{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:S5LF62FHQIHEAF5CEKGKLEADLL","short_pith_number":"pith:S5LF62FH","canonical_record":{"source":{"id":"1808.09775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-29T13:02:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"785dcc09a4e0eed115a8570a064f94145c0bb60891c4d58d34be80ff03dfc5d3","abstract_canon_sha256":"b51ab856f2809b5468b388b195cef2d4528ceb04c4fe4935f5748390f3ed9b20"},"schema_version":"1.0"},"canonical_sha256":"97565f68a7820e4017a2228ca590035aeff8697981619ab1f2847775b48ca1e0","source":{"kind":"arxiv","id":"1808.09775","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09775","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09775v1","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09775","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"S5LF62FHQIHE","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S5LF62FHQIHEAF5C","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S5LF62FH","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:S5LF62FHQIHEAF5CEKGKLEADLL","target":"record","payload":{"canonical_record":{"source":{"id":"1808.09775","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-29T13:02:43Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"785dcc09a4e0eed115a8570a064f94145c0bb60891c4d58d34be80ff03dfc5d3","abstract_canon_sha256":"b51ab856f2809b5468b388b195cef2d4528ceb04c4fe4935f5748390f3ed9b20"},"schema_version":"1.0"},"canonical_sha256":"97565f68a7820e4017a2228ca590035aeff8697981619ab1f2847775b48ca1e0","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:54.505298Z","signature_b64":"ytY80cDqUZlY8ny6aaxUa9syv4LUdIiqRxa76iTpgmy4xPiloLI0P31afSQGiuS6yR/Vk8cK+RHCX2gLgXP3Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97565f68a7820e4017a2228ca590035aeff8697981619ab1f2847775b48ca1e0","last_reissued_at":"2026-05-18T00:06:54.504765Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:54.504765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1808.09775","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":"2026-05-18T00:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VHplcP4yXbvTK01GXreAFpEjIRaIzJIk8OXMDlpj4xDpMMxPH/WP9u5AWM6hyoxP11n0HiCKeUkPIdWhHY5OCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:27:14.690844Z"},"content_sha256":"9102594293720bd6b3bd730353d49652dcd0d0712b3546eccea49b29633b7019","schema_version":"1.0","event_id":"sha256:9102594293720bd6b3bd730353d49652dcd0d0712b3546eccea49b29633b7019"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:S5LF62FHQIHEAF5CEKGKLEADLL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal Linear Broadcast Rates of the Two-Sender Unicast Index Coding Problem with Fully-Participated Interactions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"B. Sundar Rajan, Chinmayananda Arunachala, Vaneet Aggarwal","submitted_at":"2018-08-29T13:02:43Z","abstract_excerpt":"The two-sender unicast index coding problem consists of finding optimal coded transmissions from the two senders which collectively know the messages demanded by all the receivers. Each receiver demands a unique message. One important class of this problem consists of the message sets at the senders and the side-information at the receivers satisfying \\emph{fully-participated interactions}. This paper provides optimal linear broadcast rates and corresponding code constructions for all the possible cases of the two-sender unicast index coding problem with fully-participated interactions. The op"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09775","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":"2026-05-18T00:06:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"aoDlgdQ8qphv3AUZwqm4LiQl/2jo7Gtguka0zc27xWn0jRpBapoWpVU3dUsVwQbFOSldvzPC40dNWJr7LEWBAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T19:27:14.691200Z"},"content_sha256":"5142be512111841e4ea77d692c55e756a9c2994eb2f5d786b2d841d201a01dcb","schema_version":"1.0","event_id":"sha256:5142be512111841e4ea77d692c55e756a9c2994eb2f5d786b2d841d201a01dcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/S5LF62FHQIHEAF5CEKGKLEADLL/bundle.json","state_url":"https://pith.science/pith/S5LF62FHQIHEAF5CEKGKLEADLL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/S5LF62FHQIHEAF5CEKGKLEADLL/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":"2026-06-04T19:27:14Z","links":{"resolver":"https://pith.science/pith/S5LF62FHQIHEAF5CEKGKLEADLL","bundle":"https://pith.science/pith/S5LF62FHQIHEAF5CEKGKLEADLL/bundle.json","state":"https://pith.science/pith/S5LF62FHQIHEAF5CEKGKLEADLL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/S5LF62FHQIHEAF5CEKGKLEADLL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:S5LF62FHQIHEAF5CEKGKLEADLL","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":"b51ab856f2809b5468b388b195cef2d4528ceb04c4fe4935f5748390f3ed9b20","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-29T13:02:43Z","title_canon_sha256":"785dcc09a4e0eed115a8570a064f94145c0bb60891c4d58d34be80ff03dfc5d3"},"schema_version":"1.0","source":{"id":"1808.09775","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1808.09775","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1808.09775v1","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1808.09775","created_at":"2026-05-18T00:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"S5LF62FHQIHE","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"S5LF62FHQIHEAF5C","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"S5LF62FH","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:5142be512111841e4ea77d692c55e756a9c2994eb2f5d786b2d841d201a01dcb","target":"graph","created_at":"2026-05-18T00:06:54Z","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":"The two-sender unicast index coding problem consists of finding optimal coded transmissions from the two senders which collectively know the messages demanded by all the receivers. Each receiver demands a unique message. One important class of this problem consists of the message sets at the senders and the side-information at the receivers satisfying \\emph{fully-participated interactions}. This paper provides optimal linear broadcast rates and corresponding code constructions for all the possible cases of the two-sender unicast index coding problem with fully-participated interactions. The op","authors_text":"B. Sundar Rajan, Chinmayananda Arunachala, Vaneet Aggarwal","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-29T13:02:43Z","title":"Optimal Linear Broadcast Rates of the Two-Sender Unicast Index Coding Problem with Fully-Participated Interactions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.09775","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":"sha256:9102594293720bd6b3bd730353d49652dcd0d0712b3546eccea49b29633b7019","target":"record","created_at":"2026-05-18T00:06:54Z","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":"b51ab856f2809b5468b388b195cef2d4528ceb04c4fe4935f5748390f3ed9b20","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2018-08-29T13:02:43Z","title_canon_sha256":"785dcc09a4e0eed115a8570a064f94145c0bb60891c4d58d34be80ff03dfc5d3"},"schema_version":"1.0","source":{"id":"1808.09775","kind":"arxiv","version":1}},"canonical_sha256":"97565f68a7820e4017a2228ca590035aeff8697981619ab1f2847775b48ca1e0","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"97565f68a7820e4017a2228ca590035aeff8697981619ab1f2847775b48ca1e0","first_computed_at":"2026-05-18T00:06:54.504765Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:06:54.504765Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ytY80cDqUZlY8ny6aaxUa9syv4LUdIiqRxa76iTpgmy4xPiloLI0P31afSQGiuS6yR/Vk8cK+RHCX2gLgXP3Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:06:54.505298Z","signed_message":"canonical_sha256_bytes"},"source_id":"1808.09775","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9102594293720bd6b3bd730353d49652dcd0d0712b3546eccea49b29633b7019","sha256:5142be512111841e4ea77d692c55e756a9c2994eb2f5d786b2d841d201a01dcb"],"state_sha256":"87da7f989b944aaebdc4068a351da19b39293c6c14b7a3a15c1c112cd72eff1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"H4Cenx+0Ftls/FRDgQQzVb3V3BIcsAe/9BkzIkTWMWHir1/UsiFjk1VfvVqHpCxF/zlEE/gzO4YV5GZjIKrDCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T19:27:14.693501Z","bundle_sha256":"8c322cc50bafa633dacfc0e6e2274d0cc1c175c8b38c2f4de16e0f8dfc9361ea"}}