{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:SWFMVIZYITF7A4LNBFVMRDGDKQ","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":"5695d88413adda0b6e61bb022ba304d6ea0290cb1e156b814dc1d200b0716e62","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-03T16:30:58Z","title_canon_sha256":"0f750660fb3e1fb69e0e87c28718136c806046539547989e2b668cb20e03410d"},"schema_version":"1.0","source":{"id":"1508.00481","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.00481","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"arxiv_version","alias_value":"1508.00481v1","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.00481","created_at":"2026-05-18T01:35:57Z"},{"alias_kind":"pith_short_12","alias_value":"SWFMVIZYITF7","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_16","alias_value":"SWFMVIZYITF7A4LN","created_at":"2026-05-18T12:29:42Z"},{"alias_kind":"pith_short_8","alias_value":"SWFMVIZY","created_at":"2026-05-18T12:29:42Z"}],"graph_snapshots":[{"event_id":"sha256:dfdbbb62b0f592b001428d8edf4edbb85369bb7d5ec7b25f70dd9ab3c3e303af","target":"graph","created_at":"2026-05-18T01:35:57Z","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":"Test response compaction for integrated circuits (ICs) with scan-based design-for-testability (DFT) support in the presence of unknown logic values (Xs) is investigated from a combinatorial viewpoint. The theoretical foundations of X-codes, employed in an X-tolerant compaction technique called X-compact, are examined. Through the formulation of a combinatorial model of X-compact, novel design techniques are developed for X-codes to detect a specified maximum number of errors in the presence of a specified maximum number of unknown logic values, while requiring only small fan-out. The special c","authors_text":"Charles J. Colbourn, Yuichiro Fujiwara","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-03T16:30:58Z","title":"A combinatorial approach to X-tolerant compaction circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00481","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:c23e313975dc97feb1ce96dc2c4985db87e1c0c8c1a71d738444f5ec45454df9","target":"record","created_at":"2026-05-18T01:35:57Z","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":"5695d88413adda0b6e61bb022ba304d6ea0290cb1e156b814dc1d200b0716e62","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-08-03T16:30:58Z","title_canon_sha256":"0f750660fb3e1fb69e0e87c28718136c806046539547989e2b668cb20e03410d"},"schema_version":"1.0","source":{"id":"1508.00481","kind":"arxiv","version":1}},"canonical_sha256":"958acaa33844cbf0716d096ac88cc3543a66d7d022e91e4bae8f1afc54660bcd","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"958acaa33844cbf0716d096ac88cc3543a66d7d022e91e4bae8f1afc54660bcd","first_computed_at":"2026-05-18T01:35:57.988235Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:57.988235Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WLsbqfs5t852gIscds79AGq0FGv28VTtj6zUHT/ZUcIYiy2BNNHfx43E/XMlGDY4UQRx7fb0zoBZDHPFQnqyAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:57.988799Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.00481","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c23e313975dc97feb1ce96dc2c4985db87e1c0c8c1a71d738444f5ec45454df9","sha256:dfdbbb62b0f592b001428d8edf4edbb85369bb7d5ec7b25f70dd9ab3c3e303af"],"state_sha256":"dce9aa5f4496f42808e91c9f3f270d6dfc65e75ee5c8911fd310dff440b9a267"}