{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:BS5XN7CSEFULF4UK2DXLPOHGFM","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":"1ab2a59f5111450f00976adc205bf0bd8c46c9a4c229242f1478bddc16e47165","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-22T10:52:46Z","title_canon_sha256":"8c853c079fa5a3f0312f5841fb8d84a5f335d18246e0310b66b9f4a7be059ef2"},"schema_version":"1.0","source":{"id":"1703.07599","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1703.07599","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"arxiv_version","alias_value":"1703.07599v1","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1703.07599","created_at":"2026-05-18T00:48:06Z"},{"alias_kind":"pith_short_12","alias_value":"BS5XN7CSEFUL","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_16","alias_value":"BS5XN7CSEFULF4UK","created_at":"2026-05-18T12:31:08Z"},{"alias_kind":"pith_short_8","alias_value":"BS5XN7CS","created_at":"2026-05-18T12:31:08Z"}],"graph_snapshots":[{"event_id":"sha256:111acf765d2fbfae6fda3a2eb8021dd6e201ea1f487e23b379c451b8fb141335","target":"graph","created_at":"2026-05-18T00:48:06Z","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":"The $g$-good-neighbor conditional diagnosability is a new measure for fault diagnosis of systems. Xu et al. [Theor. Comput. Sci. 659 (2017) 53--63] determined the $g$-good-neighbor conditional diagnosability of $(n, k)$-star networks $S_{n, k}$ (i.e., $t_g(S_{n, k})$) with $1\\leq k\\leq n-1$ for $1\\leq g\\leq n-k$ under the PMC model and the MM$^*$ model. In this paper, we determine $t_g(S_{n, k})$ for all the remaining cases with $1\\leq k\\leq n-1$ for $1\\leq g\\leq n-1$ under the two models, from which we can obtain the $g$-good-neighbor conditional diagnosability of the star graph obtained by L","authors_text":"Min Xu, Yulong Wei","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-22T10:52:46Z","title":"On $g$-good-neighbor conditional diagnosability of $(n, k)$-star networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07599","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:c1aa6bb4b28301de783df1584543c012d76620889b97001a64d419ea00d393c0","target":"record","created_at":"2026-05-18T00:48:06Z","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":"1ab2a59f5111450f00976adc205bf0bd8c46c9a4c229242f1478bddc16e47165","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-03-22T10:52:46Z","title_canon_sha256":"8c853c079fa5a3f0312f5841fb8d84a5f335d18246e0310b66b9f4a7be059ef2"},"schema_version":"1.0","source":{"id":"1703.07599","kind":"arxiv","version":1}},"canonical_sha256":"0cbb76fc522168b2f28ad0eeb7b8e62b22b1090d6def85dabba30c8d95e3f9e4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0cbb76fc522168b2f28ad0eeb7b8e62b22b1090d6def85dabba30c8d95e3f9e4","first_computed_at":"2026-05-18T00:48:06.570066Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:06.570066Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lhC8Ksto1guiM1p44Z4w5NUFtmXN4d6xwHgtcEd4I0SsapSbUUbXGlBJFguqNJfc6m2OOFfG3j7g33KUbQBiAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:06.570653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.07599","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c1aa6bb4b28301de783df1584543c012d76620889b97001a64d419ea00d393c0","sha256:111acf765d2fbfae6fda3a2eb8021dd6e201ea1f487e23b379c451b8fb141335"],"state_sha256":"6c04d89ab8991ac1b9aac767ce3ad50b04e1a152762159f98908afd34246f86c"}