{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:3YH2ULOTO7VHT5KTAV4MCRIEB2","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":"8ed59022d08746937ea03e7d0bc613eb18bacc0e9963fcbd344dda331c2970b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-14T17:37:41Z","title_canon_sha256":"91694bcfd11a19ae7e35b872bd6eecc70e05d693874d68afe0b3c58da1e1fb7c"},"schema_version":"1.0","source":{"id":"1308.3188","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.3188","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"arxiv_version","alias_value":"1308.3188v4","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.3188","created_at":"2026-05-18T01:10:54Z"},{"alias_kind":"pith_short_12","alias_value":"3YH2ULOTO7VH","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_16","alias_value":"3YH2ULOTO7VHT5KT","created_at":"2026-05-18T12:27:32Z"},{"alias_kind":"pith_short_8","alias_value":"3YH2ULOT","created_at":"2026-05-18T12:27:32Z"}],"graph_snapshots":[{"event_id":"sha256:ec0224753e5552e4a664b4538eb0d1f051617baea1faefb697e8b6ea5200ab90","target":"graph","created_at":"2026-05-18T01:10:54Z","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 find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence (and abundance) of several hitherto unknown families of simplices in quaternionic projective spaces and the octonionic projective plane. The most noteworthy cases are 15-point simplices in HP^2 and 27-point simplices in OP^2, both of which are the largest simplices and the smallest 2-designs possible in their respective spaces. These codes are all universally optimal, by a theorem of Cohn and Kumar. We also show the existence of several p","authors_text":"Abhinav Kumar, Gregory Minton, Henry Cohn","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-14T17:37:41Z","title":"Optimal simplices and codes in projective spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.3188","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":"sha256:61399909e20a59e86537ce258ab5a8542912dcd43e723e0c41813ea5b4b4a3a1","target":"record","created_at":"2026-05-18T01:10:54Z","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":"8ed59022d08746937ea03e7d0bc613eb18bacc0e9963fcbd344dda331c2970b8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2013-08-14T17:37:41Z","title_canon_sha256":"91694bcfd11a19ae7e35b872bd6eecc70e05d693874d68afe0b3c58da1e1fb7c"},"schema_version":"1.0","source":{"id":"1308.3188","kind":"arxiv","version":4}},"canonical_sha256":"de0faa2dd377ea79f5530578c145040e98a1023faafeda041bd0b38ed10d640b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"de0faa2dd377ea79f5530578c145040e98a1023faafeda041bd0b38ed10d640b","first_computed_at":"2026-05-18T01:10:54.842424Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:10:54.842424Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nhoNwIaHAY6mXPqdzyNJTmq5ZFczWeclRPxuo9Xn2kLyqfMG9UKrvbrvRvh3iyIFf8nrC1DxWEaHeCoK9dnlAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:10:54.842957Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.3188","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61399909e20a59e86537ce258ab5a8542912dcd43e723e0c41813ea5b4b4a3a1","sha256:ec0224753e5552e4a664b4538eb0d1f051617baea1faefb697e8b6ea5200ab90"],"state_sha256":"c7fbd0a69c9beeab1ae7268776407a8940f89990b7d9932b221f2200c0580286"}