{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z6LDK36YQDK3ZG7G5IJZTXH4ZU","short_pith_number":"pith:Z6LDK36Y","canonical_record":{"source":{"id":"1511.02256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-06T22:47:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e5f3e1c83a7269bd5f753069d1d82f03afc966b63661b376743b4551248680b8","abstract_canon_sha256":"ab9ad44783963316bf5197306afa8933c22a8106363c4188b9c51c2881ea813f"},"schema_version":"1.0"},"canonical_sha256":"cf96356fd880d5bc9be6ea1399dcfccd116e2a35b445b85a7d808955269f98f7","source":{"kind":"arxiv","id":"1511.02256","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02256","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02256v1","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02256","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z6LDK36YQDK3","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z6LDK36YQDK3ZG7G","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z6LDK36Y","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z6LDK36YQDK3ZG7G5IJZTXH4ZU","target":"record","payload":{"canonical_record":{"source":{"id":"1511.02256","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-06T22:47:13Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"e5f3e1c83a7269bd5f753069d1d82f03afc966b63661b376743b4551248680b8","abstract_canon_sha256":"ab9ad44783963316bf5197306afa8933c22a8106363c4188b9c51c2881ea813f"},"schema_version":"1.0"},"canonical_sha256":"cf96356fd880d5bc9be6ea1399dcfccd116e2a35b445b85a7d808955269f98f7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:27:30.851444Z","signature_b64":"MZTSFqp0x2rTPo6anuQPFSJK0WBNn7+kX22P78jVokW5aNOJVTpUd/Xt8dNFsA6cV1HVhSF7IME6LCYKhBUzCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cf96356fd880d5bc9be6ea1399dcfccd116e2a35b445b85a7d808955269f98f7","last_reissued_at":"2026-05-18T01:27:30.850858Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:27:30.850858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1511.02256","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":"2026-05-18T01:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FuOLB3nxgBOiz4HlczMbncJ9mF7Ib0aLNgptaxSV2OLazD//Gteu49BM6CmzV00wLVNyhnvu8/PQAFMBZu6ODw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:12:49.174104Z"},"content_sha256":"dd660e057726d678782a40566591e60c3c6bcd3a2e3de08dd4b877fe11ec3ee9","schema_version":"1.0","event_id":"sha256:dd660e057726d678782a40566591e60c3c6bcd3a2e3de08dd4b877fe11ec3ee9"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z6LDK36YQDK3ZG7G5IJZTXH4ZU","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Optimality of Uncoded Cache Placement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Daniela Tuninetti, Kai Wan, Pablo Piantanida","submitted_at":"2015-11-06T22:47:13Z","abstract_excerpt":"Caching is an efficient way to reduce peak-hour network traffic congestion by storing some contents at user's local cache without knowledge of later demands. Maddah-Ali and Niesen initiated a fundamental study of caching systems; they proposed a scheme (with uncoded cache placement and linear network coding delivery) that is provably optimal to within a factor 12. In this paper, by noticing that when the cache contents and the demands are fixed, the caching problem can be seen as an index coding problem, we show the optimality of Maddah-Ali and Niesen's scheme assuming that cache placement is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02256","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":"2026-05-18T01:27:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FRy6rYbadhWsHMXX8YRiyRX1GlrTuKCqFJDLNdsvq8SVra5k5+htO/JDP6HD1JZnwQoht4R0G/8gp6mMHra2BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-12T01:12:49.174465Z"},"content_sha256":"06b7343dd0657fc41fa49719406f29faef9d770f32772e474f3286d1461c1588","schema_version":"1.0","event_id":"sha256:06b7343dd0657fc41fa49719406f29faef9d770f32772e474f3286d1461c1588"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z6LDK36YQDK3ZG7G5IJZTXH4ZU/bundle.json","state_url":"https://pith.science/pith/Z6LDK36YQDK3ZG7G5IJZTXH4ZU/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z6LDK36YQDK3ZG7G5IJZTXH4ZU/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":"2026-06-12T01:12:49Z","links":{"resolver":"https://pith.science/pith/Z6LDK36YQDK3ZG7G5IJZTXH4ZU","bundle":"https://pith.science/pith/Z6LDK36YQDK3ZG7G5IJZTXH4ZU/bundle.json","state":"https://pith.science/pith/Z6LDK36YQDK3ZG7G5IJZTXH4ZU/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z6LDK36YQDK3ZG7G5IJZTXH4ZU/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z6LDK36YQDK3ZG7G5IJZTXH4ZU","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":"ab9ad44783963316bf5197306afa8933c22a8106363c4188b9c51c2881ea813f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-06T22:47:13Z","title_canon_sha256":"e5f3e1c83a7269bd5f753069d1d82f03afc966b63661b376743b4551248680b8"},"schema_version":"1.0","source":{"id":"1511.02256","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1511.02256","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"arxiv_version","alias_value":"1511.02256v1","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1511.02256","created_at":"2026-05-18T01:27:30Z"},{"alias_kind":"pith_short_12","alias_value":"Z6LDK36YQDK3","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z6LDK36YQDK3ZG7G","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z6LDK36Y","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:06b7343dd0657fc41fa49719406f29faef9d770f32772e474f3286d1461c1588","target":"graph","created_at":"2026-05-18T01:27:30Z","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":"Caching is an efficient way to reduce peak-hour network traffic congestion by storing some contents at user's local cache without knowledge of later demands. Maddah-Ali and Niesen initiated a fundamental study of caching systems; they proposed a scheme (with uncoded cache placement and linear network coding delivery) that is provably optimal to within a factor 12. In this paper, by noticing that when the cache contents and the demands are fixed, the caching problem can be seen as an index coding problem, we show the optimality of Maddah-Ali and Niesen's scheme assuming that cache placement is ","authors_text":"Daniela Tuninetti, Kai Wan, Pablo Piantanida","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-06T22:47:13Z","title":"On the Optimality of Uncoded Cache Placement"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02256","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:dd660e057726d678782a40566591e60c3c6bcd3a2e3de08dd4b877fe11ec3ee9","target":"record","created_at":"2026-05-18T01:27:30Z","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":"ab9ad44783963316bf5197306afa8933c22a8106363c4188b9c51c2881ea813f","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-11-06T22:47:13Z","title_canon_sha256":"e5f3e1c83a7269bd5f753069d1d82f03afc966b63661b376743b4551248680b8"},"schema_version":"1.0","source":{"id":"1511.02256","kind":"arxiv","version":1}},"canonical_sha256":"cf96356fd880d5bc9be6ea1399dcfccd116e2a35b445b85a7d808955269f98f7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cf96356fd880d5bc9be6ea1399dcfccd116e2a35b445b85a7d808955269f98f7","first_computed_at":"2026-05-18T01:27:30.850858Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:27:30.850858Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"MZTSFqp0x2rTPo6anuQPFSJK0WBNn7+kX22P78jVokW5aNOJVTpUd/Xt8dNFsA6cV1HVhSF7IME6LCYKhBUzCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:27:30.851444Z","signed_message":"canonical_sha256_bytes"},"source_id":"1511.02256","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:dd660e057726d678782a40566591e60c3c6bcd3a2e3de08dd4b877fe11ec3ee9","sha256:06b7343dd0657fc41fa49719406f29faef9d770f32772e474f3286d1461c1588"],"state_sha256":"61c205da600dbf2d601aea29bce387172494080e8508f58ea2bcb6cb3f67ff1b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VIVmVR7S7AnFTifJwhrZoY9mAqAb12fJ2i+Kp8XvbTDoLIcl7CZfb8NV4WV4Vuq6kiP3Enj2aVRm/2ggU+R2Dg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-12T01:12:49.176538Z","bundle_sha256":"92ee1b1804031832a1814c7f5fd089996c4bf62c90218756032eb246cdc3c621"}}