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Stull, Elvira Mayordomo, Marianna Csornyei, Neil Lutz, Patrick Lutz, Peter Cholak","submitted_at":"2024-11-07T18:37:13Z","abstract_excerpt":"It is well known that if $A \\subseteq \\mathbb{R}^n$ is an analytic set of Hausdorff dimension $a$, then $\\dim_H(\\pi_VA)=\\min\\{a,k\\}$ for a.e.\\ $V\\in G(n,k)$, where $G(n,k)$ denotes the set of all $k$-dimensional subspaces of $\\mathbb{R}^n$ and $\\pi_V$ is the orthogonal projection of $A$ onto $V$. In this paper we study how large the exceptional set\n  \\begin{equation*}\n  \\{V\\in G(n,k) \\mid \\dim_H(\\pi_V A) < s\\}\n  \\end{equation*}\n  can be for a given $s\\le\\min\\{a,k\\}.$ We improve previously known estimates on the dimension of the exceptional set, and we show that our estimates are sharp for $k=1"},"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":"2411.04959","kind":"arxiv","version":3},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CA","submitted_at":"2024-11-07T18:37:13Z","cross_cats_sorted":[],"title_canon_sha256":"835d3f4b75d12439278d4e3a59a29961b53e6bf547ae10e8d7bd96e944b826d5","abstract_canon_sha256":"820703984a75d3f67319851d5cee3923279eaaaa976ef71f286899163d284d2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T12:03:23.182635Z","signature_b64":"JtFjPuASUeOxE7f6RmibMkgkLuN7XftSztOC57Dx6COfY9jSwn8Qv+LoTy4OeRCShhmx0LWa1wSqwL/PHjTpBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a169eaade40eaa5cd5b9919f478d5772d3924ef64dd8214e8a219cc78523dd8","last_reissued_at":"2026-07-05T12:03:23.182018Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T12:03:23.182018Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bounding the dimension of exceptional sets for orthogonal projections","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"D. 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In this paper we study how large the exceptional set\n  \\begin{equation*}\n  \\{V\\in G(n,k) \\mid \\dim_H(\\pi_V A) < s\\}\n  \\end{equation*}\n  can be for a given $s\\le\\min\\{a,k\\}.$ We improve previously known estimates on the dimension of the exceptional set, and we show that our estimates are sharp for $k=1"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.04959","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2411.04959/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2411.04959","created_at":"2026-07-05T12:03:23.182084+00:00"},{"alias_kind":"arxiv_version","alias_value":"2411.04959v3","created_at":"2026-07-05T12:03:23.182084+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2411.04959","created_at":"2026-07-05T12:03:23.182084+00:00"},{"alias_kind":"pith_short_12","alias_value":"JILJ5KW6IDVK","created_at":"2026-07-05T12:03:23.182084+00:00"},{"alias_kind":"pith_short_16","alias_value":"JILJ5KW6IDVKLTK3","created_at":"2026-07-05T12:03:23.182084+00:00"},{"alias_kind":"pith_short_8","alias_value":"JILJ5KW6","created_at":"2026-07-05T12:03:23.182084+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2509.05211","citing_title":"Algorithmic Information Bounds for Distances and Orthogonal Projections","ref_index":5,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4","json":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4.json","graph_json":"https://pith.science/api/pith-number/JILJ5KW6IDVKLTK3TEM7I6GVO4/graph.json","events_json":"https://pith.science/api/pith-number/JILJ5KW6IDVKLTK3TEM7I6GVO4/events.json","paper":"https://pith.science/paper/JILJ5KW6"},"agent_actions":{"view_html":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4","download_json":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4.json","view_paper":"https://pith.science/paper/JILJ5KW6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2411.04959&json=true","fetch_graph":"https://pith.science/api/pith-number/JILJ5KW6IDVKLTK3TEM7I6GVO4/graph.json","fetch_events":"https://pith.science/api/pith-number/JILJ5KW6IDVKLTK3TEM7I6GVO4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4/action/storage_attestation","attest_author":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4/action/author_attestation","sign_citation":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4/action/citation_signature","submit_replication":"https://pith.science/pith/JILJ5KW6IDVKLTK3TEM7I6GVO4/action/replication_record"}},"created_at":"2026-07-05T12:03:23.182084+00:00","updated_at":"2026-07-05T12:03:23.182084+00:00"}