{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:SSUQQASL5C56KJ34SON2W5OIHF","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":"ad8775c7f71ea70288803c855d25bb09a188981fe7ed45e393858118ecb070a7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-28T09:21:03Z","title_canon_sha256":"5e5056368914af04f404b474f3ca2bd1c334607851a2c59995cd496e0f28a1b4"},"schema_version":"1.0","source":{"id":"2605.29658","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2605.29658","created_at":"2026-05-29T01:05:53Z"},{"alias_kind":"arxiv_version","alias_value":"2605.29658v1","created_at":"2026-05-29T01:05:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.29658","created_at":"2026-05-29T01:05:53Z"},{"alias_kind":"pith_short_12","alias_value":"SSUQQASL5C56","created_at":"2026-05-29T01:05:53Z"},{"alias_kind":"pith_short_16","alias_value":"SSUQQASL5C56KJ34","created_at":"2026-05-29T01:05:53Z"},{"alias_kind":"pith_short_8","alias_value":"SSUQQASL","created_at":"2026-05-29T01:05:53Z"}],"graph_snapshots":[{"event_id":"sha256:86bd0900739120b6cc85e3d964fd339fac991f99713ef8be1fc21e3a1fcc3db2","target":"graph","created_at":"2026-05-29T01:05:53Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2605.29658/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Let $G_1$ denote the incidence graph of the complete graph $K_{q+1}$. We study limited augmented Zarankiewicz numbers in this family by combining exact 0--1 ILP computations for the smallest cases with a constructive search procedure followed by exact admissibility verification in the larger cases considered here. We obtain \\[ z_L(6,4)=14,\\qquad z_L(10,5)=26,\\qquad z_L(15,6)\\ge 43,\\qquad z_L(21,7)\\ge 64,\\qquad z_L(28,8)\\ge 88. \\] The first two values are exact. The three lower bounds arise from explicitly verified admissible families with $|E_2|=13$, $|E_2|=22$, and $|E_2|=32$, respectively; t","authors_text":"Gaohang Yu, Xu Yi","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-28T09:21:03Z","title":"A Computational Study of Limited Augmented Zarankiewicz Numbers in the Incidence-Graph Family of Complete Graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.29658","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:e9b5d6e9c2e657b7147550705687e6eafec7c78c94c99fc2cc3d3323a674c8e7","target":"record","created_at":"2026-05-29T01:05:53Z","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":"ad8775c7f71ea70288803c855d25bb09a188981fe7ed45e393858118ecb070a7","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.CO","submitted_at":"2026-05-28T09:21:03Z","title_canon_sha256":"5e5056368914af04f404b474f3ca2bd1c334607851a2c59995cd496e0f28a1b4"},"schema_version":"1.0","source":{"id":"2605.29658","kind":"arxiv","version":1}},"canonical_sha256":"94a908024be8bbe5277c939bab75c83948304829a5782005bb0b1c0581ca3f8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94a908024be8bbe5277c939bab75c83948304829a5782005bb0b1c0581ca3f8f","first_computed_at":"2026-05-29T01:05:53.970346Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T01:05:53.970346Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OO8s5RXj+bkvSMJukMCpMxDpn68K0Jk2Yhr1BZNC5hkWeTLeLDeYRo16uarTuiGWE6UPo+NvUGKqz6xgUYWvDQ==","signature_status":"signed_v1","signed_at":"2026-05-29T01:05:53.971094Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.29658","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e9b5d6e9c2e657b7147550705687e6eafec7c78c94c99fc2cc3d3323a674c8e7","sha256:86bd0900739120b6cc85e3d964fd339fac991f99713ef8be1fc21e3a1fcc3db2"],"state_sha256":"79320f4630a69a917b58178d9499d0c093c23516cddd7269eaca7519fe21aeb2"}