{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:KZP75SQVCGTHGZMU4KXFZDHXLC","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":"34ef501d5316d99b3603afd16780c584384cdb1786b6a352f00f8e27bec0830b","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-10T10:23:56Z","title_canon_sha256":"46e931dfabe5be6867862ab504aed234379226eea6b3247e082fb9bcddc1c5bd"},"schema_version":"1.0","source":{"id":"1606.03259","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1606.03259","created_at":"2026-05-18T00:15:00Z"},{"alias_kind":"arxiv_version","alias_value":"1606.03259v4","created_at":"2026-05-18T00:15:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1606.03259","created_at":"2026-05-18T00:15:00Z"},{"alias_kind":"pith_short_12","alias_value":"KZP75SQVCGTH","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_16","alias_value":"KZP75SQVCGTHGZMU","created_at":"2026-05-18T12:30:29Z"},{"alias_kind":"pith_short_8","alias_value":"KZP75SQV","created_at":"2026-05-18T12:30:29Z"}],"graph_snapshots":[{"event_id":"sha256:3ca70293e247ab28012eb0cb8141cba52b2dab99d77aaaed382ee751817eed14","target":"graph","created_at":"2026-05-18T00:15:00Z","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":"We derive a procedure for computing an upper bound on the number of equiangular lines in various Euclidean vector spaces by generalizing the classical pillar decomposition developed by (Lemmens and Seidel, 1973); namely, we use linear algebra and combinatorial arguments to bound the number of vectors within an equiangular set which have inner products of certain signs with a negative clique. After projection and rescaling, such sets are also certain spherical two-distance sets, and semidefinite programming techniques may be used to bound the size. Applying our method, we prove new relative bou","authors_text":"Emily J. King, Xiaoxian Tang","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-10T10:23:56Z","title":"New Upper Bounds for Equiangular Lines by Pillar Decomposition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1606.03259","kind":"arxiv","version":4},"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:bcb04d4be4eb9e165314cd444510406aa29ed46cec171f1fa4226f6ae826f4bd","target":"record","created_at":"2026-05-18T00:15:00Z","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":"34ef501d5316d99b3603afd16780c584384cdb1786b6a352f00f8e27bec0830b","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-06-10T10:23:56Z","title_canon_sha256":"46e931dfabe5be6867862ab504aed234379226eea6b3247e082fb9bcddc1c5bd"},"schema_version":"1.0","source":{"id":"1606.03259","kind":"arxiv","version":4}},"canonical_sha256":"565ffeca1511a6736594e2ae5c8cf7588ea1853cc20f780975a3e3edf8ccd2ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"565ffeca1511a6736594e2ae5c8cf7588ea1853cc20f780975a3e3edf8ccd2ae","first_computed_at":"2026-05-18T00:15:00.264343Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:15:00.264343Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"J/a5RV6QEpRepx/bud3RoekVU8FpLQCKpgZ8Pr/YeSgqZ3pDSgnrGrp6hyn8CTlOksoU3TbMffXGVz5JNN5yBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:15:00.265090Z","signed_message":"canonical_sha256_bytes"},"source_id":"1606.03259","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcb04d4be4eb9e165314cd444510406aa29ed46cec171f1fa4226f6ae826f4bd","sha256:3ca70293e247ab28012eb0cb8141cba52b2dab99d77aaaed382ee751817eed14"],"state_sha256":"6eb9e6f675ed236ea5922e16c831d850d7e4f8fda7211a2760f5d2a2330af8b1"}