{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2020:7TDFT3QANN62ON6BYBBUKPNQ4T","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":"647d8c7a74118f3a9e126c4e1bcfe73a0e707ef504b9c9813db0adea32209f7b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-04-29T14:42:48Z","title_canon_sha256":"c63f0c8dd536f6da9caba5ef09e88fd078c4bb92a7ddedcb216b587575c7e8a3"},"schema_version":"1.0","source":{"id":"2004.14241","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2004.14241","created_at":"2026-07-05T00:59:18Z"},{"alias_kind":"arxiv_version","alias_value":"2004.14241v1","created_at":"2026-07-05T00:59:18Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2004.14241","created_at":"2026-07-05T00:59:18Z"},{"alias_kind":"pith_short_12","alias_value":"7TDFT3QANN62","created_at":"2026-07-05T00:59:18Z"},{"alias_kind":"pith_short_16","alias_value":"7TDFT3QANN62ON6B","created_at":"2026-07-05T00:59:18Z"},{"alias_kind":"pith_short_8","alias_value":"7TDFT3QA","created_at":"2026-07-05T00:59:18Z"}],"graph_snapshots":[{"event_id":"sha256:3e0dd736ed624564437603ba3403c1e6057c8b380fcca2135a2d69a55562d059","target":"graph","created_at":"2026-07-05T00:59:18Z","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/2004.14241/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Constant dimension codes are e.g. used for error correction and detection in random linear network coding, so that constructions for these codes have achieved wide attention. Here, we improve over 150 lower bounds by describing better constructions for subspace distance 4.","authors_text":"Sascha Kurz","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-04-29T14:42:48Z","title":"Lifted codes and the multilevel construction for constant dimension codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2004.14241","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:caed6f00334a0fb1f6bad9633548688047fd1950db6f0dc4c8da849e0f74876e","target":"record","created_at":"2026-07-05T00:59:18Z","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":"647d8c7a74118f3a9e126c4e1bcfe73a0e707ef504b9c9813db0adea32209f7b","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2020-04-29T14:42:48Z","title_canon_sha256":"c63f0c8dd536f6da9caba5ef09e88fd078c4bb92a7ddedcb216b587575c7e8a3"},"schema_version":"1.0","source":{"id":"2004.14241","kind":"arxiv","version":1}},"canonical_sha256":"fcc659ee006b7da737c1c043453db0e4d4e88f5d3af2cecaee66a4b16f4304cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fcc659ee006b7da737c1c043453db0e4d4e88f5d3af2cecaee66a4b16f4304cf","first_computed_at":"2026-07-05T00:59:18.487196Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:59:18.487196Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"IKPeS1fhI7LvaZHR/vgbLgIAZkQXCpLhiE1+PlY55s6jBwFmL64uStxDVa5wJbgizdVVpT9Uc8Q/V+OX7SUMBw==","signature_status":"signed_v1","signed_at":"2026-07-05T00:59:18.487616Z","signed_message":"canonical_sha256_bytes"},"source_id":"2004.14241","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:caed6f00334a0fb1f6bad9633548688047fd1950db6f0dc4c8da849e0f74876e","sha256:3e0dd736ed624564437603ba3403c1e6057c8b380fcca2135a2d69a55562d059"],"state_sha256":"6e365bae9b9578ea2ff0bb588b271bc3c4e3314b3984a466589260ad6b9919f8"}