{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:LOS2DAQW2TVSGW3LM6JZBSGBBA","short_pith_number":"pith:LOS2DAQW","canonical_record":{"source":{"id":"1507.01536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-06T16:45:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f2cf6f68120188a5ed85bf0ac186004bfb04d3c06301acd1746c1c28b9a33a81","abstract_canon_sha256":"d2bd842b897649bbeb12144bb3b7495b5b1a020050fea25d38eaf8474ef9c0e6"},"schema_version":"1.0"},"canonical_sha256":"5ba5a18216d4eb235b6b679390c8c108266c32b4a8fc044f8f2dc4001eaacc7a","source":{"kind":"arxiv","id":"1507.01536","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01536","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01536v1","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01536","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"LOS2DAQW2TVS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOS2DAQW2TVSGW3L","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOS2DAQW","created_at":"2026-05-18T12:29:29Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:LOS2DAQW2TVSGW3LM6JZBSGBBA","target":"record","payload":{"canonical_record":{"source":{"id":"1507.01536","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-06T16:45:17Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"f2cf6f68120188a5ed85bf0ac186004bfb04d3c06301acd1746c1c28b9a33a81","abstract_canon_sha256":"d2bd842b897649bbeb12144bb3b7495b5b1a020050fea25d38eaf8474ef9c0e6"},"schema_version":"1.0"},"canonical_sha256":"5ba5a18216d4eb235b6b679390c8c108266c32b4a8fc044f8f2dc4001eaacc7a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:16.658226Z","signature_b64":"mcisNceCiENUFxm5tFcaYSVrK2kQr5E2yPGypJufb4Voz+6ItuxLwggUhr80t//g+CQhYm7n4yH8ilegBP45DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ba5a18216d4eb235b6b679390c8c108266c32b4a8fc044f8f2dc4001eaacc7a","last_reissued_at":"2026-05-18T01:37:16.657475Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:16.657475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1507.01536","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":"2026-05-18T01:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"a9Yp5GbfCvax3aygplTC0w1WrFHVGwJoOD2XyIOj/vn6MqAzTouzvuCkY72TbmDqEGDVftArAwpURW/V8tTUAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:31:05.655417Z"},"content_sha256":"e6fb22bbf8612ac3559c92da1661b56c40f143eb72ee42b8ba6aec3bc71331b5","schema_version":"1.0","event_id":"sha256:e6fb22bbf8612ac3559c92da1661b56c40f143eb72ee42b8ba6aec3bc71331b5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:LOS2DAQW2TVSGW3LM6JZBSGBBA","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Construction of quantum codes based on self-dual orientable embeddings of complete multipartite graphs complete multipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"quant-ph","authors_text":"Avaz Naghipour, Mohammad Ali Jafarizadeh, Sedaghat Shahmorad","submitted_at":"2015-07-06T16:45:17Z","abstract_excerpt":"This paper presents four new classes of binary quantum codes with minimum dis- tance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the com- plete graphs K4r+1 and K4s and by current graphs and rotation schemes. and s are both divisible by 4."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01536","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":"2026-05-18T01:37:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YAMcUukaGnpd904f861Ebekz3xIbW0Nw42XDaP6MG4XrxSfV9e18uo3TzmVrDjmnkW15KqWAQ6o220f6+xXJBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T20:31:05.655776Z"},"content_sha256":"bc3487c336c4967babe482896dae26e9f168f42bb1bfd9605a67b1154c7bc39c","schema_version":"1.0","event_id":"sha256:bc3487c336c4967babe482896dae26e9f168f42bb1bfd9605a67b1154c7bc39c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LOS2DAQW2TVSGW3LM6JZBSGBBA/bundle.json","state_url":"https://pith.science/pith/LOS2DAQW2TVSGW3LM6JZBSGBBA/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LOS2DAQW2TVSGW3LM6JZBSGBBA/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":"2026-06-28T20:31:05Z","links":{"resolver":"https://pith.science/pith/LOS2DAQW2TVSGW3LM6JZBSGBBA","bundle":"https://pith.science/pith/LOS2DAQW2TVSGW3LM6JZBSGBBA/bundle.json","state":"https://pith.science/pith/LOS2DAQW2TVSGW3LM6JZBSGBBA/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LOS2DAQW2TVSGW3LM6JZBSGBBA/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:LOS2DAQW2TVSGW3LM6JZBSGBBA","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":"d2bd842b897649bbeb12144bb3b7495b5b1a020050fea25d38eaf8474ef9c0e6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-06T16:45:17Z","title_canon_sha256":"f2cf6f68120188a5ed85bf0ac186004bfb04d3c06301acd1746c1c28b9a33a81"},"schema_version":"1.0","source":{"id":"1507.01536","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1507.01536","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"arxiv_version","alias_value":"1507.01536v1","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1507.01536","created_at":"2026-05-18T01:37:16Z"},{"alias_kind":"pith_short_12","alias_value":"LOS2DAQW2TVS","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_16","alias_value":"LOS2DAQW2TVSGW3L","created_at":"2026-05-18T12:29:29Z"},{"alias_kind":"pith_short_8","alias_value":"LOS2DAQW","created_at":"2026-05-18T12:29:29Z"}],"graph_snapshots":[{"event_id":"sha256:bc3487c336c4967babe482896dae26e9f168f42bb1bfd9605a67b1154c7bc39c","target":"graph","created_at":"2026-05-18T01:37:16Z","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":"This paper presents four new classes of binary quantum codes with minimum dis- tance 3 and 4, namely Class-I, Class-II, Class-III and Class-IV. The classes Class-I and Class-II are constructed based on self-dual orientable embeddings of the com- plete graphs K4r+1 and K4s and by current graphs and rotation schemes. and s are both divisible by 4.","authors_text":"Avaz Naghipour, Mohammad Ali Jafarizadeh, Sedaghat Shahmorad","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-06T16:45:17Z","title":"Construction of quantum codes based on self-dual orientable embeddings of complete multipartite graphs complete multipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.01536","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:e6fb22bbf8612ac3559c92da1661b56c40f143eb72ee42b8ba6aec3bc71331b5","target":"record","created_at":"2026-05-18T01:37:16Z","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":"d2bd842b897649bbeb12144bb3b7495b5b1a020050fea25d38eaf8474ef9c0e6","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2015-07-06T16:45:17Z","title_canon_sha256":"f2cf6f68120188a5ed85bf0ac186004bfb04d3c06301acd1746c1c28b9a33a81"},"schema_version":"1.0","source":{"id":"1507.01536","kind":"arxiv","version":1}},"canonical_sha256":"5ba5a18216d4eb235b6b679390c8c108266c32b4a8fc044f8f2dc4001eaacc7a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5ba5a18216d4eb235b6b679390c8c108266c32b4a8fc044f8f2dc4001eaacc7a","first_computed_at":"2026-05-18T01:37:16.657475Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:37:16.657475Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"mcisNceCiENUFxm5tFcaYSVrK2kQr5E2yPGypJufb4Voz+6ItuxLwggUhr80t//g+CQhYm7n4yH8ilegBP45DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:37:16.658226Z","signed_message":"canonical_sha256_bytes"},"source_id":"1507.01536","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e6fb22bbf8612ac3559c92da1661b56c40f143eb72ee42b8ba6aec3bc71331b5","sha256:bc3487c336c4967babe482896dae26e9f168f42bb1bfd9605a67b1154c7bc39c"],"state_sha256":"d966358cd732d232deea929e780ff798bba896de2d2968bb542cd425549040c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"r2N3QS/74bnhwqw8AEaGC6spCrEG/iyvdgcmz3jCHE/rgsNMfMmtlQk3nRCIvYZQBJ7rl5ySSacMffmMTRexCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T20:31:05.657766Z","bundle_sha256":"c43fdb22c2c16ce97ba4378561dc91f38c3eeb7fc452c9c70d163fbe5d8ff5eb"}}