{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:VHOHIMQ4MFBQ2ILPM3FDVHAAZA","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":"983c910329232af5b7d86fcfd1d061c4902f80c461d3f1d98d5940ef9283f2ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T17:50:16Z","title_canon_sha256":"7d17972a0bec1ba41ab87e567a1816b59a3650b4373d8eef6451a7b29bbfa5eb"},"schema_version":"1.0","source":{"id":"1308.6231","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.6231","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"arxiv_version","alias_value":"1308.6231v4","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.6231","created_at":"2026-05-18T02:17:01Z"},{"alias_kind":"pith_short_12","alias_value":"VHOHIMQ4MFBQ","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_16","alias_value":"VHOHIMQ4MFBQ2ILP","created_at":"2026-05-18T12:28:04Z"},{"alias_kind":"pith_short_8","alias_value":"VHOHIMQ4","created_at":"2026-05-18T12:28:04Z"}],"graph_snapshots":[{"event_id":"sha256:445eed29e3e50c6840ad0624ff50806a9e85a50aae68246460dcebfe5a76a770","target":"graph","created_at":"2026-05-18T02:17:01Z","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":"Equidistant codes over vector spaces are considered. For $k$-dimensional subspaces over a large vector space the largest code is always a sunflower. We present several simple constructions for such codes which might produce the largest non-sunflower codes. A novel construction, based on the Pl\\\"{u}cker embedding, for 1-intersecting codes of $k$-dimensional subspaces over $\\F_q^n$, $n \\geq \\binom{k+1}{2}$, where the code size is $\\frac{q^{k+1}-1}{q-1}$ is presented. Finally, we present a related construction which generates equidistant constant rank codes with matrices of size $n \\times \\binom{","authors_text":"Netanel Raviv, Tuvi Etzion","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T17:50:16Z","title":"Equidistant Codes in the Grassmannian"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.6231","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":"sha256:0953b05315eb2bb2457c20e56dbe07c6b914967f04baa3b903acd4f0ba0f147e","target":"record","created_at":"2026-05-18T02:17:01Z","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":"983c910329232af5b7d86fcfd1d061c4902f80c461d3f1d98d5940ef9283f2ed","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-08-28T17:50:16Z","title_canon_sha256":"7d17972a0bec1ba41ab87e567a1816b59a3650b4373d8eef6451a7b29bbfa5eb"},"schema_version":"1.0","source":{"id":"1308.6231","kind":"arxiv","version":4}},"canonical_sha256":"a9dc74321c61430d216f66ca3a9c00c8362423c20c387aa74e626528d8cedd39","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a9dc74321c61430d216f66ca3a9c00c8362423c20c387aa74e626528d8cedd39","first_computed_at":"2026-05-18T02:17:01.550756Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:17:01.550756Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"4w9ydldKY51hp3GTWQxUVnjwNbji/72beVVryBTosrBrHT9rz/hC9mD/aX3CLxc44rHcemO5TiBUvYZ34c9TCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:17:01.551456Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.6231","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0953b05315eb2bb2457c20e56dbe07c6b914967f04baa3b903acd4f0ba0f147e","sha256:445eed29e3e50c6840ad0624ff50806a9e85a50aae68246460dcebfe5a76a770"],"state_sha256":"5a629911be11a00b4966295414eee1f6b5f0731dfff5c999119b9b8419aa0d98"}