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We show that, for a Seidel matrix of order $n$ even (resp. odd), there are at most $2^{\\binom{e-2}{2}}$ (resp. $2^{\\binom{e-2}{2}+1}$) possibilities for the congruence class of $\\chi_S(x)$ modulo $2^e\\mathbb Z[x]$. As an application of these results, we obtain an improvement to the upper bound for the number of equiangular lines in $\\mathbb R^{17}$, that is, we reduce the known upper bound from $50$ to $49$."},"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":"1806.08323","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-06-21T17:07:51Z","cross_cats_sorted":[],"title_canon_sha256":"9abe265cfa3768eb1c2c8a6718bb8bedd9b27b7808281bc9fff242c03a73076a","abstract_canon_sha256":"3b3493b5f86dc11b0ec902c09809d665417398b877667b058c623cc06cb76b30"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:04.433784Z","signature_b64":"GdYPDhu2Tkwt4GnKWa/RR+u+FDXJFpJH87UqShMGzG/iN0kTTFFLSmoLdSR6u6n49UV1jI4slHxIb+59xcASAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa05327a13b89e8b96506787c5836b07156741d0fc8620fc306afbc0022b8acd","last_reissued_at":"2026-05-17T23:40:04.433239Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:04.433239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On equiangular lines in 17 dimensions and the characteristic polynomial of a Seidel matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gary R. 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