{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:LL2ROZJEIDHH3EJUIOMF55LMWR","short_pith_number":"pith:LL2ROZJE","canonical_record":{"source":{"id":"1304.3156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-10T21:59:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f583e61b2083d9795661fed24c5333e43e21e8b909fc97d1c23f025bb62e70e","abstract_canon_sha256":"25132347cc635d8b1a3ee762c7fdacfd54cbb4532808c5401401046078b214c6"},"schema_version":"1.0"},"canonical_sha256":"5af517652440ce7d913443985ef56cb441625cb022e0320ce4fe9f3c2b080fb6","source":{"kind":"arxiv","id":"1304.3156","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3156","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3156v2","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3156","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"LL2ROZJEIDHH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LL2ROZJEIDHH3EJU","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LL2ROZJE","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:LL2ROZJEIDHH3EJUIOMF55LMWR","target":"record","payload":{"canonical_record":{"source":{"id":"1304.3156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-10T21:59:17Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3f583e61b2083d9795661fed24c5333e43e21e8b909fc97d1c23f025bb62e70e","abstract_canon_sha256":"25132347cc635d8b1a3ee762c7fdacfd54cbb4532808c5401401046078b214c6"},"schema_version":"1.0"},"canonical_sha256":"5af517652440ce7d913443985ef56cb441625cb022e0320ce4fe9f3c2b080fb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:28:16.851333Z","signature_b64":"OrRN/spytQeWs0OpJo4/xJnE9yxROhvKFCpA6hBsRhwWveoixrUpDQ5VnJFUcsP03Cf9ClxVJaNXNPxCaoLZDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5af517652440ce7d913443985ef56cb441625cb022e0320ce4fe9f3c2b080fb6","last_reissued_at":"2026-05-18T03:28:16.850827Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:28:16.850827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1304.3156","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":"2026-05-18T03:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"qRi3Q7/AbXZO8p8ieOV7gyk+8+bTa0AmrRhRS0cDdt622euQ0CyY7k4zGtajQqw1Io6byuON0bJN5ceUYObECA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:04:08.695931Z"},"content_sha256":"c5a599eb83513b4a07a249db45a196cbb77794dcef7f8dc3ee0271e7aba15a53","schema_version":"1.0","event_id":"sha256:c5a599eb83513b4a07a249db45a196cbb77794dcef7f8dc3ee0271e7aba15a53"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:LL2ROZJEIDHH3EJUIOMF55LMWR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Data Secrecy in Distributed Storage Systems under Exact Repair","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"H. Vincent Poor, Robert Calderbank, Salim El Rouayheb, Sreechakra Goparaju","submitted_at":"2013-04-10T21:59:17Z","abstract_excerpt":"The problem of securing data against eavesdropping in distributed storage systems is studied. The focus is on systems that use linear codes and implement exact repair to recover from node failures.The maximum file size that can be stored securely is determined for systems in which all the available nodes help in repair (i.e., repair degree $d=n-1$, where $n$ is the total number of nodes) and for any number of compromised nodes. Similar results in the literature are restricted to the case of at most two compromised nodes. Moreover, new explicit upper bounds are given on the maximum secure file "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3156","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":"2026-05-18T03:28:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Aiq8Elck2QdoRMQJprXfkPHHbIgWravyb1gqS4e3a3DFVAEEo/z9GdSLWEdepSCIBAa1TDh14S0MY5rvC79xAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T21:04:08.696724Z"},"content_sha256":"435f1f65eeb74eb074ddc0cc397a4c64a4dec33f55eab9de51aaabc67fe06ff7","schema_version":"1.0","event_id":"sha256:435f1f65eeb74eb074ddc0cc397a4c64a4dec33f55eab9de51aaabc67fe06ff7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LL2ROZJEIDHH3EJUIOMF55LMWR/bundle.json","state_url":"https://pith.science/pith/LL2ROZJEIDHH3EJUIOMF55LMWR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LL2ROZJEIDHH3EJUIOMF55LMWR/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":"2026-06-07T21:04:08Z","links":{"resolver":"https://pith.science/pith/LL2ROZJEIDHH3EJUIOMF55LMWR","bundle":"https://pith.science/pith/LL2ROZJEIDHH3EJUIOMF55LMWR/bundle.json","state":"https://pith.science/pith/LL2ROZJEIDHH3EJUIOMF55LMWR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LL2ROZJEIDHH3EJUIOMF55LMWR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LL2ROZJEIDHH3EJUIOMF55LMWR","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":"25132347cc635d8b1a3ee762c7fdacfd54cbb4532808c5401401046078b214c6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-10T21:59:17Z","title_canon_sha256":"3f583e61b2083d9795661fed24c5333e43e21e8b909fc97d1c23f025bb62e70e"},"schema_version":"1.0","source":{"id":"1304.3156","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1304.3156","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"arxiv_version","alias_value":"1304.3156v2","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.3156","created_at":"2026-05-18T03:28:16Z"},{"alias_kind":"pith_short_12","alias_value":"LL2ROZJEIDHH","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LL2ROZJEIDHH3EJU","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LL2ROZJE","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:435f1f65eeb74eb074ddc0cc397a4c64a4dec33f55eab9de51aaabc67fe06ff7","target":"graph","created_at":"2026-05-18T03:28:16Z","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":"The problem of securing data against eavesdropping in distributed storage systems is studied. The focus is on systems that use linear codes and implement exact repair to recover from node failures.The maximum file size that can be stored securely is determined for systems in which all the available nodes help in repair (i.e., repair degree $d=n-1$, where $n$ is the total number of nodes) and for any number of compromised nodes. Similar results in the literature are restricted to the case of at most two compromised nodes. Moreover, new explicit upper bounds are given on the maximum secure file ","authors_text":"H. Vincent Poor, Robert Calderbank, Salim El Rouayheb, Sreechakra Goparaju","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-10T21:59:17Z","title":"Data Secrecy in Distributed Storage Systems under Exact Repair"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.3156","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:c5a599eb83513b4a07a249db45a196cbb77794dcef7f8dc3ee0271e7aba15a53","target":"record","created_at":"2026-05-18T03:28:16Z","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":"25132347cc635d8b1a3ee762c7fdacfd54cbb4532808c5401401046078b214c6","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-04-10T21:59:17Z","title_canon_sha256":"3f583e61b2083d9795661fed24c5333e43e21e8b909fc97d1c23f025bb62e70e"},"schema_version":"1.0","source":{"id":"1304.3156","kind":"arxiv","version":2}},"canonical_sha256":"5af517652440ce7d913443985ef56cb441625cb022e0320ce4fe9f3c2b080fb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5af517652440ce7d913443985ef56cb441625cb022e0320ce4fe9f3c2b080fb6","first_computed_at":"2026-05-18T03:28:16.850827Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:28:16.850827Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OrRN/spytQeWs0OpJo4/xJnE9yxROhvKFCpA6hBsRhwWveoixrUpDQ5VnJFUcsP03Cf9ClxVJaNXNPxCaoLZDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:28:16.851333Z","signed_message":"canonical_sha256_bytes"},"source_id":"1304.3156","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c5a599eb83513b4a07a249db45a196cbb77794dcef7f8dc3ee0271e7aba15a53","sha256:435f1f65eeb74eb074ddc0cc397a4c64a4dec33f55eab9de51aaabc67fe06ff7"],"state_sha256":"ea061d8a8c692a16fe9c914d5847d218c7f50b31c4b37c404543578d659e1594"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HoyYKCm6tSywBfFCbihQr+AEFR24uowpb0QWNRFHffzQ8B2UpfTVjZj79GGbBUXNnE7Kg1582BXXLic6rkfzDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T21:04:08.701084Z","bundle_sha256":"8c12b2f81794d7f6473d8329d1a6015d7ae6d8504c40b9823e43e833f9200343"}}