{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:C3M3MG37LLEHCTUOFCDBYF5H3W","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"c67f3b64a9910317f7fe4f82285ad49785543b0f6e8a38f0d1a581ede689dbed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-17T20:13:16Z","title_canon_sha256":"f76c18d96d369ee9c2d9b43c0d0e84030607c1e578f4086b862a21e9206d8a48"},"schema_version":"1.0","source":{"id":"1304.4955","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.4955","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1304.4955v3","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.4955","created_at":"2026-05-18T01:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"C3M3MG37LLEH","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_16","alias_value":"C3M3MG37LLEHCTUO","created_at":"2026-05-18T12:27:40Z"},{"alias_kind":"pith_short_8","alias_value":"C3M3MG37","created_at":"2026-05-18T12:27:40Z"}],"graph_snapshots":[{"event_id":"sha256:a35392682e57b4d381e786d27e53cc9f33181b2442afca74157f7beb95402360","target":"graph","created_at":"2026-05-18T01:21:32Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"This paper is concerned with restricted families of projections in $\\mathbb{R}^{3}$. Let $K \\subset \\mathbb{R}^{3}$ be a Borel set with Hausdorff dimension $\\dim K = s > 1$. If $\\mathcal{G}$ is a smooth and sufficiently well-curved one-dimensional family of two-dimensional subspaces, the main result states that there exists $\\sigma(s) > 1$ such that $\\dim \\pi_{V}(K) \\geq \\sigma(s)$ for almost all $V \\in \\mathcal{G}$. A similar result is obtained for some specific families of one-dimensional subspaces.","authors_text":"Tuomas Orponen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-17T20:13:16Z","title":"Hausdorff dimension estimates for restricted families of projections in $\\mathbb{R}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.4955","kind":"arxiv","version":3},"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":"sha256:872d83c1aa6dbc136d97fd4011b45060f0a52572c34affe7eec7b2138b089506","target":"record","created_at":"2026-05-18T01:21:32Z","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":"c67f3b64a9910317f7fe4f82285ad49785543b0f6e8a38f0d1a581ede689dbed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2013-04-17T20:13:16Z","title_canon_sha256":"f76c18d96d369ee9c2d9b43c0d0e84030607c1e578f4086b862a21e9206d8a48"},"schema_version":"1.0","source":{"id":"1304.4955","kind":"arxiv","version":3}},"canonical_sha256":"16d9b61b7f5ac8714e8e28861c17a7dd9af84cc342c5598949c7e08ab4da4f2d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"16d9b61b7f5ac8714e8e28861c17a7dd9af84cc342c5598949c7e08ab4da4f2d","first_computed_at":"2026-05-18T01:21:32.925914Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:32.925914Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"d+hUrsTsXxpuLwIgQ8RLmhcIO/ggm6RYRZUEg4ksKyqasz1rg5gSD3LW8Dh2wvJiMbigqaxzUCtZ7oOw0uSCAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:32.926519Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.4955","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:872d83c1aa6dbc136d97fd4011b45060f0a52572c34affe7eec7b2138b089506","sha256:a35392682e57b4d381e786d27e53cc9f33181b2442afca74157f7beb95402360"],"state_sha256":"f2d0e425d96e7a1326d8828a7de94ca6821b44919b51e94742cd042bdd78e258"}