{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RXHBPUN4EXQLJZFP3NUMK7SL7N","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":"5c3ea75896b3f2c5013407c0131a03b677255b192fffff1f7adbcb87e92f7ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-09T20:39:08Z","title_canon_sha256":"5950c94c80245664a5c10218c963b02d9e683c209e0060cd671a361cc9d8bbf6"},"schema_version":"1.0","source":{"id":"1802.03444","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1802.03444","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"arxiv_version","alias_value":"1802.03444v1","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.03444","created_at":"2026-05-18T00:23:51Z"},{"alias_kind":"pith_short_12","alias_value":"RXHBPUN4EXQL","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RXHBPUN4EXQLJZFP","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RXHBPUN4","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:c6207f1e9f34eba4e4e0f218f47e070bd93409da18372fa6b12a7792136a0d7a","target":"graph","created_at":"2026-05-18T00:23:51Z","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":"In 1984, Wilson proved the Erd\\H{o}s-Ko-Rado theorem for $t$-intersecting families of $k$-subsets of an $n$-set: he showed that if $n\\ge(t+1)(k-t+1)$ and $\\mathcal{F}$ is a family of $k$-subsets of an $n$-set such that any two members of $\\mathcal{F}$ have at least $t$ elements in common, then $|\\mathcal{F}|\\le\\binom{n-t}{k-t}$. His proof made essential use of a matrix whose origin is not obvious. In this paper we show that this matrix can be derived, in a sense, as a projection of $t$-$(n,k,1)$ design.","authors_text":"Chris Godsil, Krystal Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-09T20:39:08Z","title":"Using the existence of t-designs to prove Erd\\H{o}s-Ko-Rado"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03444","kind":"arxiv","version":1},"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":"sha256:8580a09b1ed9559ff249d85f291809aad1db0ce52dea1872fae602bb9e92fb6c","target":"record","created_at":"2026-05-18T00:23:51Z","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":"5c3ea75896b3f2c5013407c0131a03b677255b192fffff1f7adbcb87e92f7ce9","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-02-09T20:39:08Z","title_canon_sha256":"5950c94c80245664a5c10218c963b02d9e683c209e0060cd671a361cc9d8bbf6"},"schema_version":"1.0","source":{"id":"1802.03444","kind":"arxiv","version":1}},"canonical_sha256":"8dce17d1bc25e0b4e4afdb68c57e4bfb61d76ec2f4a83e08e7dfbc3e0ab5e9cd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8dce17d1bc25e0b4e4afdb68c57e4bfb61d76ec2f4a83e08e7dfbc3e0ab5e9cd","first_computed_at":"2026-05-18T00:23:51.619958Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:23:51.619958Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jb7zdDb2GzFHFky5cpPqzvSKMhNEZRJ0d7awIMSLKWEQrFlSfsjL45zaZLSPfu8PKe2g/h4CKbCXoYXnrAx9CQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:23:51.620506Z","signed_message":"canonical_sha256_bytes"},"source_id":"1802.03444","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8580a09b1ed9559ff249d85f291809aad1db0ce52dea1872fae602bb9e92fb6c","sha256:c6207f1e9f34eba4e4e0f218f47e070bd93409da18372fa6b12a7792136a0d7a"],"state_sha256":"d14400ec16a005edfd3f1b002905717bb38a9c3af051f2e0a6c00b7d4d32aac0"}