{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2026:64RDPLJL5VYHYFNNZUJZICP7YE","short_pith_number":"pith:64RDPLJL","canonical_record":{"source":{"id":"2608.10922","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-11T13:48:28Z","cross_cats_sorted":["math.IT","quant-ph"],"title_canon_sha256":"8026c4956b94d78ba28519175056a05a000df9d65ab9245b8bae06ad5349ed76","abstract_canon_sha256":"48c06191f1e6ed2bfd0840ce243ff8e2bf714fae1711563374d2d3af9f3804cc"},"schema_version":"1.0"},"canonical_sha256":"f72237ad2bed707c15adcd139409ffc10782628d5627f4716e2b60a891ca104f","source":{"kind":"arxiv","id":"2608.10922","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10922","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10922v1","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10922","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"64RDPLJL5VYH","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"pith_short_16","alias_value":"64RDPLJL5VYHYFNN","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"pith_short_8","alias_value":"64RDPLJL","created_at":"2026-08-12T01:23:49Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2026:64RDPLJL5VYHYFNNZUJZICP7YE","target":"record","payload":{"canonical_record":{"source":{"id":"2608.10922","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-11T13:48:28Z","cross_cats_sorted":["math.IT","quant-ph"],"title_canon_sha256":"8026c4956b94d78ba28519175056a05a000df9d65ab9245b8bae06ad5349ed76","abstract_canon_sha256":"48c06191f1e6ed2bfd0840ce243ff8e2bf714fae1711563374d2d3af9f3804cc"},"schema_version":"1.0"},"canonical_sha256":"f72237ad2bed707c15adcd139409ffc10782628d5627f4716e2b60a891ca104f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-08-12T01:23:49.517422Z","signature_b64":"c3XJZ+Bd5xO3Butvar7ruNhC3BZzR45bgxiWo0G5fpJ5sGMsc6XmL2HyzLEooLJGeVcbPhi78l5r1jjhw03lDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f72237ad2bed707c15adcd139409ffc10782628d5627f4716e2b60a891ca104f","last_reissued_at":"2026-08-12T01:23:49.515810Z","signature_status":"signed_v1","first_computed_at":"2026-08-12T01:23:49.515810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2608.10922","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":"2026-08-12T01:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"54OudGB1P3lSe+2A53x9avkwMU7rmqOpFvvQfHehK0F695S3a6m7TTbLV9Hsu82g/Ii+G8LnMcWOAJ6onkBSDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:28:49.756377Z"},"content_sha256":"799b169f40bbc16842cdfcb4d69bda358f347ae75e1690c5486fc3a64e54568d","schema_version":"1.0","event_id":"sha256:799b169f40bbc16842cdfcb4d69bda358f347ae75e1690c5486fc3a64e54568d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2026:64RDPLJL5VYHYFNNZUJZICP7YE","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds for Pure Disjoint $(r,\\delta)$-Quantum Locally Recoverable Codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT","quant-ph"],"primary_cat":"cs.IT","authors_text":"Evagoras Stylianou, Holger Boche","submitted_at":"2026-08-11T13:48:28Z","abstract_excerpt":"We study pure disjoint $(r,\\delta)$-quantum locally recoverable codes (qLRCs) without assuming a stabilizer structure. We formulate local Knill--Laflamme conditions for recovery from up to $\\delta-1$ erasures within a recovery block, and introduce blockwise Shor--Laflamme and unitary weight enumerators that capture how error weight is distributed across recovery sets. We establish several properties of these enumerators and use them to derive a Singleton-like bound that strengthens the known bound for disjoint $(r,\\delta)$-qLRCs under a purity assumption, as well as a linear-programming upper "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10922","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/2608.10922/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":"2026-08-12T01:23:49Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wUS4J1NdgkR8D19Ukd3u4r7DHIvQp/7H3Wy5+c8DUuqRj5IJ9LT11Kl8GUSxd4eEDaK/1VYaFB/blCcAjjOeDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-14T17:28:49.756931Z"},"content_sha256":"e69ee3a6602da8c7bcc53a46c809f0f8e1f30a83a9adabd4a8fae0a67bd622e2","schema_version":"1.0","event_id":"sha256:e69ee3a6602da8c7bcc53a46c809f0f8e1f30a83a9adabd4a8fae0a67bd622e2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/64RDPLJL5VYHYFNNZUJZICP7YE/bundle.json","state_url":"https://pith.science/pith/64RDPLJL5VYHYFNNZUJZICP7YE/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/64RDPLJL5VYHYFNNZUJZICP7YE/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":"2026-08-14T17:28:49Z","links":{"resolver":"https://pith.science/pith/64RDPLJL5VYHYFNNZUJZICP7YE","bundle":"https://pith.science/pith/64RDPLJL5VYHYFNNZUJZICP7YE/bundle.json","state":"https://pith.science/pith/64RDPLJL5VYHYFNNZUJZICP7YE/state.json","well_known_bundle":"https://pith.science/.well-known/pith/64RDPLJL5VYHYFNNZUJZICP7YE/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2026:64RDPLJL5VYHYFNNZUJZICP7YE","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":"48c06191f1e6ed2bfd0840ce243ff8e2bf714fae1711563374d2d3af9f3804cc","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-11T13:48:28Z","title_canon_sha256":"8026c4956b94d78ba28519175056a05a000df9d65ab9245b8bae06ad5349ed76"},"schema_version":"1.0","source":{"id":"2608.10922","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2608.10922","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"arxiv_version","alias_value":"2608.10922v1","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2608.10922","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"pith_short_12","alias_value":"64RDPLJL5VYH","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"pith_short_16","alias_value":"64RDPLJL5VYHYFNN","created_at":"2026-08-12T01:23:49Z"},{"alias_kind":"pith_short_8","alias_value":"64RDPLJL","created_at":"2026-08-12T01:23:49Z"}],"graph_snapshots":[{"event_id":"sha256:e69ee3a6602da8c7bcc53a46c809f0f8e1f30a83a9adabd4a8fae0a67bd622e2","target":"graph","created_at":"2026-08-12T01:23:49Z","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/2608.10922/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study pure disjoint $(r,\\delta)$-quantum locally recoverable codes (qLRCs) without assuming a stabilizer structure. We formulate local Knill--Laflamme conditions for recovery from up to $\\delta-1$ erasures within a recovery block, and introduce blockwise Shor--Laflamme and unitary weight enumerators that capture how error weight is distributed across recovery sets. We establish several properties of these enumerators and use them to derive a Singleton-like bound that strengthens the known bound for disjoint $(r,\\delta)$-qLRCs under a purity assumption, as well as a linear-programming upper ","authors_text":"Evagoras Stylianou, Holger Boche","cross_cats":["math.IT","quant-ph"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-11T13:48:28Z","title":"Bounds for Pure Disjoint $(r,\\delta)$-Quantum Locally Recoverable Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2608.10922","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":"sha256:799b169f40bbc16842cdfcb4d69bda358f347ae75e1690c5486fc3a64e54568d","target":"record","created_at":"2026-08-12T01:23:49Z","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":"48c06191f1e6ed2bfd0840ce243ff8e2bf714fae1711563374d2d3af9f3804cc","cross_cats_sorted":["math.IT","quant-ph"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2026-08-11T13:48:28Z","title_canon_sha256":"8026c4956b94d78ba28519175056a05a000df9d65ab9245b8bae06ad5349ed76"},"schema_version":"1.0","source":{"id":"2608.10922","kind":"arxiv","version":1}},"canonical_sha256":"f72237ad2bed707c15adcd139409ffc10782628d5627f4716e2b60a891ca104f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f72237ad2bed707c15adcd139409ffc10782628d5627f4716e2b60a891ca104f","first_computed_at":"2026-08-12T01:23:49.515810Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-08-12T01:23:49.515810Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"c3XJZ+Bd5xO3Butvar7ruNhC3BZzR45bgxiWo0G5fpJ5sGMsc6XmL2HyzLEooLJGeVcbPhi78l5r1jjhw03lDw==","signature_status":"signed_v1","signed_at":"2026-08-12T01:23:49.517422Z","signed_message":"canonical_sha256_bytes"},"source_id":"2608.10922","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:799b169f40bbc16842cdfcb4d69bda358f347ae75e1690c5486fc3a64e54568d","sha256:e69ee3a6602da8c7bcc53a46c809f0f8e1f30a83a9adabd4a8fae0a67bd622e2"],"state_sha256":"6ad7cd39a68d11862a32ebfe20463e66ccf60953cfa4ca7b4b674a08619f2ad8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6ZJ+mmVNJJjV+nzoJeg2pdBxIyuimmrQcrqN5rsHrPptXNXWhidJGZxgl6GmG0f1Z6UD5rEHobxsZ5FnsaE3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-14T17:28:49.765534Z","bundle_sha256":"8042c23de44dec58c93d1e946361628e6238c87cf3c5698cff731475adab5f68"}}