{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:DXY7AJTM4SWSSO4QQFW7ELSEE6","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":"85907ea5128814dd3ccf84f32208a3ba641cdc493c823c84e9ba5e0cf4d5d35c","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T15:59:48Z","title_canon_sha256":"b7415e4bdf45478570782e1426c035022cb4d7f1cab2aaff3826355b1b7a4b50"},"schema_version":"1.0","source":{"id":"1510.00293","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00293","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00293v1","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00293","created_at":"2026-05-18T01:31:19Z"},{"alias_kind":"pith_short_12","alias_value":"DXY7AJTM4SWS","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"DXY7AJTM4SWSSO4Q","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"DXY7AJTM","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:86f1ff05dc3156432b00b937f1ba2b9a5fc9307be5ac31bc37483abfbdb0a9b1","target":"graph","created_at":"2026-05-18T01:31:19Z","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 this paper, we present a new lower bound on the size of separating hash families of type {w_1^{q-1},w_2} where w_1 < w_2. Our result extends the paper by Guo et al. on binary frameproof codes. This bound compares well against known general bounds, and is especially useful when trying to bound the size of strong separating hash families. We also show that our new bound is tight by constructing hash families that meet the new bound with equality.","authors_text":"Chuan Guo, Douglas R. Stinson","cross_cats":["cs.DM","math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T15:59:48Z","title":"A tight bound on the size of certain separating hash families"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00293","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":"sha256:3f55508cb3601096307b488643bf5bbee9008ee175bdd1f7d18565f02f904e84","target":"record","created_at":"2026-05-18T01:31:19Z","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":"85907ea5128814dd3ccf84f32208a3ba641cdc493c823c84e9ba5e0cf4d5d35c","cross_cats_sorted":["cs.DM","math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-10-01T15:59:48Z","title_canon_sha256":"b7415e4bdf45478570782e1426c035022cb4d7f1cab2aaff3826355b1b7a4b50"},"schema_version":"1.0","source":{"id":"1510.00293","kind":"arxiv","version":1}},"canonical_sha256":"1df1f0266ce4ad293b90816df22e4427a23f0d0361f21984eb88718d5af9f2a2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1df1f0266ce4ad293b90816df22e4427a23f0d0361f21984eb88718d5af9f2a2","first_computed_at":"2026-05-18T01:31:19.679181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:19.679181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"seTATtQRakmh/azgga+43KCy0YB5IgZMO7SDwlz3jFduJEkgO/qgExBXZ74a90I2MKr/J9upYP7yERfsd627DA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:19.679786Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00293","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3f55508cb3601096307b488643bf5bbee9008ee175bdd1f7d18565f02f904e84","sha256:86f1ff05dc3156432b00b937f1ba2b9a5fc9307be5ac31bc37483abfbdb0a9b1"],"state_sha256":"b04d5839618b002529fb989343c4d35a47a9a90bf8611a92a7fbf50b68b75027"}