{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:HUTRQQGS7VWAPSR2H7HVI3BP3N","short_pith_number":"pith:HUTRQQGS","canonical_record":{"source":{"id":"1601.05690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-21T16:02:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"89555e80d4cdde6c80d7104a18e37ba8bd9b0c3e7d7bb73ff65102eeec267736","abstract_canon_sha256":"14e486968ffdb7926e34cd9ba3453be4c5413f8816c43bd97693a9120f6b6e91"},"schema_version":"1.0"},"canonical_sha256":"3d271840d2fd6c07ca3a3fcf546c2fdb5ff86d446f5f9777d3107b6e7c96d349","source":{"kind":"arxiv","id":"1601.05690","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05690","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05690v1","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05690","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"HUTRQQGS7VWA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HUTRQQGS7VWAPSR2","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HUTRQQGS","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:HUTRQQGS7VWAPSR2H7HVI3BP3N","target":"record","payload":{"canonical_record":{"source":{"id":"1601.05690","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-21T16:02:58Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"89555e80d4cdde6c80d7104a18e37ba8bd9b0c3e7d7bb73ff65102eeec267736","abstract_canon_sha256":"14e486968ffdb7926e34cd9ba3453be4c5413f8816c43bd97693a9120f6b6e91"},"schema_version":"1.0"},"canonical_sha256":"3d271840d2fd6c07ca3a3fcf546c2fdb5ff86d446f5f9777d3107b6e7c96d349","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:13.222148Z","signature_b64":"cX6c79Six8wVp/TLyXTQa18RyjugBd1Zl9+4U/X/vjtVivMSFOOe9OBgnqWv3Ce/p8ysF8VqwKx/hVBQBBj/AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d271840d2fd6c07ca3a3fcf546c2fdb5ff86d446f5f9777d3107b6e7c96d349","last_reissued_at":"2026-05-18T01:22:13.221588Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:13.221588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1601.05690","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":"2026-05-18T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"19fBvs6kh+FA7mpO0zyDwHx6LUKPhpSWE3Y9WLbDxP1m1HOnnz5lXnUfKFAZkWx2vCoOz3qPTWiwyhLUYoSmDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T10:21:02.140945Z"},"content_sha256":"256d019935f9841abb3f4981f9eac042d3049d2a9582972bf45a0dbeb910f3c3","schema_version":"1.0","event_id":"sha256:256d019935f9841abb3f4981f9eac042d3049d2a9582972bf45a0dbeb910f3c3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:HUTRQQGS7VWAPSR2H7HVI3BP3N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A New Converse Bound for Coded Caching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Chien-Yi Wang, Michael Gastpar, Sung Hoon Lim","submitted_at":"2016-01-21T16:02:58Z","abstract_excerpt":"An information-theoretic lower bound is developed for the caching system studied by Maddah-Ali and Niesen. By comparing the proposed lower bound with the decentralized coded caching scheme of Maddah-Ali and Niesen, the optimal memory--rate tradeoff is characterized to within a multiplicative gap of $4.7$ for the worst case, improving the previous analytical gap of $12$. Furthermore, for the case when users' requests follow the uniform distribution, the multiplicative gap is tightened to $4.7$, improving the previous analytical gap of $72$. As an independent result of interest, for the single-u"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05690","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":"2026-05-18T01:22:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MU14IZzKxC1jY3x/0V5na092A+tILGhNJE5DiQQwMQXr9yLu39/y9KemKLEaqtKh+2I+AmEF92zLJuTf+JSiCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-19T10:21:02.141284Z"},"content_sha256":"d7fa76c099bc021368e9750765086e6fc04dd487b0241142315e575fc95752d4","schema_version":"1.0","event_id":"sha256:d7fa76c099bc021368e9750765086e6fc04dd487b0241142315e575fc95752d4"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HUTRQQGS7VWAPSR2H7HVI3BP3N/bundle.json","state_url":"https://pith.science/pith/HUTRQQGS7VWAPSR2H7HVI3BP3N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HUTRQQGS7VWAPSR2H7HVI3BP3N/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":"2026-05-19T10:21:02Z","links":{"resolver":"https://pith.science/pith/HUTRQQGS7VWAPSR2H7HVI3BP3N","bundle":"https://pith.science/pith/HUTRQQGS7VWAPSR2H7HVI3BP3N/bundle.json","state":"https://pith.science/pith/HUTRQQGS7VWAPSR2H7HVI3BP3N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HUTRQQGS7VWAPSR2H7HVI3BP3N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:HUTRQQGS7VWAPSR2H7HVI3BP3N","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":"14e486968ffdb7926e34cd9ba3453be4c5413f8816c43bd97693a9120f6b6e91","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-21T16:02:58Z","title_canon_sha256":"89555e80d4cdde6c80d7104a18e37ba8bd9b0c3e7d7bb73ff65102eeec267736"},"schema_version":"1.0","source":{"id":"1601.05690","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1601.05690","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"arxiv_version","alias_value":"1601.05690v1","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1601.05690","created_at":"2026-05-18T01:22:13Z"},{"alias_kind":"pith_short_12","alias_value":"HUTRQQGS7VWA","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"HUTRQQGS7VWAPSR2","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"HUTRQQGS","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:d7fa76c099bc021368e9750765086e6fc04dd487b0241142315e575fc95752d4","target":"graph","created_at":"2026-05-18T01:22:13Z","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":"An information-theoretic lower bound is developed for the caching system studied by Maddah-Ali and Niesen. By comparing the proposed lower bound with the decentralized coded caching scheme of Maddah-Ali and Niesen, the optimal memory--rate tradeoff is characterized to within a multiplicative gap of $4.7$ for the worst case, improving the previous analytical gap of $12$. Furthermore, for the case when users' requests follow the uniform distribution, the multiplicative gap is tightened to $4.7$, improving the previous analytical gap of $72$. As an independent result of interest, for the single-u","authors_text":"Chien-Yi Wang, Michael Gastpar, Sung Hoon Lim","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-21T16:02:58Z","title":"A New Converse Bound for Coded Caching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.05690","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":"sha256:256d019935f9841abb3f4981f9eac042d3049d2a9582972bf45a0dbeb910f3c3","target":"record","created_at":"2026-05-18T01:22:13Z","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":"14e486968ffdb7926e34cd9ba3453be4c5413f8816c43bd97693a9120f6b6e91","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-01-21T16:02:58Z","title_canon_sha256":"89555e80d4cdde6c80d7104a18e37ba8bd9b0c3e7d7bb73ff65102eeec267736"},"schema_version":"1.0","source":{"id":"1601.05690","kind":"arxiv","version":1}},"canonical_sha256":"3d271840d2fd6c07ca3a3fcf546c2fdb5ff86d446f5f9777d3107b6e7c96d349","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3d271840d2fd6c07ca3a3fcf546c2fdb5ff86d446f5f9777d3107b6e7c96d349","first_computed_at":"2026-05-18T01:22:13.221588Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:22:13.221588Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cX6c79Six8wVp/TLyXTQa18RyjugBd1Zl9+4U/X/vjtVivMSFOOe9OBgnqWv3Ce/p8ysF8VqwKx/hVBQBBj/AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:22:13.222148Z","signed_message":"canonical_sha256_bytes"},"source_id":"1601.05690","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:256d019935f9841abb3f4981f9eac042d3049d2a9582972bf45a0dbeb910f3c3","sha256:d7fa76c099bc021368e9750765086e6fc04dd487b0241142315e575fc95752d4"],"state_sha256":"1f8154e0086adbd63d1e1ddcac9e1f1165902efc7b86f6aee22d68ab988d32d6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y6de3LuIFuAF6gdY/AdDXQusnZvz9tj0J8UuXX3PIkFcycj7QyWUvJ7qRtCCHlGU1qfhgeM+nY5fMz0CNaUKAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-19T10:21:02.142871Z","bundle_sha256":"e3c4c49707e5c860a9c638edae9d8d931b8a9ee3a183c74d44fa9a4d63c90f98"}}