{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:TLRNLIXJIOPKJDCENSL6NIXN2N","short_pith_number":"pith:TLRNLIXJ","canonical_record":{"source":{"id":"0910.2263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-10-12T22:32:39Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d1a155c2a2800b21aee1dd0405e8b3ec9d235e1569975185714a0d3089a090fd","abstract_canon_sha256":"8ef7d4a0a7643dfa3d7f0d7aba6adc3799a675efce848b57aaf147967d2939a5"},"schema_version":"1.0"},"canonical_sha256":"9ae2d5a2e9439ea48c446c97e6a2edd34415595f664d65391403b6fbf8751741","source":{"kind":"arxiv","id":"0910.2263","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2263","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2263v2","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2263","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"TLRNLIXJIOPK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TLRNLIXJIOPKJDCE","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TLRNLIXJ","created_at":"2026-05-18T12:26:01Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:TLRNLIXJIOPKJDCENSL6NIXN2N","target":"record","payload":{"canonical_record":{"source":{"id":"0910.2263","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-10-12T22:32:39Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"d1a155c2a2800b21aee1dd0405e8b3ec9d235e1569975185714a0d3089a090fd","abstract_canon_sha256":"8ef7d4a0a7643dfa3d7f0d7aba6adc3799a675efce848b57aaf147967d2939a5"},"schema_version":"1.0"},"canonical_sha256":"9ae2d5a2e9439ea48c446c97e6a2edd34415595f664d65391403b6fbf8751741","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:59:11.184683Z","signature_b64":"cT2xhj/7En/AsxY4MudKc88EW9VOoxHEu7qIB+bEK2MWzXxEae8NUwL/gozp3q7M4Yhg/8zVyRpR6uK0NNSqCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ae2d5a2e9439ea48c446c97e6a2edd34415595f664d65391403b6fbf8751741","last_reissued_at":"2026-05-18T00:59:11.184097Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:59:11.184097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0910.2263","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":"2026-05-18T00:59:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QFDDudjH02MHCB3YRTGA84a7DLNY47XSjh3yjGO82ExM77a44HSAH5+Z4ce/AUO1tHwVZ7EMXAAD/eI7eQCHDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T23:47:55.803913Z"},"content_sha256":"ca539f4a2b428a0c577b189848a355c0a4412ccff22f928ae0793c891137e921","schema_version":"1.0","event_id":"sha256:ca539f4a2b428a0c577b189848a355c0a4412ccff22f928ae0793c891137e921"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:TLRNLIXJIOPKJDCENSL6NIXN2N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Aditya Ramamoorthy, Muriel Medard, Shurui Huang","submitted_at":"2009-10-12T22:32:39Z","abstract_excerpt":"Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2263","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":"2026-05-18T00:59:11Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"s4pXp4XVaO89DgK9mmo2w/1WfXaj3BdqGToj6QdEIfbdq1BOsytRb/JyIFVnzd7vZbfms83gNq7hk/b2Fy/ZDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-24T23:47:55.804283Z"},"content_sha256":"7ce3fd3767890f6a638bf88fd62aebb9ef3f2a93ad3773468bea6fca933ba083","schema_version":"1.0","event_id":"sha256:7ce3fd3767890f6a638bf88fd62aebb9ef3f2a93ad3773468bea6fca933ba083"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/TLRNLIXJIOPKJDCENSL6NIXN2N/bundle.json","state_url":"https://pith.science/pith/TLRNLIXJIOPKJDCENSL6NIXN2N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/TLRNLIXJIOPKJDCENSL6NIXN2N/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":"2026-05-24T23:47:55Z","links":{"resolver":"https://pith.science/pith/TLRNLIXJIOPKJDCENSL6NIXN2N","bundle":"https://pith.science/pith/TLRNLIXJIOPKJDCENSL6NIXN2N/bundle.json","state":"https://pith.science/pith/TLRNLIXJIOPKJDCENSL6NIXN2N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/TLRNLIXJIOPKJDCENSL6NIXN2N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:TLRNLIXJIOPKJDCENSL6NIXN2N","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":"8ef7d4a0a7643dfa3d7f0d7aba6adc3799a675efce848b57aaf147967d2939a5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-10-12T22:32:39Z","title_canon_sha256":"d1a155c2a2800b21aee1dd0405e8b3ec9d235e1569975185714a0d3089a090fd"},"schema_version":"1.0","source":{"id":"0910.2263","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0910.2263","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"arxiv_version","alias_value":"0910.2263v2","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0910.2263","created_at":"2026-05-18T00:59:11Z"},{"alias_kind":"pith_short_12","alias_value":"TLRNLIXJIOPK","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_16","alias_value":"TLRNLIXJIOPKJDCE","created_at":"2026-05-18T12:26:01Z"},{"alias_kind":"pith_short_8","alias_value":"TLRNLIXJ","created_at":"2026-05-18T12:26:01Z"}],"graph_snapshots":[{"event_id":"sha256:7ce3fd3767890f6a638bf88fd62aebb9ef3f2a93ad3773468bea6fca933ba083","target":"graph","created_at":"2026-05-18T00:59:11Z","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":"Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of","authors_text":"Aditya Ramamoorthy, Muriel Medard, Shurui Huang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-10-12T22:32:39Z","title":"Minimum cost mirror sites using network coding: Replication vs. coding at the source nodes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0910.2263","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:ca539f4a2b428a0c577b189848a355c0a4412ccff22f928ae0793c891137e921","target":"record","created_at":"2026-05-18T00:59:11Z","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":"8ef7d4a0a7643dfa3d7f0d7aba6adc3799a675efce848b57aaf147967d2939a5","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2009-10-12T22:32:39Z","title_canon_sha256":"d1a155c2a2800b21aee1dd0405e8b3ec9d235e1569975185714a0d3089a090fd"},"schema_version":"1.0","source":{"id":"0910.2263","kind":"arxiv","version":2}},"canonical_sha256":"9ae2d5a2e9439ea48c446c97e6a2edd34415595f664d65391403b6fbf8751741","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"9ae2d5a2e9439ea48c446c97e6a2edd34415595f664d65391403b6fbf8751741","first_computed_at":"2026-05-18T00:59:11.184097Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:11.184097Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cT2xhj/7En/AsxY4MudKc88EW9VOoxHEu7qIB+bEK2MWzXxEae8NUwL/gozp3q7M4Yhg/8zVyRpR6uK0NNSqCg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:11.184683Z","signed_message":"canonical_sha256_bytes"},"source_id":"0910.2263","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca539f4a2b428a0c577b189848a355c0a4412ccff22f928ae0793c891137e921","sha256:7ce3fd3767890f6a638bf88fd62aebb9ef3f2a93ad3773468bea6fca933ba083"],"state_sha256":"0ed977dafd6bc254cd39fcd6725002bf0e462f94f5fb5936f1823968011ca1e5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W/2HzKLC4Q61OW3ZFJbLElymSXfBZOJ8sfnQxd+qq+egIoas6YXhelQ3B3xn/j7amXPND75aKu+j3W3YnO/MDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-24T23:47:55.806888Z","bundle_sha256":"0c55e47fd2da700a746f830c7464c7511cd95348d42ccd695918be9c73749f6d"}}