{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:NILRKBA6OLOQCGL7UI4YCPZZIJ","short_pith_number":"pith:NILRKBA6","canonical_record":{"source":{"id":"1007.1697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-10T05:01:41Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ec25bfd61084398db400104f1bbd8f8bc974920d8a0f5d9c8b2441cd793cebb2","abstract_canon_sha256":"990ae8b58b0b65d72f63d1503ddec8e898961cd02150921ab6387e9e70b5281e"},"schema_version":"1.0"},"canonical_sha256":"6a1715041e72dd01197fa239813f39425d5d3b5a08069c3d189b8094b55f17aa","source":{"kind":"arxiv","id":"1007.1697","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1697","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1697v1","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1697","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"pith_short_12","alias_value":"NILRKBA6OLOQ","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NILRKBA6OLOQCGL7","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NILRKBA6","created_at":"2026-07-04T17:31:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:NILRKBA6OLOQCGL7UI4YCPZZIJ","target":"record","payload":{"canonical_record":{"source":{"id":"1007.1697","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-10T05:01:41Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"ec25bfd61084398db400104f1bbd8f8bc974920d8a0f5d9c8b2441cd793cebb2","abstract_canon_sha256":"990ae8b58b0b65d72f63d1503ddec8e898961cd02150921ab6387e9e70b5281e"},"schema_version":"1.0"},"canonical_sha256":"6a1715041e72dd01197fa239813f39425d5d3b5a08069c3d189b8094b55f17aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:31:34.372280Z","signature_b64":"cHVkMFCog6Jdl+PeLBr9lV24oABKHpasuHycUQ36C+vfG/HZkOUg7oYGDfK8Ab/G7RjuI5izft84QMrTsY4sBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6a1715041e72dd01197fa239813f39425d5d3b5a08069c3d189b8094b55f17aa","last_reissued_at":"2026-07-04T17:31:34.371876Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:31:34.371876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1007.1697","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":"2026-07-04T17:31:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1yQ/U8x+Utn9x23ziP8j5RhShExJOBnrtO2o4XlUmrGBUmv2YMe0mgWJocdAwtY/v903fzazhoqndEqyQoHcDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:48:04.064042Z"},"content_sha256":"726afaa65d418f4da5f58ddabe44e553030bce79e9ea2eacff65decec732aba2","schema_version":"1.0","event_id":"sha256:726afaa65d418f4da5f58ddabe44e553030bce79e9ea2eacff65decec732aba2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:NILRKBA6OLOQCGL7UI4YCPZZIJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum Cyclic Code","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Piyush P Kurur, Sagarmoy Dutta","submitted_at":"2010-07-10T05:01:41Z","abstract_excerpt":"In this paper, we define and study \\emph{quantum cyclic codes}, a generalisation of cyclic codes to the quantum setting. Previously studied examples of quantum cyclic codes were all quantum codes obtained from classical cyclic codes via the CSS construction. However, the codes that we study are much more general. In particular, we construct cyclic stabiliser codes with parameters $[[5,1,3]]$, $[[17,1,7]]$ and $[[17,9,3]]$, all of which are \\emph{not} CSS. The $[[5,1,3]]$ code is the well known Laflamme code and to the best of our knowledge the other two are new examples. Our definition of cycl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1697","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1007.1697/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T17:31:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JHCHARfZHUiQpj59sSp12jhAZ9PsQhYwqh7OB5DiXzG7lS8EasiToZB5y2eo0LGXR0Cn3xGK0we7zfw6A8UBCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T11:48:04.064976Z"},"content_sha256":"bdb84b7b8159aa7f6e084e76d3a4f9f38e12faa74c4133a3bc55b9e5d01d1f4f","schema_version":"1.0","event_id":"sha256:bdb84b7b8159aa7f6e084e76d3a4f9f38e12faa74c4133a3bc55b9e5d01d1f4f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NILRKBA6OLOQCGL7UI4YCPZZIJ/bundle.json","state_url":"https://pith.science/pith/NILRKBA6OLOQCGL7UI4YCPZZIJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NILRKBA6OLOQCGL7UI4YCPZZIJ/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":"2026-08-04T11:48:04Z","links":{"resolver":"https://pith.science/pith/NILRKBA6OLOQCGL7UI4YCPZZIJ","bundle":"https://pith.science/pith/NILRKBA6OLOQCGL7UI4YCPZZIJ/bundle.json","state":"https://pith.science/pith/NILRKBA6OLOQCGL7UI4YCPZZIJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NILRKBA6OLOQCGL7UI4YCPZZIJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:NILRKBA6OLOQCGL7UI4YCPZZIJ","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":"990ae8b58b0b65d72f63d1503ddec8e898961cd02150921ab6387e9e70b5281e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-10T05:01:41Z","title_canon_sha256":"ec25bfd61084398db400104f1bbd8f8bc974920d8a0f5d9c8b2441cd793cebb2"},"schema_version":"1.0","source":{"id":"1007.1697","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.1697","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"arxiv_version","alias_value":"1007.1697v1","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.1697","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"pith_short_12","alias_value":"NILRKBA6OLOQ","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"pith_short_16","alias_value":"NILRKBA6OLOQCGL7","created_at":"2026-07-04T17:31:34Z"},{"alias_kind":"pith_short_8","alias_value":"NILRKBA6","created_at":"2026-07-04T17:31:34Z"}],"graph_snapshots":[{"event_id":"sha256:bdb84b7b8159aa7f6e084e76d3a4f9f38e12faa74c4133a3bc55b9e5d01d1f4f","target":"graph","created_at":"2026-07-04T17:31:34Z","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/1007.1697/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"In this paper, we define and study \\emph{quantum cyclic codes}, a generalisation of cyclic codes to the quantum setting. Previously studied examples of quantum cyclic codes were all quantum codes obtained from classical cyclic codes via the CSS construction. However, the codes that we study are much more general. In particular, we construct cyclic stabiliser codes with parameters $[[5,1,3]]$, $[[17,1,7]]$ and $[[17,9,3]]$, all of which are \\emph{not} CSS. The $[[5,1,3]]$ code is the well known Laflamme code and to the best of our knowledge the other two are new examples. Our definition of cycl","authors_text":"Piyush P Kurur, Sagarmoy Dutta","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-10T05:01:41Z","title":"Quantum Cyclic Code"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.1697","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":"sha256:726afaa65d418f4da5f58ddabe44e553030bce79e9ea2eacff65decec732aba2","target":"record","created_at":"2026-07-04T17:31:34Z","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":"990ae8b58b0b65d72f63d1503ddec8e898961cd02150921ab6387e9e70b5281e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2010-07-10T05:01:41Z","title_canon_sha256":"ec25bfd61084398db400104f1bbd8f8bc974920d8a0f5d9c8b2441cd793cebb2"},"schema_version":"1.0","source":{"id":"1007.1697","kind":"arxiv","version":1}},"canonical_sha256":"6a1715041e72dd01197fa239813f39425d5d3b5a08069c3d189b8094b55f17aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6a1715041e72dd01197fa239813f39425d5d3b5a08069c3d189b8094b55f17aa","first_computed_at":"2026-07-04T17:31:34.371876Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:31:34.371876Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cHVkMFCog6Jdl+PeLBr9lV24oABKHpasuHycUQ36C+vfG/HZkOUg7oYGDfK8Ab/G7RjuI5izft84QMrTsY4sBg==","signature_status":"signed_v1","signed_at":"2026-07-04T17:31:34.372280Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.1697","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:726afaa65d418f4da5f58ddabe44e553030bce79e9ea2eacff65decec732aba2","sha256:bdb84b7b8159aa7f6e084e76d3a4f9f38e12faa74c4133a3bc55b9e5d01d1f4f"],"state_sha256":"65753a57fb9edf63e5e323f487519ccffca68e3f0af175721dcf535992e8a500"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sZ2p8eZNu1rNB1I6Xst/kYMn77BQoDBtWynUwRdNxH1R/XV8Srsm56l9xQQTOiVAPY6BCQ/UCgYWofQATLa1AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T11:48:04.078198Z","bundle_sha256":"4b45b30cf2481692128de252aa02c3b083691743d77467a00fb1a1dba2e1aab1"}}