{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:VKNOKRNSKNSWZENLGGGYQUUJ3Z","short_pith_number":"pith:VKNOKRNS","canonical_record":{"source":{"id":"1207.6052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-25T16:52:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f18f68676d73fdbed9c500b198c3a9f35326fa5c67230c59df67ea202c6bd8b6","abstract_canon_sha256":"d86f2dc2426753578c0324cfc29aa4d52d0ba09723c69a514f9cea9aa071bfea"},"schema_version":"1.0"},"canonical_sha256":"aa9ae545b253656c91ab318d885289de42244f8a547f5f7941b128a83323cb20","source":{"kind":"arxiv","id":"1207.6052","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6052","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6052v1","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6052","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"VKNOKRNSKNSW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VKNOKRNSKNSWZENL","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VKNOKRNS","created_at":"2026-05-18T12:27:25Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:VKNOKRNSKNSWZENLGGGYQUUJ3Z","target":"record","payload":{"canonical_record":{"source":{"id":"1207.6052","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-25T16:52:42Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"f18f68676d73fdbed9c500b198c3a9f35326fa5c67230c59df67ea202c6bd8b6","abstract_canon_sha256":"d86f2dc2426753578c0324cfc29aa4d52d0ba09723c69a514f9cea9aa071bfea"},"schema_version":"1.0"},"canonical_sha256":"aa9ae545b253656c91ab318d885289de42244f8a547f5f7941b128a83323cb20","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:09.587937Z","signature_b64":"8AMcD06Fp7sm6AiIplAGhBcpnBz8eHF/jkeSuObAxEbxiJMvH6GVWe/RrQ79Xr4L5YiCD4Y3ZNzRLVoJMnoKDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa9ae545b253656c91ab318d885289de42244f8a547f5f7941b128a83323cb20","last_reissued_at":"2026-05-18T03:50:09.586967Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:09.586967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1207.6052","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":"2026-05-18T03:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W6PL0Sml1IklZ2RN/yIvQQ9Px3ngdHl7+yTfeSqzcESkOJSbuzCVj30si0qmt6ai2GkQPKZqxZTQ7hbahXVKAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:04:32.377386Z"},"content_sha256":"d1b34276ac18aafcbc40ba0e1e1987fe5e83d8e568ed780693e5cd44c72d2c21","schema_version":"1.0","event_id":"sha256:d1b34276ac18aafcbc40ba0e1e1987fe5e83d8e568ed780693e5cd44c72d2c21"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:VKNOKRNSKNSWZENLGGGYQUUJ3Z","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Coding Delay Analysis of Dense and Chunked Network Codes over Line Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Amir H. Banihashemi, Anoosheh Heidarzadeh","submitted_at":"2012-07-25T16:52:42Z","abstract_excerpt":"In this paper, we analyze the coding delay and the average coding delay of random linear network codes (a.k.a. dense codes) and chunked codes (CC), which are an attractive alternative to dense codes due to their lower complexity, over line networks with Bernoulli losses and deterministic regular or Poisson transmissions. Our results, which include upper bounds on the delay and the average delay, are (i) for dense codes, in some cases more general, and in some other cases tighter, than the existing bounds, and provide a more clear picture of the speed of convergence of dense codes to the (min-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6052","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":"2026-05-18T03:50:09Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BG/CNggUCjNQQw9RGVPrg5TqzG3yTBgWC23qmPNlImgaymGMDyAo+751URcJvw8MF9XMjUoY2H12N66jCAcdDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-20T11:04:32.377723Z"},"content_sha256":"e415fa3e3778cabd82a333477ff2e9b1395d875a243d1aa66db6c01c2c0cb9aa","schema_version":"1.0","event_id":"sha256:e415fa3e3778cabd82a333477ff2e9b1395d875a243d1aa66db6c01c2c0cb9aa"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VKNOKRNSKNSWZENLGGGYQUUJ3Z/bundle.json","state_url":"https://pith.science/pith/VKNOKRNSKNSWZENLGGGYQUUJ3Z/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VKNOKRNSKNSWZENLGGGYQUUJ3Z/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":"2026-06-20T11:04:32Z","links":{"resolver":"https://pith.science/pith/VKNOKRNSKNSWZENLGGGYQUUJ3Z","bundle":"https://pith.science/pith/VKNOKRNSKNSWZENLGGGYQUUJ3Z/bundle.json","state":"https://pith.science/pith/VKNOKRNSKNSWZENLGGGYQUUJ3Z/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VKNOKRNSKNSWZENLGGGYQUUJ3Z/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:VKNOKRNSKNSWZENLGGGYQUUJ3Z","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":"d86f2dc2426753578c0324cfc29aa4d52d0ba09723c69a514f9cea9aa071bfea","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-25T16:52:42Z","title_canon_sha256":"f18f68676d73fdbed9c500b198c3a9f35326fa5c67230c59df67ea202c6bd8b6"},"schema_version":"1.0","source":{"id":"1207.6052","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.6052","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"arxiv_version","alias_value":"1207.6052v1","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.6052","created_at":"2026-05-18T03:50:09Z"},{"alias_kind":"pith_short_12","alias_value":"VKNOKRNSKNSW","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_16","alias_value":"VKNOKRNSKNSWZENL","created_at":"2026-05-18T12:27:25Z"},{"alias_kind":"pith_short_8","alias_value":"VKNOKRNS","created_at":"2026-05-18T12:27:25Z"}],"graph_snapshots":[{"event_id":"sha256:e415fa3e3778cabd82a333477ff2e9b1395d875a243d1aa66db6c01c2c0cb9aa","target":"graph","created_at":"2026-05-18T03:50:09Z","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 analyze the coding delay and the average coding delay of random linear network codes (a.k.a. dense codes) and chunked codes (CC), which are an attractive alternative to dense codes due to their lower complexity, over line networks with Bernoulli losses and deterministic regular or Poisson transmissions. Our results, which include upper bounds on the delay and the average delay, are (i) for dense codes, in some cases more general, and in some other cases tighter, than the existing bounds, and provide a more clear picture of the speed of convergence of dense codes to the (min-c","authors_text":"Amir H. Banihashemi, Anoosheh Heidarzadeh","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-25T16:52:42Z","title":"Coding Delay Analysis of Dense and Chunked Network Codes over Line Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.6052","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:d1b34276ac18aafcbc40ba0e1e1987fe5e83d8e568ed780693e5cd44c72d2c21","target":"record","created_at":"2026-05-18T03:50:09Z","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":"d86f2dc2426753578c0324cfc29aa4d52d0ba09723c69a514f9cea9aa071bfea","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2012-07-25T16:52:42Z","title_canon_sha256":"f18f68676d73fdbed9c500b198c3a9f35326fa5c67230c59df67ea202c6bd8b6"},"schema_version":"1.0","source":{"id":"1207.6052","kind":"arxiv","version":1}},"canonical_sha256":"aa9ae545b253656c91ab318d885289de42244f8a547f5f7941b128a83323cb20","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"aa9ae545b253656c91ab318d885289de42244f8a547f5f7941b128a83323cb20","first_computed_at":"2026-05-18T03:50:09.586967Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:50:09.586967Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"8AMcD06Fp7sm6AiIplAGhBcpnBz8eHF/jkeSuObAxEbxiJMvH6GVWe/RrQ79Xr4L5YiCD4Y3ZNzRLVoJMnoKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:50:09.587937Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.6052","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d1b34276ac18aafcbc40ba0e1e1987fe5e83d8e568ed780693e5cd44c72d2c21","sha256:e415fa3e3778cabd82a333477ff2e9b1395d875a243d1aa66db6c01c2c0cb9aa"],"state_sha256":"a88ee2b3b6eda8eb13d9b36adf776510ea5681e830f0ca8e6524a8e6abb96d32"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cnKi9zN4VXpGMeaCXWvOfEF5bSJ8juPlbcCOTXGYftPA4+Mh8mqImCa84TVzK9JqV0Y2BpTDuXChL7/B1dAUBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-20T11:04:32.379620Z","bundle_sha256":"47386eb48c41e9975e9e03e70de93d32b65d4cff520f50304e15f12dd3f00af4"}}