{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ZZEYYRBZFPL5VOJFBXNTVMARRC","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":"9f9169ed06108d79bda3abdfb4435c82a6e205b52c570c6b92a1ac671d29a278","cross_cats_sorted":["math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-17T20:47:43Z","title_canon_sha256":"ebb61a3e93f7df63260ed76b15f6ca8cd095ca9fc315e4c8447faa37f19f2468"},"schema_version":"1.0","source":{"id":"1502.05030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.05030","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"arxiv_version","alias_value":"1502.05030v2","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.05030","created_at":"2026-05-18T02:26:12Z"},{"alias_kind":"pith_short_12","alias_value":"ZZEYYRBZFPL5","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"ZZEYYRBZFPL5VOJF","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"ZZEYYRBZ","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:40ee4ac369d0498d225ce57e83d686802933d20a8c9ea7f55dc12c4210c41748","target":"graph","created_at":"2026-05-18T02:26:12Z","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":"Let $X$ be any subset of the interval $[-1,1]$. A subset $I$ of the unit sphere in $R^n$ will be called \\emph{$X$-avoiding} if $<u,v >\\notin X$ for any $u,v \\in I$. The problem of determining the maximum surface measure of a $\\{ 0 \\}$-avoiding set was first stated in a 1974 note by Witsenhausen; there the upper bound of $1/n$ times the surface measure of the sphere is derived from a simple averaging argument. A consequence of the Frankl-Wilson theorem is that this fraction decreases exponentially, but until now the $1/3$ upper bound for the case $n=3$ has not moved. We improve this bound to $0","authors_text":"Evan DeCorte, Oleg Pikhurko","cross_cats":["math.MG","math.OC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-17T20:47:43Z","title":"Spherical sets avoiding a prescribed set of angles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05030","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":"sha256:145d5613872ead8fc8fc8fff197753ecf6cd110ab565f4e4304c24892370e07b","target":"record","created_at":"2026-05-18T02:26:12Z","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":"9f9169ed06108d79bda3abdfb4435c82a6e205b52c570c6b92a1ac671d29a278","cross_cats_sorted":["math.MG","math.OC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-02-17T20:47:43Z","title_canon_sha256":"ebb61a3e93f7df63260ed76b15f6ca8cd095ca9fc315e4c8447faa37f19f2468"},"schema_version":"1.0","source":{"id":"1502.05030","kind":"arxiv","version":2}},"canonical_sha256":"ce498c44392bd7dab9250ddb3ab01188b1ca277401bb7e9ca4311e03f2d23aae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ce498c44392bd7dab9250ddb3ab01188b1ca277401bb7e9ca4311e03f2d23aae","first_computed_at":"2026-05-18T02:26:12.314762Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:26:12.314762Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"LBmnqsbRK3lvCKeEPdUKc8HhIeek5jusTtFUHF6UYopHljULxum3GpgRJ1IINhRbGscyohM/0pST4Otaz23nCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:26:12.315268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.05030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:145d5613872ead8fc8fc8fff197753ecf6cd110ab565f4e4304c24892370e07b","sha256:40ee4ac369d0498d225ce57e83d686802933d20a8c9ea7f55dc12c4210c41748"],"state_sha256":"771939fe8bb77c2e41ab32f31995782503cb0e5cfa91ae527fb45fead8b43eab"}