{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:R4QMHLW4I6JZXGKJDBS56F5G5U","short_pith_number":"pith:R4QMHLW4","canonical_record":{"source":{"id":"1711.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-21T04:40:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c7375a0936651df678d3f818d34d5d9926721d5d0523a48d0b96c66ec656ce82","abstract_canon_sha256":"9de092f7912c8c4e25cbcf01c3149c617ad73ddc8177cb2acf7898003956c45a"},"schema_version":"1.0"},"canonical_sha256":"8f20c3aedc47939b99491865df17a6ed0721d4b9e06792ca325775ff23d39021","source":{"kind":"arxiv","id":"1711.07631","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07631","created_at":"2026-05-18T00:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07631v2","created_at":"2026-05-18T00:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07631","created_at":"2026-05-18T00:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"R4QMHLW4I6JZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4QMHLW4I6JZXGKJ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4QMHLW4","created_at":"2026-05-18T12:31:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:R4QMHLW4I6JZXGKJDBS56F5G5U","target":"record","payload":{"canonical_record":{"source":{"id":"1711.07631","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-21T04:40:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c7375a0936651df678d3f818d34d5d9926721d5d0523a48d0b96c66ec656ce82","abstract_canon_sha256":"9de092f7912c8c4e25cbcf01c3149c617ad73ddc8177cb2acf7898003956c45a"},"schema_version":"1.0"},"canonical_sha256":"8f20c3aedc47939b99491865df17a6ed0721d4b9e06792ca325775ff23d39021","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:13:05.051268Z","signature_b64":"Yxpfcw8bSs5/6M2bzEgBI0CRXuVIZ71i06BPP9/AAEr527wua6Alxy0e+b0NCx49KOKIDakPIE+robxEMcE7Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f20c3aedc47939b99491865df17a6ed0721d4b9e06792ca325775ff23d39021","last_reissued_at":"2026-05-18T00:13:05.050662Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:13:05.050662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.07631","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":"2026-05-18T00:13:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"8bBI3glGnNLesXPU/NfqxMxbgBexxc9xM5laC0hXAEvhR8rdq2hJUP7Pu+RfKxDEXM2vB2ZtPIwo17IP4qivBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:28:15.624688Z"},"content_sha256":"c75107ad213178e5ec44f56511a41ee6e428c0fd918773dd0077806b3a7e665f","schema_version":"1.0","event_id":"sha256:c75107ad213178e5ec44f56511a41ee6e428c0fd918773dd0077806b3a7e665f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:R4QMHLW4I6JZXGKJDBS56F5G5U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Bounds on Fractional Repetition Codes using Hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Krishna Gopal Benerjee, Manish K Gupta","submitted_at":"2017-11-21T04:40:17Z","abstract_excerpt":"In the \\textit{Distributed Storage Systems} (DSSs), an encoded fraction of information is stored in the distributed fashion on different chunk servers. Recently a new paradigm of \\textit{Fractional Repetition} (FR) codes have been introduced, in which, encoded data information is stored on distributed servers, where encoding is done using a \\textit{Maximum Distance Separable} (MDS) code and a smart replication of packets. In this work, we have shown that an FR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07631","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":""},"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":"2026-05-18T00:13:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pw71Xnbx/S1DlpVhJCZYmey29IZq8mMFY7t4/aXjEvPnA5NNHJ2SZw2UPmkFgdMiNfn8VdVBdx8qIHlE/pe2Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T18:28:15.625375Z"},"content_sha256":"3f60525c3ab0eab3efe657ef59a03afa502bff435f4bff581580290c029f314a","schema_version":"1.0","event_id":"sha256:3f60525c3ab0eab3efe657ef59a03afa502bff435f4bff581580290c029f314a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/R4QMHLW4I6JZXGKJDBS56F5G5U/bundle.json","state_url":"https://pith.science/pith/R4QMHLW4I6JZXGKJDBS56F5G5U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/R4QMHLW4I6JZXGKJDBS56F5G5U/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":"2026-05-31T18:28:15Z","links":{"resolver":"https://pith.science/pith/R4QMHLW4I6JZXGKJDBS56F5G5U","bundle":"https://pith.science/pith/R4QMHLW4I6JZXGKJDBS56F5G5U/bundle.json","state":"https://pith.science/pith/R4QMHLW4I6JZXGKJDBS56F5G5U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/R4QMHLW4I6JZXGKJDBS56F5G5U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:R4QMHLW4I6JZXGKJDBS56F5G5U","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":"9de092f7912c8c4e25cbcf01c3149c617ad73ddc8177cb2acf7898003956c45a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-21T04:40:17Z","title_canon_sha256":"c7375a0936651df678d3f818d34d5d9926721d5d0523a48d0b96c66ec656ce82"},"schema_version":"1.0","source":{"id":"1711.07631","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.07631","created_at":"2026-05-18T00:13:05Z"},{"alias_kind":"arxiv_version","alias_value":"1711.07631v2","created_at":"2026-05-18T00:13:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.07631","created_at":"2026-05-18T00:13:05Z"},{"alias_kind":"pith_short_12","alias_value":"R4QMHLW4I6JZ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_16","alias_value":"R4QMHLW4I6JZXGKJ","created_at":"2026-05-18T12:31:39Z"},{"alias_kind":"pith_short_8","alias_value":"R4QMHLW4","created_at":"2026-05-18T12:31:39Z"}],"graph_snapshots":[{"event_id":"sha256:3f60525c3ab0eab3efe657ef59a03afa502bff435f4bff581580290c029f314a","target":"graph","created_at":"2026-05-18T00:13:05Z","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 the \\textit{Distributed Storage Systems} (DSSs), an encoded fraction of information is stored in the distributed fashion on different chunk servers. Recently a new paradigm of \\textit{Fractional Repetition} (FR) codes have been introduced, in which, encoded data information is stored on distributed servers, where encoding is done using a \\textit{Maximum Distance Separable} (MDS) code and a smart replication of packets. In this work, we have shown that an FR code is equivalent to a hypergraph. Using the correspondence, the properties and the bounds of a hypergraph are directly mapped to the ","authors_text":"Krishna Gopal Benerjee, Manish K Gupta","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-21T04:40:17Z","title":"Bounds on Fractional Repetition Codes using Hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.07631","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:c75107ad213178e5ec44f56511a41ee6e428c0fd918773dd0077806b3a7e665f","target":"record","created_at":"2026-05-18T00:13:05Z","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":"9de092f7912c8c4e25cbcf01c3149c617ad73ddc8177cb2acf7898003956c45a","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-21T04:40:17Z","title_canon_sha256":"c7375a0936651df678d3f818d34d5d9926721d5d0523a48d0b96c66ec656ce82"},"schema_version":"1.0","source":{"id":"1711.07631","kind":"arxiv","version":2}},"canonical_sha256":"8f20c3aedc47939b99491865df17a6ed0721d4b9e06792ca325775ff23d39021","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8f20c3aedc47939b99491865df17a6ed0721d4b9e06792ca325775ff23d39021","first_computed_at":"2026-05-18T00:13:05.050662Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:13:05.050662Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Yxpfcw8bSs5/6M2bzEgBI0CRXuVIZ71i06BPP9/AAEr527wua6Alxy0e+b0NCx49KOKIDakPIE+robxEMcE7Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:13:05.051268Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.07631","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c75107ad213178e5ec44f56511a41ee6e428c0fd918773dd0077806b3a7e665f","sha256:3f60525c3ab0eab3efe657ef59a03afa502bff435f4bff581580290c029f314a"],"state_sha256":"88f3eed043fd9a3d899564726259712b48284f46928c49f873e9733f83e8052a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tkpq+j0/q1XuUTjn2LX1z+quRwBFpEVxSN+yDsMt6+FQ2G0JwuJl+FFa4FdmD1KQY6AKGNvHr/dbps//eVK+Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T18:28:15.629243Z","bundle_sha256":"e88b3d0a808686858cd5fdf8ce5cdbadb59c89cf36a7fb9d5de00a14058b0190"}}