias_value":"J7SOHGSGEOP5","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_16","alias_value":"J7SOHGSGEOP5LK6J","created_at":"2026-05-18T12:26:32.869790+00:00"},{"alias_kind":"pith_short_8","alias_value":"J7SOHGSG","created_at":"2026-05-18T12:26:32.869790+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/J7SOHGSGEOP5LK6JOUWO53HQ55","json":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55.json","graph_json":"https://pith.science/api/pith-number/J7SOHGSGEOP5LK6JOUWO53HQ55/graph.json","events_json":"https://pith.science/api/pith-number/J7SOHGSGEOP5LK6JOUWO53HQ55/events.json","paper":"https://pith.science/paper/J7SOHGSG"},"agent_actions":{"view_html":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55","download_json":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55.json","view_paper":"https://pith.science/paper/J7SOHGSG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1106.5776&json=true","fetch_graph":"https://pith.science/api/pith-number/J7SOHGSGEOP5LK6JOUWO53HQ55/graph.json","fetch_events":"https://pith.science/api/pith-number/J7SOHGSGEOP5LK6JOUWO53HQ55/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55/action/timestamp_anchor","attest_storage":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55/action/storage_attestation","attest_author":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55/action/author_attestation","sign_citation":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55/action/citation_signature","submit_replication":"https://pith.science/pith/J7SOHGSGEOP5LK6JOUWO53HQ55/action/replication_record"}},"created_at":"2026-05-18T04:19:11.727061+00:00","updated_at":"2026-05-18T04:19:11.727061+00:00"}