{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:TK6Q6XRTEXR3Q3BWINDNJATJLR","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":"a1c27be014a830c42c5a503a654c6005cbd4f54daafe1cfa7853be84db121f5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-21T15:35:05Z","title_canon_sha256":"a3417b57b6c3575e525bc5fb4e15176b51e81a6f250faf9a41114a227a25c35c"},"schema_version":"1.0","source":{"id":"1606.06620","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.06620","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"arxiv_version","alias_value":"1606.06620v2","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.06620","created_at":"2026-05-18T00:41:18Z"},{"alias_kind":"pith_short_12","alias_value":"TK6Q6XRTEXR3","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"TK6Q6XRTEXR3Q3BW","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"TK6Q6XRT","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:cb2bf2de93a3b9835d068ec41b8daee53ffe7ef5148bea1cbaaa92df7468ad5e","target":"graph","created_at":"2026-05-18T00:41:18Z","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":"A family of lines through the origin in Euclidean space is called equiangular if any pair of lines defines the same angle. The problem of estimating the maximum cardinality of such a family in $\\mathbb{R}^n$ was extensively studied for the last 70 years. Motivated by a question of Lemmens and Seidel from 1973, in this paper we prove that for every fixed angle $\\theta$ and sufficiently large $n$ there are at most $2n-2$ lines in $\\mathbb{R}^n$ with common angle $\\theta$. Moreover, this is achievable only for $\\theta = \\arccos(1/3)$. We also show that for any set of $k$ fixed angles, one can fin","authors_text":"Benny Sudakov, Felix Dr\\\"axler, Igor Balla, Peter Keevash","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-21T15:35:05Z","title":"Equiangular Lines and Spherical Codes in Euclidean Space"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.06620","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":"sha256:6d39a47068db93883111a3d7a33d94abee150f254af4ab0b3ada78121b75e1fd","target":"record","created_at":"2026-05-18T00:41:18Z","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":"a1c27be014a830c42c5a503a654c6005cbd4f54daafe1cfa7853be84db121f5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-21T15:35:05Z","title_canon_sha256":"a3417b57b6c3575e525bc5fb4e15176b51e81a6f250faf9a41114a227a25c35c"},"schema_version":"1.0","source":{"id":"1606.06620","kind":"arxiv","version":2}},"canonical_sha256":"9abd0f5e3325e3b86c364346d482695c6fdb9c59f96b0ab9d7bf0960c5360812","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9abd0f5e3325e3b86c364346d482695c6fdb9c59f96b0ab9d7bf0960c5360812","first_computed_at":"2026-05-18T00:41:18.365357Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:18.365357Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sL7p6RzYKbM83m8ThGMz8/o2qvpYAQJGPhOXOssgUNXjJLw1In2Q5568rzMVuvVlCQ0WIf+ym5zxBaSE4l0KCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:18.366104Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.06620","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6d39a47068db93883111a3d7a33d94abee150f254af4ab0b3ada78121b75e1fd","sha256:cb2bf2de93a3b9835d068ec41b8daee53ffe7ef5148bea1cbaaa92df7468ad5e"],"state_sha256":"6d4291837a4e602deeea337f49b1bba93ffc26c3bd64cf20caa54ec37a5aeb8f"}