{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:N7Y6UGW4AUOKUNYRLN5MHIPAFR","short_pith_number":"pith:N7Y6UGW4","canonical_record":{"source":{"id":"1601.08190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-29T16:48:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"382124662800c407f8e522c18005305754f4346affec253fcebac85164ecd30f","abstract_canon_sha256":"1615732d27ba3795f9cdf5c69e231d7c57b4f96008fa06e02b9a87a4a917a381"},"schema_version":"1.0"},"canonical_sha256":"6ff1ea1adc051caa37115b7ac3a1e02c7e8258eca4d82b5b391f931fc7a474aa","source":{"kind":"arxiv","id":"1601.08190","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08190","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08190v1","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08190","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"N7Y6UGW4AUOK","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7Y6UGW4AUOKUNYR","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7Y6UGW4","created_at":"2026-05-18T12:30:32Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:N7Y6UGW4AUOKUNYRLN5MHIPAFR","target":"record","payload":{"canonical_record":{"source":{"id":"1601.08190","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-29T16:48:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"382124662800c407f8e522c18005305754f4346affec253fcebac85164ecd30f","abstract_canon_sha256":"1615732d27ba3795f9cdf5c69e231d7c57b4f96008fa06e02b9a87a4a917a381"},"schema_version":"1.0"},"canonical_sha256":"6ff1ea1adc051caa37115b7ac3a1e02c7e8258eca4d82b5b391f931fc7a474aa","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:21:40.128673Z","signature_b64":"ymYCFWBv6WtUnoXfZLqmWu8VVVFtAt9N2xyg29l42rk88LLOhVqiKK10PNNayolPOzu06DGJnPIlf5abKc2WBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6ff1ea1adc051caa37115b7ac3a1e02c7e8258eca4d82b5b391f931fc7a474aa","last_reissued_at":"2026-05-18T01:21:40.128171Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:21:40.128171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.08190","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":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TqzBOe5GshwQIuXncX0y0FIkT7TqI8w32xQJUrjjj1Lx8xwk19kdU+0otTys05R9VpM79iJuS/3ii1BKFHlhDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:12:44.138580Z"},"content_sha256":"b9f8d2bca4532574c111ae71478290d8c74e864b68fe2a5e725156f751cc690b","schema_version":"1.0","event_id":"sha256:b9f8d2bca4532574c111ae71478290d8c74e864b68fe2a5e725156f751cc690b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:N7Y6UGW4AUOKUNYRLN5MHIPAFR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On MBR codes with replication","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"M. Nikhil Krishnan, P. Vijay Kumar","submitted_at":"2016-01-29T16:48:58Z","abstract_excerpt":"An early paper by Rashmi et. al. presented the construction of an $(n,k,d=n-1)$ MBR regenerating code featuring the inherent double replication of all code symbols and repair-by-transfer (RBT), both of which are important in practice. We first show that no MBR code can contain even a single code symbol that is replicated more than twice. We then go on to present two new families of MBR codes which feature double replication of all systematic message symbols. The codes also possess a set of $d$ nodes whose contents include the message symbols and which can be repaired through help-by-transfer ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08190","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":"2026-05-18T01:21:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nj25wAUGa7TrLWSvcaLa2t+naaPE2R9tMzKc+PAb5dArg5F9GQD71LhgIxLnLaUPnR1kZriYyzhN40A0LiZjDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T21:12:44.139267Z"},"content_sha256":"dbcc8bdf78020015ede818577600ee12dd34c6942c8d473dfde3554c80923ab6","schema_version":"1.0","event_id":"sha256:dbcc8bdf78020015ede818577600ee12dd34c6942c8d473dfde3554c80923ab6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/N7Y6UGW4AUOKUNYRLN5MHIPAFR/bundle.json","state_url":"https://pith.science/pith/N7Y6UGW4AUOKUNYRLN5MHIPAFR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/N7Y6UGW4AUOKUNYRLN5MHIPAFR/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":"2026-05-30T21:12:44Z","links":{"resolver":"https://pith.science/pith/N7Y6UGW4AUOKUNYRLN5MHIPAFR","bundle":"https://pith.science/pith/N7Y6UGW4AUOKUNYRLN5MHIPAFR/bundle.json","state":"https://pith.science/pith/N7Y6UGW4AUOKUNYRLN5MHIPAFR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/N7Y6UGW4AUOKUNYRLN5MHIPAFR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:N7Y6UGW4AUOKUNYRLN5MHIPAFR","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":"1615732d27ba3795f9cdf5c69e231d7c57b4f96008fa06e02b9a87a4a917a381","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-29T16:48:58Z","title_canon_sha256":"382124662800c407f8e522c18005305754f4346affec253fcebac85164ecd30f"},"schema_version":"1.0","source":{"id":"1601.08190","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.08190","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"arxiv_version","alias_value":"1601.08190v1","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.08190","created_at":"2026-05-18T01:21:40Z"},{"alias_kind":"pith_short_12","alias_value":"N7Y6UGW4AUOK","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_16","alias_value":"N7Y6UGW4AUOKUNYR","created_at":"2026-05-18T12:30:32Z"},{"alias_kind":"pith_short_8","alias_value":"N7Y6UGW4","created_at":"2026-05-18T12:30:32Z"}],"graph_snapshots":[{"event_id":"sha256:dbcc8bdf78020015ede818577600ee12dd34c6942c8d473dfde3554c80923ab6","target":"graph","created_at":"2026-05-18T01:21:40Z","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":"An early paper by Rashmi et. al. presented the construction of an $(n,k,d=n-1)$ MBR regenerating code featuring the inherent double replication of all code symbols and repair-by-transfer (RBT), both of which are important in practice. We first show that no MBR code can contain even a single code symbol that is replicated more than twice. We then go on to present two new families of MBR codes which feature double replication of all systematic message symbols. The codes also possess a set of $d$ nodes whose contents include the message symbols and which can be repaired through help-by-transfer (","authors_text":"M. Nikhil Krishnan, P. Vijay Kumar","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-29T16:48:58Z","title":"On MBR codes with replication"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.08190","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:b9f8d2bca4532574c111ae71478290d8c74e864b68fe2a5e725156f751cc690b","target":"record","created_at":"2026-05-18T01:21:40Z","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":"1615732d27ba3795f9cdf5c69e231d7c57b4f96008fa06e02b9a87a4a917a381","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-29T16:48:58Z","title_canon_sha256":"382124662800c407f8e522c18005305754f4346affec253fcebac85164ecd30f"},"schema_version":"1.0","source":{"id":"1601.08190","kind":"arxiv","version":1}},"canonical_sha256":"6ff1ea1adc051caa37115b7ac3a1e02c7e8258eca4d82b5b391f931fc7a474aa","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6ff1ea1adc051caa37115b7ac3a1e02c7e8258eca4d82b5b391f931fc7a474aa","first_computed_at":"2026-05-18T01:21:40.128171Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:21:40.128171Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ymYCFWBv6WtUnoXfZLqmWu8VVVFtAt9N2xyg29l42rk88LLOhVqiKK10PNNayolPOzu06DGJnPIlf5abKc2WBw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:21:40.128673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.08190","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b9f8d2bca4532574c111ae71478290d8c74e864b68fe2a5e725156f751cc690b","sha256:dbcc8bdf78020015ede818577600ee12dd34c6942c8d473dfde3554c80923ab6"],"state_sha256":"85b7dda81aaf39d57a7f9df0b22b4ab36fd2a8c92b933334b78a166955a38255"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QkxSA3gdbkoQulef5M/d3H8vvVCUZxipz2B76Vt9y+DLguy/mKoA9wy8Y9gdzmVgwFEiO5vT6XWa59RxTWyoAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T21:12:44.143075Z","bundle_sha256":"cbe6756f87bdb45f083d847e1de101868e0a113003b84a6c6101324c57396f07"}}