{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:T6S3FUMSUNH63NJ5OJB6TA33E3","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":"d262b73d47f6612fdc9d98473f74c0f79faed136a1cc1cf591351f14762a829b","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-16T12:47:48Z","title_canon_sha256":"0aede2b49e30626369e63e382e32ae9664a3133fdb07b25577ac62a26a3b163f"},"schema_version":"1.0","source":{"id":"1612.05447","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.05447","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"arxiv_version","alias_value":"1612.05447v1","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.05447","created_at":"2026-05-18T00:54:51Z"},{"alias_kind":"pith_short_12","alias_value":"T6S3FUMSUNH6","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_16","alias_value":"T6S3FUMSUNH63NJ5","created_at":"2026-05-18T12:30:44Z"},{"alias_kind":"pith_short_8","alias_value":"T6S3FUMS","created_at":"2026-05-18T12:30:44Z"}],"graph_snapshots":[{"event_id":"sha256:6552db86fd5785606d1dd73cdabb9293620df61db74c2e58ba13a8b9f7df68eb","target":"graph","created_at":"2026-05-18T00:54:51Z","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 study the problem of classifying deep holes of Reed-Solomon codes. We show that this problem is equivalent to the problem of classifying MDS extensions of Reed-Solomon codes by one digit. This equivalence allows us to improve recent results on the former problem. In particular, we classify deep holes of Reed-Solomon codes of dimension greater than half the alphabet size.\n  We also give a complete classification of deep holes of Reed Solomon codes with redundancy three in all dimensions.","authors_text":"Krishna Kaipa","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-16T12:47:48Z","title":"Deep holes and MDS extensions of Reed-Solomon codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.05447","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:c43a24a96a835fa3b33df171b37d11362dc33606357c60215e7bc299040cd08d","target":"record","created_at":"2026-05-18T00:54:51Z","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":"d262b73d47f6612fdc9d98473f74c0f79faed136a1cc1cf591351f14762a829b","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-16T12:47:48Z","title_canon_sha256":"0aede2b49e30626369e63e382e32ae9664a3133fdb07b25577ac62a26a3b163f"},"schema_version":"1.0","source":{"id":"1612.05447","kind":"arxiv","version":1}},"canonical_sha256":"9fa5b2d192a34fedb53d7243e9837b26fff132f58ae96d332b5373f68ab9bbe5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9fa5b2d192a34fedb53d7243e9837b26fff132f58ae96d332b5373f68ab9bbe5","first_computed_at":"2026-05-18T00:54:51.762500Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:54:51.762500Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JrV/XP8ION/TyBVnJbU6dQ/4s6yCkJQ/aunqn6GdJTgseX9sI+d83eQNPAbsAc+VIOePlR6Do3qrzMZISqt4Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:54:51.763126Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.05447","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c43a24a96a835fa3b33df171b37d11362dc33606357c60215e7bc299040cd08d","sha256:6552db86fd5785606d1dd73cdabb9293620df61db74c2e58ba13a8b9f7df68eb"],"state_sha256":"c74fc0d252f84ea7a5696b334ff2d572bbc867528d82e85f6b148df746b85e3c"}