{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:AIGYF6NKYY6NANAL67KLZ33ALD","short_pith_number":"pith:AIGYF6NK","canonical_record":{"source":{"id":"1603.00092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-02-29T23:27:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e7653d3ec293b05e3add64e3a4750b7d56e24a7a0141bd45f926032b3c6d40a0","abstract_canon_sha256":"7f7c913c03ffc25a77d4b179d2c43d318d105de23c7d3270ca9a5320a4c2af8e"},"schema_version":"1.0"},"canonical_sha256":"020d82f9aac63cd0340bf7d4bcef6058f9e1aa0017566ebb84b155e5f3641e8b","source":{"kind":"arxiv","id":"1603.00092","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00092","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00092v2","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00092","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"AIGYF6NKYY6N","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AIGYF6NKYY6NANAL","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AIGYF6NK","created_at":"2026-05-18T12:30:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:AIGYF6NKYY6NANAL67KLZ33ALD","target":"record","payload":{"canonical_record":{"source":{"id":"1603.00092","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-02-29T23:27:26Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e7653d3ec293b05e3add64e3a4750b7d56e24a7a0141bd45f926032b3c6d40a0","abstract_canon_sha256":"7f7c913c03ffc25a77d4b179d2c43d318d105de23c7d3270ca9a5320a4c2af8e"},"schema_version":"1.0"},"canonical_sha256":"020d82f9aac63cd0340bf7d4bcef6058f9e1aa0017566ebb84b155e5f3641e8b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:40.498138Z","signature_b64":"RU+L/9+K/afqWTerd61fWUp1wr5IWAxWBOed7wDKfxlq1J2SbNCG6AiaYQ+gjs+zxZxEavGEM+6N4Lsw5eL3Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"020d82f9aac63cd0340bf7d4bcef6058f9e1aa0017566ebb84b155e5f3641e8b","last_reissued_at":"2026-05-18T00:22:40.497736Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:40.497736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1603.00092","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":"2026-05-18T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pDxa7oCzaGhj37kmB2/+NFDbVOjiK1Sd75FSwTrXf9NPc8erEJkJKwtYLx85rGNPKGrsFjdWtDulb/0QRm3LBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:31:17.359337Z"},"content_sha256":"2900f13f3b9413bf0b6814bc6dfbc2bd59af664dc0aabc3462e4fc5da3bbc29e","schema_version":"1.0","event_id":"sha256:2900f13f3b9413bf0b6814bc6dfbc2bd59af664dc0aabc3462e4fc5da3bbc29e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:AIGYF6NKYY6NANAL67KLZ33ALD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chandra Thapa, Lawrence Ong, Sarah J. Johnson","submitted_at":"2016-02-29T23:27:26Z","abstract_excerpt":"We consider a graphical approach to index coding. While cycles have been shown to provide coding gain, only disjoint cycles and cliques (a specific type of overlapping cycles) have been exploited in existing literature. In this paper, we define a more general form of overlapping cycles, called the interlinked-cycle (IC) structure, that generalizes cycles and cliques. We propose a scheme, called the interlinked-cycle-cover (ICC) scheme, that leverages IC structures in digraphs to construct scalar linear index codes. We characterize a class of infinitely many digraphs where our proposed scheme i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00092","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":"2026-05-18T00:22:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"k2vMWcPQ8wqOCWy3C3khxOMDdiTSop+e4LztDPHanaY/O0DjdBKuvTUx/2JzK8+V4dJDy5qiT5XljOMR0h42Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-01T12:31:17.359690Z"},"content_sha256":"aa864355e7b428f2d713cf562f5fd587d54f41885734068cde45631fd72bf3b2","schema_version":"1.0","event_id":"sha256:aa864355e7b428f2d713cf562f5fd587d54f41885734068cde45631fd72bf3b2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AIGYF6NKYY6NANAL67KLZ33ALD/bundle.json","state_url":"https://pith.science/pith/AIGYF6NKYY6NANAL67KLZ33ALD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AIGYF6NKYY6NANAL67KLZ33ALD/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":"2026-06-01T12:31:17Z","links":{"resolver":"https://pith.science/pith/AIGYF6NKYY6NANAL67KLZ33ALD","bundle":"https://pith.science/pith/AIGYF6NKYY6NANAL67KLZ33ALD/bundle.json","state":"https://pith.science/pith/AIGYF6NKYY6NANAL67KLZ33ALD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AIGYF6NKYY6NANAL67KLZ33ALD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:AIGYF6NKYY6NANAL67KLZ33ALD","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":"7f7c913c03ffc25a77d4b179d2c43d318d105de23c7d3270ca9a5320a4c2af8e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-02-29T23:27:26Z","title_canon_sha256":"e7653d3ec293b05e3add64e3a4750b7d56e24a7a0141bd45f926032b3c6d40a0"},"schema_version":"1.0","source":{"id":"1603.00092","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.00092","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"arxiv_version","alias_value":"1603.00092v2","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.00092","created_at":"2026-05-18T00:22:40Z"},{"alias_kind":"pith_short_12","alias_value":"AIGYF6NKYY6N","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_16","alias_value":"AIGYF6NKYY6NANAL","created_at":"2026-05-18T12:30:07Z"},{"alias_kind":"pith_short_8","alias_value":"AIGYF6NK","created_at":"2026-05-18T12:30:07Z"}],"graph_snapshots":[{"event_id":"sha256:aa864355e7b428f2d713cf562f5fd587d54f41885734068cde45631fd72bf3b2","target":"graph","created_at":"2026-05-18T00:22:40Z","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 a graphical approach to index coding. While cycles have been shown to provide coding gain, only disjoint cycles and cliques (a specific type of overlapping cycles) have been exploited in existing literature. In this paper, we define a more general form of overlapping cycles, called the interlinked-cycle (IC) structure, that generalizes cycles and cliques. We propose a scheme, called the interlinked-cycle-cover (ICC) scheme, that leverages IC structures in digraphs to construct scalar linear index codes. We characterize a class of infinitely many digraphs where our proposed scheme i","authors_text":"Chandra Thapa, Lawrence Ong, Sarah J. Johnson","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-02-29T23:27:26Z","title":"Interlinked Cycles for Index Coding: Generalizing Cycles and Cliques"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.00092","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":"sha256:2900f13f3b9413bf0b6814bc6dfbc2bd59af664dc0aabc3462e4fc5da3bbc29e","target":"record","created_at":"2026-05-18T00:22:40Z","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":"7f7c913c03ffc25a77d4b179d2c43d318d105de23c7d3270ca9a5320a4c2af8e","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-02-29T23:27:26Z","title_canon_sha256":"e7653d3ec293b05e3add64e3a4750b7d56e24a7a0141bd45f926032b3c6d40a0"},"schema_version":"1.0","source":{"id":"1603.00092","kind":"arxiv","version":2}},"canonical_sha256":"020d82f9aac63cd0340bf7d4bcef6058f9e1aa0017566ebb84b155e5f3641e8b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"020d82f9aac63cd0340bf7d4bcef6058f9e1aa0017566ebb84b155e5f3641e8b","first_computed_at":"2026-05-18T00:22:40.497736Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:22:40.497736Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RU+L/9+K/afqWTerd61fWUp1wr5IWAxWBOed7wDKfxlq1J2SbNCG6AiaYQ+gjs+zxZxEavGEM+6N4Lsw5eL3Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:22:40.498138Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.00092","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2900f13f3b9413bf0b6814bc6dfbc2bd59af664dc0aabc3462e4fc5da3bbc29e","sha256:aa864355e7b428f2d713cf562f5fd587d54f41885734068cde45631fd72bf3b2"],"state_sha256":"3f18aead6574172661c2c757d91521611d577a8ab1bb51684f0178396bd75a5b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dOdjrnzpdV/ENBMk7kKjDJa5pFOYowRMkD+Wc60Z1aMvwWpWXt7khKhflq5PMXaOAVR6DBSQa8dUg8X8lxMdBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-01T12:31:17.361692Z","bundle_sha256":"b26b50568054b9a1492a05e9ee1b4fad9d2f8c6ad62fa39d9190f493131f0774"}}