{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2024:H6QUDAWW2EX3PKP6N25RAGUJQV","short_pith_number":"pith:H6QUDAWW","canonical_record":{"source":{"id":"2409.16753","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-09-25T09:04:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9a5becf8c00b9092e10baf03b43c3307c5e76b775ac011fb4b3ca8d69469f528","abstract_canon_sha256":"74a55d87a1cf932dd0efa00dfeff873b788b0bdbd5109c8f9f5a3c82fa2f593e"},"schema_version":"1.0"},"canonical_sha256":"3fa14182d6d12fb7a9fe6ebb101a898569079e3f0b9dfab50f719fec25abbdf5","source":{"kind":"arxiv","id":"2409.16753","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16753","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16753v2","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16753","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"pith_short_12","alias_value":"H6QUDAWW2EX3","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"pith_short_16","alias_value":"H6QUDAWW2EX3PKP6","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"pith_short_8","alias_value":"H6QUDAWW","created_at":"2026-07-05T11:49:04Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2024:H6QUDAWW2EX3PKP6N25RAGUJQV","target":"record","payload":{"canonical_record":{"source":{"id":"2409.16753","kind":"arxiv","version":2},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-09-25T09:04:20Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"9a5becf8c00b9092e10baf03b43c3307c5e76b775ac011fb4b3ca8d69469f528","abstract_canon_sha256":"74a55d87a1cf932dd0efa00dfeff873b788b0bdbd5109c8f9f5a3c82fa2f593e"},"schema_version":"1.0"},"canonical_sha256":"3fa14182d6d12fb7a9fe6ebb101a898569079e3f0b9dfab50f719fec25abbdf5","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:49:04.324942Z","signature_b64":"gfpgcSwvAQRWAEWn4EqF8HM4KiixWRgrUxGzY0y3czuT6ZdBjHNzYd+G9vV9IkPcG+uByDg1eF99PTSgw/FtAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3fa14182d6d12fb7a9fe6ebb101a898569079e3f0b9dfab50f719fec25abbdf5","last_reissued_at":"2026-07-05T11:49:04.324345Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:49:04.324345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2409.16753","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T11:49:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FnJdadqGTe/54aVB2j17Q7+20UOpXsnqdHX+VCZPoQwoWHR0xLNb0moNY3C3tatIqZeLMsiFB8BXrbLQ261VAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T13:44:45.903268Z"},"content_sha256":"75951dddb6c0e87d77007c63fe63c5b11410cdf60513cfb0c2de6485861abf30","schema_version":"1.0","event_id":"sha256:75951dddb6c0e87d77007c63fe63c5b11410cdf60513cfb0c2de6485861abf30"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2024:H6QUDAWW2EX3PKP6N25RAGUJQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Perfect Hermitian rank-metric codes","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Usman Mushrraf","submitted_at":"2024-09-25T09:04:20Z","abstract_excerpt":"This study investigates Hermitian rank-metric codes, a special class of rank-metric codes, focusing on perfect codes and on the analysis of their covering properties. Firstly, we establish bounds on the size of spheres in the space of Hermitian matrices and, as a consequence, we show that non-trivial perfect codes do not exist in the Hermitian case. We conclude the paper by examining their covering density."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16753","kind":"arxiv","version":2},"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/2409.16753/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":"2026-07-05T11:49:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SHI0Skt1FdZiLG2vIifp1vkdwYhTKJhgjixwEB7rToMelh1WubiN2qgl+ID5Ox0vGlBWaxsr2i7PBdEuQBuzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-11T13:44:45.903894Z"},"content_sha256":"17fa161f14e65d75854a78c1a3359eaa3af512e02558e84b39616579afcedc72","schema_version":"1.0","event_id":"sha256:17fa161f14e65d75854a78c1a3359eaa3af512e02558e84b39616579afcedc72"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H6QUDAWW2EX3PKP6N25RAGUJQV/bundle.json","state_url":"https://pith.science/pith/H6QUDAWW2EX3PKP6N25RAGUJQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H6QUDAWW2EX3PKP6N25RAGUJQV/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":"2026-08-11T13:44:45Z","links":{"resolver":"https://pith.science/pith/H6QUDAWW2EX3PKP6N25RAGUJQV","bundle":"https://pith.science/pith/H6QUDAWW2EX3PKP6N25RAGUJQV/bundle.json","state":"https://pith.science/pith/H6QUDAWW2EX3PKP6N25RAGUJQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H6QUDAWW2EX3PKP6N25RAGUJQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2024:H6QUDAWW2EX3PKP6N25RAGUJQV","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":"74a55d87a1cf932dd0efa00dfeff873b788b0bdbd5109c8f9f5a3c82fa2f593e","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-09-25T09:04:20Z","title_canon_sha256":"9a5becf8c00b9092e10baf03b43c3307c5e76b775ac011fb4b3ca8d69469f528"},"schema_version":"1.0","source":{"id":"2409.16753","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2409.16753","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"arxiv_version","alias_value":"2409.16753v2","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2409.16753","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"pith_short_12","alias_value":"H6QUDAWW2EX3","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"pith_short_16","alias_value":"H6QUDAWW2EX3PKP6","created_at":"2026-07-05T11:49:04Z"},{"alias_kind":"pith_short_8","alias_value":"H6QUDAWW","created_at":"2026-07-05T11:49:04Z"}],"graph_snapshots":[{"event_id":"sha256:17fa161f14e65d75854a78c1a3359eaa3af512e02558e84b39616579afcedc72","target":"graph","created_at":"2026-07-05T11:49:04Z","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/2409.16753/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This study investigates Hermitian rank-metric codes, a special class of rank-metric codes, focusing on perfect codes and on the analysis of their covering properties. Firstly, we establish bounds on the size of spheres in the space of Hermitian matrices and, as a consequence, we show that non-trivial perfect codes do not exist in the Hermitian case. We conclude the paper by examining their covering density.","authors_text":"Usman Mushrraf","cross_cats":["math.IT"],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-09-25T09:04:20Z","title":"Perfect Hermitian rank-metric codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.16753","kind":"arxiv","version":2},"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":"sha256:75951dddb6c0e87d77007c63fe63c5b11410cdf60513cfb0c2de6485861abf30","target":"record","created_at":"2026-07-05T11:49:04Z","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":"74a55d87a1cf932dd0efa00dfeff873b788b0bdbd5109c8f9f5a3c82fa2f593e","cross_cats_sorted":["math.IT"],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"cs.IT","submitted_at":"2024-09-25T09:04:20Z","title_canon_sha256":"9a5becf8c00b9092e10baf03b43c3307c5e76b775ac011fb4b3ca8d69469f528"},"schema_version":"1.0","source":{"id":"2409.16753","kind":"arxiv","version":2}},"canonical_sha256":"3fa14182d6d12fb7a9fe6ebb101a898569079e3f0b9dfab50f719fec25abbdf5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3fa14182d6d12fb7a9fe6ebb101a898569079e3f0b9dfab50f719fec25abbdf5","first_computed_at":"2026-07-05T11:49:04.324345Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:49:04.324345Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gfpgcSwvAQRWAEWn4EqF8HM4KiixWRgrUxGzY0y3czuT6ZdBjHNzYd+G9vV9IkPcG+uByDg1eF99PTSgw/FtAg==","signature_status":"signed_v1","signed_at":"2026-07-05T11:49:04.324942Z","signed_message":"canonical_sha256_bytes"},"source_id":"2409.16753","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:75951dddb6c0e87d77007c63fe63c5b11410cdf60513cfb0c2de6485861abf30","sha256:17fa161f14e65d75854a78c1a3359eaa3af512e02558e84b39616579afcedc72"],"state_sha256":"41d83aacff249a0ed0fde102e97841ea998e0a595062bbdc753e6fe4f5e7e746"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t0IC/I5eli0PzWDKgu5nNoPJQF9UfS2PBBc5xtWU4d0XlChCMG2G3hK7cviU+n4TWJqHq01NhnjGaa2r0UZuBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-11T13:44:45.908712Z","bundle_sha256":"5b6807a77dbfcf2e5e3975454e927afcfe34921e2775ef9e156b4c2eebf464ef"}}