{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:A4BYBM4KXCE3S36AXIWU3JNLIO","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":"4678e9f797ef83ad34d89acddf38838af3d5ebc97f3746a6259949aa003189e3","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-10T14:10:13Z","title_canon_sha256":"bebf3f1a59f96ab4458edaa99c06088c078c2d5df2167cbd4fc1cabd2ddde12a"},"schema_version":"1.0","source":{"id":"1111.2477","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.2477","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"arxiv_version","alias_value":"1111.2477v1","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.2477","created_at":"2026-05-18T02:19:08Z"},{"alias_kind":"pith_short_12","alias_value":"A4BYBM4KXCE3","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_16","alias_value":"A4BYBM4KXCE3S36A","created_at":"2026-05-18T12:26:24Z"},{"alias_kind":"pith_short_8","alias_value":"A4BYBM4K","created_at":"2026-05-18T12:26:24Z"}],"graph_snapshots":[{"event_id":"sha256:246d4ffa619559f63879aab4eebf791018f47a8146f93f8bf4581286d44d1ac5","target":"graph","created_at":"2026-05-18T02:19:08Z","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 call a subset $C$ of vertices of a graph $G$ a $(1,\\leq \\ell)$-identifying code if for all subsets $X$ of vertices with size at most $\\ell$, the sets $\\{c\\in C |\\exists u \\in X, d(u,c)\\leq 1\\}$ are distinct. The concept of identifying codes was introduced in 1998 by Karpovsky, Chakrabarty and Levitin. Identifying codes have been studied in various grids. In particular, it has been shown that there exists a $(1,\\leq 2)$-identifying code in the king grid with density 3/7 and that there are no such identifying codes with density smaller than 5/12. Using a suitable frame and a discharging proce","authors_text":"Aline Parreau (IF), Florent Foucaud (LaBRI), Tero Laihonen","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-10T14:10:13Z","title":"An improved lower bound for (1,<=2)-identifying codes in the king grid"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2477","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:dc8fce0a8b0cf0a4bc1dc8fdecef20cb0306ff4ead044fae08b68dfaaa915503","target":"record","created_at":"2026-05-18T02:19:08Z","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":"4678e9f797ef83ad34d89acddf38838af3d5ebc97f3746a6259949aa003189e3","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-11-10T14:10:13Z","title_canon_sha256":"bebf3f1a59f96ab4458edaa99c06088c078c2d5df2167cbd4fc1cabd2ddde12a"},"schema_version":"1.0","source":{"id":"1111.2477","kind":"arxiv","version":1}},"canonical_sha256":"070380b38ab889b96fc0ba2d4da5ab43a007dd22cda6a3e60ca38aff298dbd91","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"070380b38ab889b96fc0ba2d4da5ab43a007dd22cda6a3e60ca38aff298dbd91","first_computed_at":"2026-05-18T02:19:08.769203Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:08.769203Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jmhmwWCaURO/kB/RW0XqAAB7YKsD0Vn1v7nu8LR9V2wqwXHEHkKMM6QUFk/EL3X1yNuAMRgyzrUxjbgiqsl+Cg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:08.769701Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.2477","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dc8fce0a8b0cf0a4bc1dc8fdecef20cb0306ff4ead044fae08b68dfaaa915503","sha256:246d4ffa619559f63879aab4eebf791018f47a8146f93f8bf4581286d44d1ac5"],"state_sha256":"ecd18dcd4efbba78692bcac11d60858c158fd6847955e328d1f3cfbd78cbd51b"}