{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:RNUWZSYCEIL25XFDSGB6S7S4KS","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":"873c65e6bd916c52621bef7ffef3ee2eac2ea12b208433c6f5f5cb23bfda4df7","cross_cats_sorted":["cs.NI","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2006-06-12T15:35:01Z","title_canon_sha256":"16a9039961633c8da5afbbe2c3ad7931182113b7b523191a6e0bae39d80e8aab"},"schema_version":"1.0","source":{"id":"cs/0606049","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"cs/0606049","created_at":"2026-05-18T00:58:56Z"},{"alias_kind":"arxiv_version","alias_value":"cs/0606049v1","created_at":"2026-05-18T00:58:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.cs/0606049","created_at":"2026-05-18T00:58:56Z"},{"alias_kind":"pith_short_12","alias_value":"RNUWZSYCEIL2","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"RNUWZSYCEIL25XFD","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"RNUWZSYC","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:72cce9bfc1137b6cfc94ed1d39b26987c29f6998d87fdf16182e42ef40e8c286","target":"graph","created_at":"2026-05-18T00:58:56Z","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":"We consider the problem of constructing an erasure code for storage over a network when the data sources are distributed. Specifically, we assume that there are n storage nodes with limited memory and k<n sources generating the data. We want a data collector, who can appear anywhere in the network, to query any k storage nodes and be able to retrieve the data. We introduce Decentralized Erasure Codes, which are linear codes with a specific randomized structure inspired by network coding on random bipartite graphs. We show that decentralized erasure codes are optimally sparse, and lead to reduc","authors_text":"Alexandros G. Dimakis, Kannan Ramchandran, Vinod Prabhakaran","cross_cats":["cs.NI","math.IT"],"headline":"","license":"","primary_cat":"cs.IT","submitted_at":"2006-06-12T15:35:01Z","title":"Decentralized Erasure Codes for Distributed Networked Storage"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"cs/0606049","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":"sha256:654e298ee750d9a8f617316136dbc46b6794e9bc3e7d9e5fd246b0f22fe0bb05","target":"record","created_at":"2026-05-18T00:58:56Z","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":"873c65e6bd916c52621bef7ffef3ee2eac2ea12b208433c6f5f5cb23bfda4df7","cross_cats_sorted":["cs.NI","math.IT"],"license":"","primary_cat":"cs.IT","submitted_at":"2006-06-12T15:35:01Z","title_canon_sha256":"16a9039961633c8da5afbbe2c3ad7931182113b7b523191a6e0bae39d80e8aab"},"schema_version":"1.0","source":{"id":"cs/0606049","kind":"arxiv","version":1}},"canonical_sha256":"8b696ccb022217aedca39183e97e5c54b5494f9f47129a386db98e136b231229","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b696ccb022217aedca39183e97e5c54b5494f9f47129a386db98e136b231229","first_computed_at":"2026-05-18T00:58:56.275545Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:56.275545Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZFGue7BrbhtvBUJlge3v1FNYxI7edc6Q6MEF9AKAqzpPqKczh4xVqPtFDqoCGViJYm40M8rbysqc5IBoTCwQCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:56.276188Z","signed_message":"canonical_sha256_bytes"},"source_id":"cs/0606049","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:654e298ee750d9a8f617316136dbc46b6794e9bc3e7d9e5fd246b0f22fe0bb05","sha256:72cce9bfc1137b6cfc94ed1d39b26987c29f6998d87fdf16182e42ef40e8c286"],"state_sha256":"92584806b2015e6343fc1e78533c9b56edb3f07c136d2cd90be7b7a71f9978dc"}