{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:HWYR6KLB5B42KDITTAJ6C7YL7P","short_pith_number":"pith:HWYR6KLB","canonical_record":{"source":{"id":"1711.06487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-17T10:44:38Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"0e78e999b844b95854287f60efc3e51fd94caf7fc540f36e97a0f12cd2d8dc00","abstract_canon_sha256":"b2dccf2fb8e4ffd2459be78f45f475c97a4449f66406284094ae642f2f2f66db"},"schema_version":"1.0"},"canonical_sha256":"3db11f2961e879a50d139813e17f0bfbd9cd8a49b4ea17bdd97a905fea01a075","source":{"kind":"arxiv","id":"1711.06487","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06487","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06487v1","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06487","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"pith_short_12","alias_value":"HWYR6KLB5B42","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HWYR6KLB5B42KDIT","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HWYR6KLB","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:HWYR6KLB5B42KDITTAJ6C7YL7P","target":"record","payload":{"canonical_record":{"source":{"id":"1711.06487","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-17T10:44:38Z","cross_cats_sorted":["math.CO","math.IT"],"title_canon_sha256":"0e78e999b844b95854287f60efc3e51fd94caf7fc540f36e97a0f12cd2d8dc00","abstract_canon_sha256":"b2dccf2fb8e4ffd2459be78f45f475c97a4449f66406284094ae642f2f2f66db"},"schema_version":"1.0"},"canonical_sha256":"3db11f2961e879a50d139813e17f0bfbd9cd8a49b4ea17bdd97a905fea01a075","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:20.968348Z","signature_b64":"ix1PxJJGEOrwIHsrQ2K7PnTEeLwLULeZXXQORO3LOPBonkmD14KttEJ4lltEnhlJi+4NMLcn07cANyoOkErKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3db11f2961e879a50d139813e17f0bfbd9cd8a49b4ea17bdd97a905fea01a075","last_reissued_at":"2026-05-18T00:30:20.967514Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:20.967514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.06487","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":"2026-05-18T00:30:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kEGknGlKOf9fRVq4Ai/kG7baRx4UR7JQMoVJDagrXNykNg7yrfKdhcQ0vTsibMB4GH+qO76CxL4fKzGUjIGUAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:21:15.867452Z"},"content_sha256":"31a7c193df6fb56697eab60a27466d5db474da9ece1153c2f22975ebdda76f7e","schema_version":"1.0","event_id":"sha256:31a7c193df6fb56697eab60a27466d5db474da9ece1153c2f22975ebdda76f7e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:HWYR6KLB5B42KDITTAJ6C7YL7P","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Index Codes via a Duality between Index Coding and Network Coding","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.IT"],"primary_cat":"cs.IT","authors_text":"Ashok Choudhary, Prasad Krishnan, Vamsi Krishna Gummadi","submitted_at":"2017-11-17T10:44:38Z","abstract_excerpt":"In Index Coding, the goal is to use a broadcast channel as efficiently as possible to communicate information from a source to multiple receivers which can possess some of the information symbols at the source as side-information. In this work, we present a duality relationship between index coding (IC) and multiple-unicast network coding (NC). It is known that the IC problem can be represented using a side-information graph $G$ (with number of vertices $n$ equal to the number of source symbols). The size of the maximum acyclic induced subgraph, denoted by $MAIS$ is a lower bound on the \\texti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06487","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":"2026-05-18T00:30:20Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Mrfcqj+D11nwMgeF3STPg9RvQd6kvyxRGkIlhbJMHn96wPDeltS1XnZsM8LlgTjX/tweN5/lg294/e75DOxxCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T14:21:15.867805Z"},"content_sha256":"652c02daeb673299d166efa73f125968085ff7148aaea8b35bbbb40a47b71f85","schema_version":"1.0","event_id":"sha256:652c02daeb673299d166efa73f125968085ff7148aaea8b35bbbb40a47b71f85"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HWYR6KLB5B42KDITTAJ6C7YL7P/bundle.json","state_url":"https://pith.science/pith/HWYR6KLB5B42KDITTAJ6C7YL7P/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HWYR6KLB5B42KDITTAJ6C7YL7P/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":"2026-06-23T14:21:15Z","links":{"resolver":"https://pith.science/pith/HWYR6KLB5B42KDITTAJ6C7YL7P","bundle":"https://pith.science/pith/HWYR6KLB5B42KDITTAJ6C7YL7P/bundle.json","state":"https://pith.science/pith/HWYR6KLB5B42KDITTAJ6C7YL7P/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HWYR6KLB5B42KDITTAJ6C7YL7P/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:HWYR6KLB5B42KDITTAJ6C7YL7P","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":"b2dccf2fb8e4ffd2459be78f45f475c97a4449f66406284094ae642f2f2f66db","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-17T10:44:38Z","title_canon_sha256":"0e78e999b844b95854287f60efc3e51fd94caf7fc540f36e97a0f12cd2d8dc00"},"schema_version":"1.0","source":{"id":"1711.06487","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.06487","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"arxiv_version","alias_value":"1711.06487v1","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.06487","created_at":"2026-05-18T00:30:20Z"},{"alias_kind":"pith_short_12","alias_value":"HWYR6KLB5B42","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"HWYR6KLB5B42KDIT","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"HWYR6KLB","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:652c02daeb673299d166efa73f125968085ff7148aaea8b35bbbb40a47b71f85","target":"graph","created_at":"2026-05-18T00:30:20Z","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 Index Coding, the goal is to use a broadcast channel as efficiently as possible to communicate information from a source to multiple receivers which can possess some of the information symbols at the source as side-information. In this work, we present a duality relationship between index coding (IC) and multiple-unicast network coding (NC). It is known that the IC problem can be represented using a side-information graph $G$ (with number of vertices $n$ equal to the number of source symbols). The size of the maximum acyclic induced subgraph, denoted by $MAIS$ is a lower bound on the \\texti","authors_text":"Ashok Choudhary, Prasad Krishnan, Vamsi Krishna Gummadi","cross_cats":["math.CO","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-17T10:44:38Z","title":"Optimal Index Codes via a Duality between Index Coding and Network Coding"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06487","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":"sha256:31a7c193df6fb56697eab60a27466d5db474da9ece1153c2f22975ebdda76f7e","target":"record","created_at":"2026-05-18T00:30:20Z","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":"b2dccf2fb8e4ffd2459be78f45f475c97a4449f66406284094ae642f2f2f66db","cross_cats_sorted":["math.CO","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-11-17T10:44:38Z","title_canon_sha256":"0e78e999b844b95854287f60efc3e51fd94caf7fc540f36e97a0f12cd2d8dc00"},"schema_version":"1.0","source":{"id":"1711.06487","kind":"arxiv","version":1}},"canonical_sha256":"3db11f2961e879a50d139813e17f0bfbd9cd8a49b4ea17bdd97a905fea01a075","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3db11f2961e879a50d139813e17f0bfbd9cd8a49b4ea17bdd97a905fea01a075","first_computed_at":"2026-05-18T00:30:20.967514Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:20.967514Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ix1PxJJGEOrwIHsrQ2K7PnTEeLwLULeZXXQORO3LOPBonkmD14KttEJ4lltEnhlJi+4NMLcn07cANyoOkErKAA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:20.968348Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.06487","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31a7c193df6fb56697eab60a27466d5db474da9ece1153c2f22975ebdda76f7e","sha256:652c02daeb673299d166efa73f125968085ff7148aaea8b35bbbb40a47b71f85"],"state_sha256":"0a9a05ba076b114ebdb08b77c2587e5910a490b73d7872d315799a36c7584e0d"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"RCRqwhhDhMOTmnvRzpwUf2hZBvL6oaNzJRfO8iE624t3O54IpjoqbHTXo4KNnt4N+ltmHPSI9HxNJZgWL1vdBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T14:21:15.869787Z","bundle_sha256":"9a5523d95b740ab6e4dfdcb7e2540b3772c4b887eadf466bb361fbcee6e10893"}}