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Acoording to the nonexistence of strongly regular graph $(75,32,10,16)$ \\cite{aza15}, Larmen-Rogers-Seidel Theorem \\cite{lar77} and Lemmen-Seidel bounds on equiangular lines with common angle $\\frac 1 3$ \\cite{lem73}, we can prove that there are no 76 equiangular lines in $\\mathbb{R}^{19}$. As a corollary, there is no strongly regular graph $(76,35,18,14)$. Similar discussion can prove that there are no 96 equiangular lines in $\\mathbb{R}^{20}$."},"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":"1511.08569","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2015-11-27T06:50:37Z","cross_cats_sorted":[],"title_canon_sha256":"1eeca824f52c783d626a81f665fab4d3bdae278e0ef13545925837d3eea640ea","abstract_canon_sha256":"7937694c69b5af4a4dd26664b1d4d019c60f7a0ba7dc1074c0b3016b7ed67a44"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:08:32.409528Z","signature_b64":"6s6s4/8eQd7fmEwhfcglD4sN/RI0Alix2bfHnKRQrXH82yDmO506k80Lh9T0okbDs3gBdx7AtT6GPc96m1rSBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a48a500bc4e79b151341ecfb013f55a880f6dc4476b8edb8780e631501b6f12e","last_reissued_at":"2026-05-18T01:08:32.408787Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:08:32.408787Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"There are no 76 equiangular lines in $R^{19}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Wei-Hsuan Yu","submitted_at":"2015-11-27T06:50:37Z","abstract_excerpt":"Maximum size of equiangular lines in $\\mathbb{R}^{19}$ has been known in the range between 72 to 76 since 1973. 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