{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:MSUYLOXBOJG33P25UGPRYELWLX","short_pith_number":"pith:MSUYLOXB","canonical_record":{"source":{"id":"1506.05558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-18T06:52:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6db9fe3d7b5622e5788bbf59db1f06aab3474a96e10bf81fb6d0b2aba7a19702","abstract_canon_sha256":"92d6e78a3af1bd98c152cd3c8f81e6f0920985b2b623b7de4eee0ec2a7315dc1"},"schema_version":"1.0"},"canonical_sha256":"64a985bae1724dbdbf5da19f1c11765dee94c4ab5f46bd21af301fe7b8bbb872","source":{"kind":"arxiv","id":"1506.05558","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05558","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05558v1","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05558","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"MSUYLOXBOJG3","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MSUYLOXBOJG33P25","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MSUYLOXB","created_at":"2026-05-18T12:29:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:MSUYLOXBOJG33P25UGPRYELWLX","target":"record","payload":{"canonical_record":{"source":{"id":"1506.05558","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-18T06:52:15Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6db9fe3d7b5622e5788bbf59db1f06aab3474a96e10bf81fb6d0b2aba7a19702","abstract_canon_sha256":"92d6e78a3af1bd98c152cd3c8f81e6f0920985b2b623b7de4eee0ec2a7315dc1"},"schema_version":"1.0"},"canonical_sha256":"64a985bae1724dbdbf5da19f1c11765dee94c4ab5f46bd21af301fe7b8bbb872","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:44:10.401543Z","signature_b64":"8hcQzN5W4p/xlHfDaaSLZTRi+nLPzRHv24l4N5wE9jsR6CT2Y83poypWAITTaqrvJdDt9TSHPOz5cn3trjmZAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"64a985bae1724dbdbf5da19f1c11765dee94c4ab5f46bd21af301fe7b8bbb872","last_reissued_at":"2026-05-18T01:44:10.400738Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:44:10.400738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1506.05558","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":"2026-05-18T01:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qYX++AwoYTDDf7nDNwtx+0BVmeYPfMcWFjmUjKCDj600O0a1mvmVo2L3aP4/q/TvVHr9EzYRZklVz3jlRycfAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:18:13.394030Z"},"content_sha256":"92ced1e0c597451409d8c27489839ffb4b9fbfd562937327dd4bce19a0c28259","schema_version":"1.0","event_id":"sha256:92ced1e0c597451409d8c27489839ffb4b9fbfd562937327dd4bce19a0c28259"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:MSUYLOXBOJG33P25UGPRYELWLX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Singleton Bound for Generalized Ferrers Diagram Rank Metric Codes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"B. Sundar Rajan, Srikanth B. Pai","submitted_at":"2015-06-18T06:52:15Z","abstract_excerpt":"In this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an upper bound presented by Etzion and Silberstein respectively. Also we introduce generalized Ferrers diagram rank metric code which is a Ferrers diagram rank metric code where the underlying rank metric code is not necessarily linear. A new Singleton bound for generalized Ferrers diagram rank metric code is obtained using our technique."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05558","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":"2026-05-18T01:44:10Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h5SliWjfx1/T01mjJ8MFyW2ayy7z0WDvwwDPpCmKyTmjmakz0raqk49vslKHQBLNBYbv1VGZpRMR9A4xOzqmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T18:18:13.394389Z"},"content_sha256":"8e351b831a04184dd86422d8977fe72370783dee7e8cc3824677a482a4cf7b71","schema_version":"1.0","event_id":"sha256:8e351b831a04184dd86422d8977fe72370783dee7e8cc3824677a482a4cf7b71"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/MSUYLOXBOJG33P25UGPRYELWLX/bundle.json","state_url":"https://pith.science/pith/MSUYLOXBOJG33P25UGPRYELWLX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/MSUYLOXBOJG33P25UGPRYELWLX/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":"2026-06-04T18:18:13Z","links":{"resolver":"https://pith.science/pith/MSUYLOXBOJG33P25UGPRYELWLX","bundle":"https://pith.science/pith/MSUYLOXBOJG33P25UGPRYELWLX/bundle.json","state":"https://pith.science/pith/MSUYLOXBOJG33P25UGPRYELWLX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/MSUYLOXBOJG33P25UGPRYELWLX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:MSUYLOXBOJG33P25UGPRYELWLX","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":"92d6e78a3af1bd98c152cd3c8f81e6f0920985b2b623b7de4eee0ec2a7315dc1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-18T06:52:15Z","title_canon_sha256":"6db9fe3d7b5622e5788bbf59db1f06aab3474a96e10bf81fb6d0b2aba7a19702"},"schema_version":"1.0","source":{"id":"1506.05558","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.05558","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"arxiv_version","alias_value":"1506.05558v1","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.05558","created_at":"2026-05-18T01:44:10Z"},{"alias_kind":"pith_short_12","alias_value":"MSUYLOXBOJG3","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_16","alias_value":"MSUYLOXBOJG33P25","created_at":"2026-05-18T12:29:32Z"},{"alias_kind":"pith_short_8","alias_value":"MSUYLOXB","created_at":"2026-05-18T12:29:32Z"}],"graph_snapshots":[{"event_id":"sha256:8e351b831a04184dd86422d8977fe72370783dee7e8cc3824677a482a4cf7b71","target":"graph","created_at":"2026-05-18T01:44:10Z","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 this paper, we will employ the technique used in the proof of classical Singleton bound to derive upper bounds for rank metric codes and Ferrers diagram rank metric codes. These upper bounds yield the rank distance Singleton bound and an upper bound presented by Etzion and Silberstein respectively. Also we introduce generalized Ferrers diagram rank metric code which is a Ferrers diagram rank metric code where the underlying rank metric code is not necessarily linear. A new Singleton bound for generalized Ferrers diagram rank metric code is obtained using our technique.","authors_text":"B. Sundar Rajan, Srikanth B. Pai","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-18T06:52:15Z","title":"A Singleton Bound for Generalized Ferrers Diagram Rank Metric Codes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.05558","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":"sha256:92ced1e0c597451409d8c27489839ffb4b9fbfd562937327dd4bce19a0c28259","target":"record","created_at":"2026-05-18T01:44:10Z","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":"92d6e78a3af1bd98c152cd3c8f81e6f0920985b2b623b7de4eee0ec2a7315dc1","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-06-18T06:52:15Z","title_canon_sha256":"6db9fe3d7b5622e5788bbf59db1f06aab3474a96e10bf81fb6d0b2aba7a19702"},"schema_version":"1.0","source":{"id":"1506.05558","kind":"arxiv","version":1}},"canonical_sha256":"64a985bae1724dbdbf5da19f1c11765dee94c4ab5f46bd21af301fe7b8bbb872","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"64a985bae1724dbdbf5da19f1c11765dee94c4ab5f46bd21af301fe7b8bbb872","first_computed_at":"2026-05-18T01:44:10.400738Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:44:10.400738Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8hcQzN5W4p/xlHfDaaSLZTRi+nLPzRHv24l4N5wE9jsR6CT2Y83poypWAITTaqrvJdDt9TSHPOz5cn3trjmZAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:44:10.401543Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.05558","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:92ced1e0c597451409d8c27489839ffb4b9fbfd562937327dd4bce19a0c28259","sha256:8e351b831a04184dd86422d8977fe72370783dee7e8cc3824677a482a4cf7b71"],"state_sha256":"e66ce221a0cff1b14e831b255cbe89ffc14128abb5a4e3e8903518d1b101f3d3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aX5e6xHWf/qfFXPBf4nAtXJBTby8o8DW+zunFQJsJMjiqaYL1HapoFC7bWtFrqdCxdh0msCihyoBi/a4low4CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T18:18:13.396540Z","bundle_sha256":"16a2aa4382e9a9ca43374a8c32eb6bad577edd48db2b4f5203822b8bac4840f3"}}