{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:M6WEVLT5V57ZDM7XRCCZYFV6C3","short_pith_number":"pith:M6WEVLT5","canonical_record":{"source":{"id":"1401.5168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-21T03:36:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c23444decba427272df977a40e877da62cca97c0e9040ff7954be3aa6ca6c6b1","abstract_canon_sha256":"b32540cd6b229acf8915634bc94aee1ce6f5959c43a0862598cdffe06966dcf2"},"schema_version":"1.0"},"canonical_sha256":"67ac4aae7daf7f91b3f788859c16be16d77c3d5317ac4744de57d773081f1078","source":{"kind":"arxiv","id":"1401.5168","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5168","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5168v1","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5168","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"M6WEVLT5V57Z","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M6WEVLT5V57ZDM7X","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M6WEVLT5","created_at":"2026-05-18T12:28:38Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:M6WEVLT5V57ZDM7XRCCZYFV6C3","target":"record","payload":{"canonical_record":{"source":{"id":"1401.5168","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-21T03:36:07Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"c23444decba427272df977a40e877da62cca97c0e9040ff7954be3aa6ca6c6b1","abstract_canon_sha256":"b32540cd6b229acf8915634bc94aee1ce6f5959c43a0862598cdffe06966dcf2"},"schema_version":"1.0"},"canonical_sha256":"67ac4aae7daf7f91b3f788859c16be16d77c3d5317ac4744de57d773081f1078","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:01:34.653665Z","signature_b64":"yXjWshkC2dF3GHZ5fC3UpM1vIUg7b9nMp3EVYBCWVmxIU+pzhWWeOoxUi76L9nteZ+3k7DvMRbwQIRjKhQ3ABA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"67ac4aae7daf7f91b3f788859c16be16d77c3d5317ac4744de57d773081f1078","last_reissued_at":"2026-05-18T03:01:34.652746Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:01:34.652746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1401.5168","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":"2026-05-18T03:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"biMB4M684NI+U8Cw8S10jcZWpGntOAiJQVrrOVyJWmWDKrw3gBsS2/NPKQX8aHRbJvAI1SJ1ZmuLKj1hT9wABg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:53:54.755878Z"},"content_sha256":"5379a76bfbde85503ffec5ad4affe5b1bf7e1f2a28a0b77d37e0f555d4c7062a","schema_version":"1.0","event_id":"sha256:5379a76bfbde85503ffec5ad4affe5b1bf7e1f2a28a0b77d37e0f555d4c7062a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:M6WEVLT5V57ZDM7XRCCZYFV6C3","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distributed Storage Schemes over Unidirectional Ring Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Fang-Wei Fu, Jiyong Lu, Xuan Guang","submitted_at":"2014-01-21T03:36:07Z","abstract_excerpt":"In this paper, we study distributed storage problems over unidirectional ring networks. A lower bound on the reconstructing bandwidth to recover total original data for each user is proposed, and it is achievable for arbitrary parameters. If a distributed storage scheme can achieve this lower bound with equality for each user, we say it an optimal reconstructing distributed storage scheme (ORDSS). Furthermore, the repair problem for a failed storage node in ORDSSes is under consideration and a tight lower bound on the repair bandwidth for each storage node is obtained. Particularly, we indicat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5168","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":"2026-05-18T03:01:34Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tBwXQ7TWQTxJhz9t4L2/j130cMcdlsywepXZAVj0IBZgOv7h9aHGbXWfWv5D8Al9s1/QubcfynkI8yapBQLcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-27T06:53:54.756217Z"},"content_sha256":"db6fcecff89b27ecc8d123c12462d8f9cbe6a4b7883fde58b3b321feec3bbc76","schema_version":"1.0","event_id":"sha256:db6fcecff89b27ecc8d123c12462d8f9cbe6a4b7883fde58b3b321feec3bbc76"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M6WEVLT5V57ZDM7XRCCZYFV6C3/bundle.json","state_url":"https://pith.science/pith/M6WEVLT5V57ZDM7XRCCZYFV6C3/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M6WEVLT5V57ZDM7XRCCZYFV6C3/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":"2026-06-27T06:53:54Z","links":{"resolver":"https://pith.science/pith/M6WEVLT5V57ZDM7XRCCZYFV6C3","bundle":"https://pith.science/pith/M6WEVLT5V57ZDM7XRCCZYFV6C3/bundle.json","state":"https://pith.science/pith/M6WEVLT5V57ZDM7XRCCZYFV6C3/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M6WEVLT5V57ZDM7XRCCZYFV6C3/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:M6WEVLT5V57ZDM7XRCCZYFV6C3","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":"b32540cd6b229acf8915634bc94aee1ce6f5959c43a0862598cdffe06966dcf2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-21T03:36:07Z","title_canon_sha256":"c23444decba427272df977a40e877da62cca97c0e9040ff7954be3aa6ca6c6b1"},"schema_version":"1.0","source":{"id":"1401.5168","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1401.5168","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"arxiv_version","alias_value":"1401.5168v1","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1401.5168","created_at":"2026-05-18T03:01:34Z"},{"alias_kind":"pith_short_12","alias_value":"M6WEVLT5V57Z","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_16","alias_value":"M6WEVLT5V57ZDM7X","created_at":"2026-05-18T12:28:38Z"},{"alias_kind":"pith_short_8","alias_value":"M6WEVLT5","created_at":"2026-05-18T12:28:38Z"}],"graph_snapshots":[{"event_id":"sha256:db6fcecff89b27ecc8d123c12462d8f9cbe6a4b7883fde58b3b321feec3bbc76","target":"graph","created_at":"2026-05-18T03:01:34Z","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 study distributed storage problems over unidirectional ring networks. A lower bound on the reconstructing bandwidth to recover total original data for each user is proposed, and it is achievable for arbitrary parameters. If a distributed storage scheme can achieve this lower bound with equality for each user, we say it an optimal reconstructing distributed storage scheme (ORDSS). Furthermore, the repair problem for a failed storage node in ORDSSes is under consideration and a tight lower bound on the repair bandwidth for each storage node is obtained. Particularly, we indicat","authors_text":"Fang-Wei Fu, Jiyong Lu, Xuan Guang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-21T03:36:07Z","title":"Distributed Storage Schemes over Unidirectional Ring Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5168","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":"sha256:5379a76bfbde85503ffec5ad4affe5b1bf7e1f2a28a0b77d37e0f555d4c7062a","target":"record","created_at":"2026-05-18T03:01:34Z","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":"b32540cd6b229acf8915634bc94aee1ce6f5959c43a0862598cdffe06966dcf2","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2014-01-21T03:36:07Z","title_canon_sha256":"c23444decba427272df977a40e877da62cca97c0e9040ff7954be3aa6ca6c6b1"},"schema_version":"1.0","source":{"id":"1401.5168","kind":"arxiv","version":1}},"canonical_sha256":"67ac4aae7daf7f91b3f788859c16be16d77c3d5317ac4744de57d773081f1078","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"67ac4aae7daf7f91b3f788859c16be16d77c3d5317ac4744de57d773081f1078","first_computed_at":"2026-05-18T03:01:34.652746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:01:34.652746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"yXjWshkC2dF3GHZ5fC3UpM1vIUg7b9nMp3EVYBCWVmxIU+pzhWWeOoxUi76L9nteZ+3k7DvMRbwQIRjKhQ3ABA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:01:34.653665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1401.5168","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5379a76bfbde85503ffec5ad4affe5b1bf7e1f2a28a0b77d37e0f555d4c7062a","sha256:db6fcecff89b27ecc8d123c12462d8f9cbe6a4b7883fde58b3b321feec3bbc76"],"state_sha256":"a69e97fd4dd8aa12ea470056cdbdc853138bd4a59fa3cc011a8ff4cc299b8e1f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"3gPQv3Q1JZLsxLN8StFCzrjSgfhK1d1c7iTFe+4/GHUrFR4Hmj31hO/Gw0Xq2TYflOTs5Pw2jBTkvDTh4PXaDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-27T06:53:54.758028Z","bundle_sha256":"be2c98e8adf7f8bed6cf9ba2db026caa134e0b9a09683df5db7e5ba100e662c0"}}