{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:C5LDAOX2M4HQUQIR5CVBRVLU3Z","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":"cb273106e7eb28382d96ef5434d1021f1e7d4df80730843cd96f949966d42127","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-07-28T01:06:37Z","title_canon_sha256":"6943ea01b902b795a559118af32bba5a02905fa74cd36444369be548d734aa37"},"schema_version":"1.0","source":{"id":"2207.13844","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2207.13844","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"arxiv_version","alias_value":"2207.13844v2","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2207.13844","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_12","alias_value":"C5LDAOX2M4HQ","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_16","alias_value":"C5LDAOX2M4HQUQIR","created_at":"2026-07-05T08:00:28Z"},{"alias_kind":"pith_short_8","alias_value":"C5LDAOX2","created_at":"2026-07-05T08:00:28Z"}],"graph_snapshots":[{"event_id":"sha256:ef23de2a149ddb6aafd84d1c3b10cec89b2d9b0846f43e0c648d6038a30fca1c","target":"graph","created_at":"2026-07-05T08:00:28Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2207.13844/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $\\gamma:[0,1]\\rightarrow \\mathbb{S}^{2}$ be a non-degenerate curve in $\\mathbb{R}^3$, that is to say, $\\det\\big(\\gamma(\\theta),\\gamma'(\\theta),\\gamma\"(\\theta)\\big)\\neq 0$. For each $\\theta\\in[0,1]$, let $V_\\theta=\\gamma(\\theta)^\\perp$ and let $\\pi_\\theta:\\mathbb{R}^3\\rightarrow V_\\theta$ be the orthogonal projections. We prove that if $A\\subset \\mathbb{R}^3$ is a Borel set, then for a.e. $\\theta\\in [0,1]$ we have $\\text{dim}(\\pi_\\theta(A))=\\min\\{2,\\text{dim} A\\}$. More generally, we prove an exceptional set estimate. For $A\\subset\\mathbb{R}^3$ and $0\\le s\\le 2$, define $E_s(A):=\\{\\theta\\in","authors_text":"Dominique Maldague, Hong Wang, Larry Guth, Shaoming Guo, Shengwen Gan, Terence L. J. Harris","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-07-28T01:06:37Z","title":"On restricted projections to planes in $\\mathbb{R}^3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.13844","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:ac5ef6049f8b788f4a20443f58b179aa4678d71421ddfb6f0d9a6a4b041655d4","target":"record","created_at":"2026-07-05T08:00:28Z","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":"cb273106e7eb28382d96ef5434d1021f1e7d4df80730843cd96f949966d42127","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-07-28T01:06:37Z","title_canon_sha256":"6943ea01b902b795a559118af32bba5a02905fa74cd36444369be548d734aa37"},"schema_version":"1.0","source":{"id":"2207.13844","kind":"arxiv","version":2}},"canonical_sha256":"1756303afa670f0a4111e8aa18d574de752bf5a59d2d28216b62f408b13cd730","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1756303afa670f0a4111e8aa18d574de752bf5a59d2d28216b62f408b13cd730","first_computed_at":"2026-07-05T08:00:28.330489Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T08:00:28.330489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GzQQrQBfYIwhwGvkrmJg8hefFj3PNPTncqqucGBHlaym5YG2ypj89ez6PFMWt11vby8LVtE1w1gcEgeRCNkIAQ==","signature_status":"signed_v1","signed_at":"2026-07-05T08:00:28.330976Z","signed_message":"canonical_sha256_bytes"},"source_id":"2207.13844","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac5ef6049f8b788f4a20443f58b179aa4678d71421ddfb6f0d9a6a4b041655d4","sha256:ef23de2a149ddb6aafd84d1c3b10cec89b2d9b0846f43e0c648d6038a30fca1c"],"state_sha256":"feaf6ecebd3e38c4ed0c85067b17d4792100ff36e16dc6e3b1bbf72d4761a860"}