{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:RBTDIIZFBA7IWBWYWD72R3JI7R","short_pith_number":"pith:RBTDIIZF","canonical_record":{"source":{"id":"1403.7933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:57Z","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"title_canon_sha256":"1edce5abdc55a41f15b2f99c0bb4bd5ce21f4eb6ddf0d4b524b63e0ebab9062c","abstract_canon_sha256":"d968285e4c7abe8d4d45263c741da769a9580ef79eba4dfbc22584af060e252c"},"schema_version":"1.0"},"canonical_sha256":"8866342325083e8b06d8b0ffa8ed28fc50d81e3082cc993cc111f0bda0668d31","source":{"kind":"arxiv","id":"1403.7933","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7933","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7933v1","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7933","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"RBTDIIZFBA7I","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RBTDIIZFBA7IWBWY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RBTDIIZF","created_at":"2026-05-18T12:28:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:RBTDIIZFBA7IWBWYWD72R3JI7R","target":"record","payload":{"canonical_record":{"source":{"id":"1403.7933","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:57Z","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"title_canon_sha256":"1edce5abdc55a41f15b2f99c0bb4bd5ce21f4eb6ddf0d4b524b63e0ebab9062c","abstract_canon_sha256":"d968285e4c7abe8d4d45263c741da769a9580ef79eba4dfbc22584af060e252c"},"schema_version":"1.0"},"canonical_sha256":"8866342325083e8b06d8b0ffa8ed28fc50d81e3082cc993cc111f0bda0668d31","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:55:12.109966Z","signature_b64":"z2aNSGCxqIh8dlWH0WGTw9XEp58v3++OzYlyRCi/RewoSknRGYdjCfsAIIBlNjf799HlY5MyH4/Yq4CHTHinAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8866342325083e8b06d8b0ffa8ed28fc50d81e3082cc993cc111f0bda0668d31","last_reissued_at":"2026-05-18T02:55:12.109504Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:55:12.109504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.7933","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"AVCXqYgRX6rclEmU/rLL8/BJUKP4TS2ZdS4ZQPkeP7Zl8DXRn04X6suzDpJ0icB/Z6tGUmgcjz8wAQVPmxS0Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:21:35.997326Z"},"content_sha256":"7277fe90a04c1f42f6419e6e887b2cb391800ced7a0ce73ef9562729306a21e9","schema_version":"1.0","event_id":"sha256:7277fe90a04c1f42f6419e6e887b2cb391800ced7a0ce73ef9562729306a21e9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:RBTDIIZFBA7IWBWYWD72R3JI7R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Additive codes over $GF(4)$ from circulant graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","cs.IT","math.IT"],"primary_cat":"math.CO","authors_text":"Meiqin Wei, Ruihu Li, Xueliang Li, Yaping Mao","submitted_at":"2014-03-31T09:58:57Z","abstract_excerpt":"In $2006$, Danielsen and Parker \\cite{DP} proved that every self-dual additive code over $GF(4)$ is equivalent to a graph code. So, graph is an important tool for searching (proposed) optimum codes. In this paper, we introduce a new method of searching (proposed) optimum additive codes from circulant graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7933","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:55:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+6J5lyrlc6QY5B9qYVac7+cMEF/lAkHCFrUEpdaMJUc9BmilCCBVZyWLQFw2PolvhV2E8ElNj0HFv9e0V0X1CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T15:21:35.997680Z"},"content_sha256":"f60c6a5e0d64b04ceabf51fda46e6fa0be81a351fc142d5850f7bd58524ca5dc","schema_version":"1.0","event_id":"sha256:f60c6a5e0d64b04ceabf51fda46e6fa0be81a351fc142d5850f7bd58524ca5dc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RBTDIIZFBA7IWBWYWD72R3JI7R/bundle.json","state_url":"https://pith.science/pith/RBTDIIZFBA7IWBWYWD72R3JI7R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RBTDIIZFBA7IWBWYWD72R3JI7R/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-01T15:21:35Z","links":{"resolver":"https://pith.science/pith/RBTDIIZFBA7IWBWYWD72R3JI7R","bundle":"https://pith.science/pith/RBTDIIZFBA7IWBWYWD72R3JI7R/bundle.json","state":"https://pith.science/pith/RBTDIIZFBA7IWBWYWD72R3JI7R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RBTDIIZFBA7IWBWYWD72R3JI7R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RBTDIIZFBA7IWBWYWD72R3JI7R","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":"d968285e4c7abe8d4d45263c741da769a9580ef79eba4dfbc22584af060e252c","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:57Z","title_canon_sha256":"1edce5abdc55a41f15b2f99c0bb4bd5ce21f4eb6ddf0d4b524b63e0ebab9062c"},"schema_version":"1.0","source":{"id":"1403.7933","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.7933","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"arxiv_version","alias_value":"1403.7933v1","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.7933","created_at":"2026-05-18T02:55:12Z"},{"alias_kind":"pith_short_12","alias_value":"RBTDIIZFBA7I","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RBTDIIZFBA7IWBWY","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RBTDIIZF","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:f60c6a5e0d64b04ceabf51fda46e6fa0be81a351fc142d5850f7bd58524ca5dc","target":"graph","created_at":"2026-05-18T02:55:12Z","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":"In $2006$, Danielsen and Parker \\cite{DP} proved that every self-dual additive code over $GF(4)$ is equivalent to a graph code. So, graph is an important tool for searching (proposed) optimum codes. In this paper, we introduce a new method of searching (proposed) optimum additive codes from circulant graphs.","authors_text":"Meiqin Wei, Ruihu Li, Xueliang Li, Yaping Mao","cross_cats":["cs.DM","cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:57Z","title":"Additive codes over $GF(4)$ from circulant graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.7933","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":"sha256:7277fe90a04c1f42f6419e6e887b2cb391800ced7a0ce73ef9562729306a21e9","target":"record","created_at":"2026-05-18T02:55:12Z","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":"d968285e4c7abe8d4d45263c741da769a9580ef79eba4dfbc22584af060e252c","cross_cats_sorted":["cs.DM","cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-03-31T09:58:57Z","title_canon_sha256":"1edce5abdc55a41f15b2f99c0bb4bd5ce21f4eb6ddf0d4b524b63e0ebab9062c"},"schema_version":"1.0","source":{"id":"1403.7933","kind":"arxiv","version":1}},"canonical_sha256":"8866342325083e8b06d8b0ffa8ed28fc50d81e3082cc993cc111f0bda0668d31","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8866342325083e8b06d8b0ffa8ed28fc50d81e3082cc993cc111f0bda0668d31","first_computed_at":"2026-05-18T02:55:12.109504Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:55:12.109504Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"z2aNSGCxqIh8dlWH0WGTw9XEp58v3++OzYlyRCi/RewoSknRGYdjCfsAIIBlNjf799HlY5MyH4/Yq4CHTHinAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:55:12.109966Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.7933","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7277fe90a04c1f42f6419e6e887b2cb391800ced7a0ce73ef9562729306a21e9","sha256:f60c6a5e0d64b04ceabf51fda46e6fa0be81a351fc142d5850f7bd58524ca5dc"],"state_sha256":"fc85a184e8323404f9c81b9d6a54beeb5f9bbf6cea1d684e9e2a253eb6800739"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lTJqpoGFETr+nkYuIIfEfjl5KZHzWET9ccwCWfkScdbv5EElvAh+e/R4ZpSfBinn2O3vV9s5XAqjPY7dL5w/Dw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T15:21:35.999624Z","bundle_sha256":"a0744410b3307d252f3aa12195d98d68ab760d6aac901b6a664e4704417abde3"}}