{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:C5LDAOX2M4HQUQIR5CVBRVLU3Z","short_pith_number":"pith:C5LDAOX2","canonical_record":{"source":{"id":"2207.13844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-07-28T01:06:37Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6943ea01b902b795a559118af32bba5a02905fa74cd36444369be548d734aa37","abstract_canon_sha256":"cb273106e7eb28382d96ef5434d1021f1e7d4df80730843cd96f949966d42127"},"schema_version":"1.0"},"canonical_sha256":"1756303afa670f0a4111e8aa18d574de752bf5a59d2d28216b62f408b13cd730","source":{"kind":"arxiv","id":"2207.13844","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"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:C5LDAOX2M4HQUQIR5CVBRVLU3Z","target":"record","payload":{"canonical_record":{"source":{"id":"2207.13844","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2022-07-28T01:06:37Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"6943ea01b902b795a559118af32bba5a02905fa74cd36444369be548d734aa37","abstract_canon_sha256":"cb273106e7eb28382d96ef5434d1021f1e7d4df80730843cd96f949966d42127"},"schema_version":"1.0"},"canonical_sha256":"1756303afa670f0a4111e8aa18d574de752bf5a59d2d28216b62f408b13cd730","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T08:00:28.330976Z","signature_b64":"GzQQrQBfYIwhwGvkrmJg8hefFj3PNPTncqqucGBHlaym5YG2ypj89ez6PFMWt11vby8LVtE1w1gcEgeRCNkIAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1756303afa670f0a4111e8aa18d574de752bf5a59d2d28216b62f408b13cd730","last_reissued_at":"2026-07-05T08:00:28.330489Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T08:00:28.330489Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2207.13844","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"72bkaiE9M9bDpehJXFoaYBPBMcyEIKn7rdzttZ1Z2NLiEHKzbj2CYoZyuop/xG/7b2HjpXXmEXyBC883iQDwAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:38:58.296856Z"},"content_sha256":"ac5ef6049f8b788f4a20443f58b179aa4678d71421ddfb6f0d9a6a4b041655d4","schema_version":"1.0","event_id":"sha256:ac5ef6049f8b788f4a20443f58b179aa4678d71421ddfb6f0d9a6a4b041655d4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:C5LDAOX2M4HQUQIR5CVBRVLU3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On restricted projections to planes in $\\mathbb{R}^3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.CA","authors_text":"Dominique Maldague, Hong Wang, Larry Guth, Shaoming Guo, Shengwen Gan, Terence L. J. Harris","submitted_at":"2022-07-28T01:06:37Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2207.13844","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2207.13844/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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T08:00:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZbFaP9FY4xZKeFsHL2oD8Bp12RR69A4DPUdGgnrg7qdESo/cu6mhfVdT6kzXnlWe04tqjhk35UEL5s6O6+YYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T12:38:58.297355Z"},"content_sha256":"ef23de2a149ddb6aafd84d1c3b10cec89b2d9b0846f43e0c648d6038a30fca1c","schema_version":"1.0","event_id":"sha256:ef23de2a149ddb6aafd84d1c3b10cec89b2d9b0846f43e0c648d6038a30fca1c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C5LDAOX2M4HQUQIR5CVBRVLU3Z/bundle.json","state_url":"https://pith.science/pith/C5LDAOX2M4HQUQIR5CVBRVLU3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C5LDAOX2M4HQUQIR5CVBRVLU3Z/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T12:38:58Z","links":{"resolver":"https://pith.science/pith/C5LDAOX2M4HQUQIR5CVBRVLU3Z","bundle":"https://pith.science/pith/C5LDAOX2M4HQUQIR5CVBRVLU3Z/bundle.json","state":"https://pith.science/pith/C5LDAOX2M4HQUQIR5CVBRVLU3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C5LDAOX2M4HQUQIR5CVBRVLU3Z/bundle.json"},"state":{"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"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zTHCMfeeETCbLQNvEQbB9QL3qA9T3TSSH+A/xi26xhahxg8bJ0/CfDWwCJ3cUe+oUKq9SPavxoSX/Gn0nWlJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T12:38:58.302489Z","bundle_sha256":"0d25f7fb772ffd6dfbaa21315b37a198594a3b0735a1db5636f1087dbf3682ad"}}