{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:UIN44PHODJ6TVJAPO24NHJ3NBI","short_pith_number":"pith:UIN44PHO","schema_version":"1.0","canonical_sha256":"a21bce3cee1a7d3aa40f76b8d3a76d0a2d8a3a9c78bf165a382c155e44ea20e5","source":{"kind":"arxiv","id":"1302.6550","version":2},"attestation_state":"computed","paper":{"title":"On restricted families of projections in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Katrin F\\\"assler, Tuomas Orponen","submitted_at":"2013-02-26T19:30:51Z","abstract_excerpt":"We study projections onto non-degenerate one-dimensional families of lines and planes in $\\mathbb{R}^{3}$. Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most $1/2$-dimensional sets $B \\subset \\mathbb{R}^{3}$ is typically preserved under one-dimensional families of projections onto lines. We improve the result by an $\\varepsilon$, proving that if $\\dim_{\\mathrm{H}} B = s > 1/2$, then the packing dimension of the projections is almost surely at least $\\sigma(s) > 1/2$. For projections onto planes, we obtain a similar bound, with t"},"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":"1302.6550","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-02-26T19:30:51Z","cross_cats_sorted":[],"title_canon_sha256":"238a27ce2f2cfca5a1a826b8ee98ac37c5b30a041fcbe4a7112f002079875aa9","abstract_canon_sha256":"328c157cb769e9ce46535e8379b3af9078c45768d9cb92a212c1e718af28148a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:32:46.538574Z","signature_b64":"F/F5eLGE3BNEeNNYX97oloKVsZ+awcqw1gkr9v54b8P8+m5d/kXuo+r/vnysl7Fvl6Hn9OUNJSw9C82K15sQAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a21bce3cee1a7d3aa40f76b8d3a76d0a2d8a3a9c78bf165a382c155e44ea20e5","last_reissued_at":"2026-05-18T02:32:46.538162Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:32:46.538162Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On restricted families of projections in R^3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Katrin F\\\"assler, Tuomas Orponen","submitted_at":"2013-02-26T19:30:51Z","abstract_excerpt":"We study projections onto non-degenerate one-dimensional families of lines and planes in $\\mathbb{R}^{3}$. Using the classical potential theoretic approach of R. Kaufman, one can show that the Hausdorff dimension of at most $1/2$-dimensional sets $B \\subset \\mathbb{R}^{3}$ is typically preserved under one-dimensional families of projections onto lines. We improve the result by an $\\varepsilon$, proving that if $\\dim_{\\mathrm{H}} B = s > 1/2$, then the packing dimension of the projections is almost surely at least $\\sigma(s) > 1/2$. For projections onto planes, we obtain a similar bound, with t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6550","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":"1302.6550","created_at":"2026-05-18T02:32:46.538222+00:00"},{"alias_kind":"arxiv_version","alias_value":"1302.6550v2","created_at":"2026-05-18T02:32:46.538222+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.6550","created_at":"2026-05-18T02:32:46.538222+00:00"},{"alias_kind":"pith_short_12","alias_value":"UIN44PHODJ6T","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_16","alias_value":"UIN44PHODJ6TVJAP","created_at":"2026-05-18T12:28:02.375192+00:00"},{"alias_kind":"pith_short_8","alias_value":"UIN44PHO","created_at":"2026-05-18T12:28:02.375192+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/UIN44PHODJ6TVJAPO24NHJ3NBI","json":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI.json","graph_json":"https://pith.science/api/pith-number/UIN44PHODJ6TVJAPO24NHJ3NBI/graph.json","events_json":"https://pith.science/api/pith-number/UIN44PHODJ6TVJAPO24NHJ3NBI/events.json","paper":"https://pith.science/paper/UIN44PHO"},"agent_actions":{"view_html":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI","download_json":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI.json","view_paper":"https://pith.science/paper/UIN44PHO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1302.6550&json=true","fetch_graph":"https://pith.science/api/pith-number/UIN44PHODJ6TVJAPO24NHJ3NBI/graph.json","fetch_events":"https://pith.science/api/pith-number/UIN44PHODJ6TVJAPO24NHJ3NBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI/action/storage_attestation","attest_author":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI/action/author_attestation","sign_citation":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI/action/citation_signature","submit_replication":"https://pith.science/pith/UIN44PHODJ6TVJAPO24NHJ3NBI/action/replication_record"}},"created_at":"2026-05-18T02:32:46.538222+00:00","updated_at":"2026-05-18T02:32:46.538222+00:00"}