{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:3DOORTLQ253NTNLB7U3653DDON","short_pith_number":"pith:3DOORTLQ","canonical_record":{"source":{"id":"1612.09071","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T08:37:41Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"68de6bb2cf17cc986797cbea5977f40c6a247f4f0080e28dd5c444349eaf42c4","abstract_canon_sha256":"ee7d5e17c9dc15d314b145cd2c3fa6964fa95a9c21a4734c71da02fee96d8891"},"schema_version":"1.0"},"canonical_sha256":"d8dce8cd70d776d9b561fd37eeec6373486bc9f2b689b0dd03b3e7f115345ad3","source":{"kind":"arxiv","id":"1612.09071","version":4},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09071","created_at":"2026-05-18T00:43:55Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09071v4","created_at":"2026-05-18T00:43:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09071","created_at":"2026-05-18T00:43:55Z"},{"alias_kind":"pith_short_12","alias_value":"3DOORTLQ253N","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DOORTLQ253NTNLB","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DOORTLQ","created_at":"2026-05-18T12:29:55Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:3DOORTLQ253NTNLB7U3653DDON","target":"record","payload":{"canonical_record":{"source":{"id":"1612.09071","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T08:37:41Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"68de6bb2cf17cc986797cbea5977f40c6a247f4f0080e28dd5c444349eaf42c4","abstract_canon_sha256":"ee7d5e17c9dc15d314b145cd2c3fa6964fa95a9c21a4734c71da02fee96d8891"},"schema_version":"1.0"},"canonical_sha256":"d8dce8cd70d776d9b561fd37eeec6373486bc9f2b689b0dd03b3e7f115345ad3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:43:55.977075Z","signature_b64":"s2BI5C76ZyvAVNAWrraeHoLpS8SAnydlPlPuqQq17mFyhSafE7d0E3IrqDc1ilWhTy9fbN3u4FMoI9hZqmcsCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d8dce8cd70d776d9b561fd37eeec6373486bc9f2b689b0dd03b3e7f115345ad3","last_reissued_at":"2026-05-18T00:43:55.976486Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:43:55.976486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1612.09071","source_version":4,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:43:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BqUMbsOF+rv+lYTMxKh4d43u9JF0wcAYG+bjRWV6ky+s42n+16xqWt9GVhRvpf3KTrQztCG+BMI1V496eCZwBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:20:34.350855Z"},"content_sha256":"c8ad8e7e6f6132a4be43bcf046681b85f5333d703c51340b47256f06a0e43721","schema_version":"1.0","event_id":"sha256:c8ad8e7e6f6132a4be43bcf046681b85f5333d703c51340b47256f06a0e43721"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:3DOORTLQ253NTNLB7U3653DDON","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Fundamental Limits of Caching: Improved Bounds with Coded Prefetching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jes\\'us G\\'omez-Vilardeb\\'o","submitted_at":"2016-12-29T08:37:41Z","abstract_excerpt":"We consider a cache network in which a single server is connected to multiple users via a shared error free link. The server has access to a database with $N$ files of equal length $F$, and serves $K$ users each with a cache memory of $MF$ bits. A novel centralized coded caching scheme is proposed for scenarios with more users than files $N\\leq K$ and cache capacities satisfying $\\frac{1}{K}\\leq M\\leq\\frac{N}{K}$. The proposed scheme outperforms the best rate-memory region known in the literature if $N\\leq K\\leq\\frac{N^{2}+1}{2}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09071","kind":"arxiv","version":4},"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":"2026-05-18T00:43:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Id3B+mar9lopectui+ct14WEti4OcKZDFrY3BEcYqHlFkU1Nqks0GUdqnymAxJVMuFM69goOOBfBedDJTMAAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T09:20:34.351197Z"},"content_sha256":"f995caf6a22403a87cb3f3d843bc04e12fe75c9706cfd9344f30d5009f96781b","schema_version":"1.0","event_id":"sha256:f995caf6a22403a87cb3f3d843bc04e12fe75c9706cfd9344f30d5009f96781b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3DOORTLQ253NTNLB7U3653DDON/bundle.json","state_url":"https://pith.science/pith/3DOORTLQ253NTNLB7U3653DDON/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3DOORTLQ253NTNLB7U3653DDON/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":"2026-05-30T09:20:34Z","links":{"resolver":"https://pith.science/pith/3DOORTLQ253NTNLB7U3653DDON","bundle":"https://pith.science/pith/3DOORTLQ253NTNLB7U3653DDON/bundle.json","state":"https://pith.science/pith/3DOORTLQ253NTNLB7U3653DDON/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3DOORTLQ253NTNLB7U3653DDON/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:3DOORTLQ253NTNLB7U3653DDON","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":"ee7d5e17c9dc15d314b145cd2c3fa6964fa95a9c21a4734c71da02fee96d8891","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T08:37:41Z","title_canon_sha256":"68de6bb2cf17cc986797cbea5977f40c6a247f4f0080e28dd5c444349eaf42c4"},"schema_version":"1.0","source":{"id":"1612.09071","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1612.09071","created_at":"2026-05-18T00:43:55Z"},{"alias_kind":"arxiv_version","alias_value":"1612.09071v4","created_at":"2026-05-18T00:43:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.09071","created_at":"2026-05-18T00:43:55Z"},{"alias_kind":"pith_short_12","alias_value":"3DOORTLQ253N","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_16","alias_value":"3DOORTLQ253NTNLB","created_at":"2026-05-18T12:29:55Z"},{"alias_kind":"pith_short_8","alias_value":"3DOORTLQ","created_at":"2026-05-18T12:29:55Z"}],"graph_snapshots":[{"event_id":"sha256:f995caf6a22403a87cb3f3d843bc04e12fe75c9706cfd9344f30d5009f96781b","target":"graph","created_at":"2026-05-18T00:43:55Z","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 cache network in which a single server is connected to multiple users via a shared error free link. The server has access to a database with $N$ files of equal length $F$, and serves $K$ users each with a cache memory of $MF$ bits. A novel centralized coded caching scheme is proposed for scenarios with more users than files $N\\leq K$ and cache capacities satisfying $\\frac{1}{K}\\leq M\\leq\\frac{N}{K}$. The proposed scheme outperforms the best rate-memory region known in the literature if $N\\leq K\\leq\\frac{N^{2}+1}{2}$.","authors_text":"Jes\\'us G\\'omez-Vilardeb\\'o","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T08:37:41Z","title":"Fundamental Limits of Caching: Improved Bounds with Coded Prefetching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.09071","kind":"arxiv","version":4},"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:c8ad8e7e6f6132a4be43bcf046681b85f5333d703c51340b47256f06a0e43721","target":"record","created_at":"2026-05-18T00:43:55Z","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":"ee7d5e17c9dc15d314b145cd2c3fa6964fa95a9c21a4734c71da02fee96d8891","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2016-12-29T08:37:41Z","title_canon_sha256":"68de6bb2cf17cc986797cbea5977f40c6a247f4f0080e28dd5c444349eaf42c4"},"schema_version":"1.0","source":{"id":"1612.09071","kind":"arxiv","version":4}},"canonical_sha256":"d8dce8cd70d776d9b561fd37eeec6373486bc9f2b689b0dd03b3e7f115345ad3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d8dce8cd70d776d9b561fd37eeec6373486bc9f2b689b0dd03b3e7f115345ad3","first_computed_at":"2026-05-18T00:43:55.976486Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:43:55.976486Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"s2BI5C76ZyvAVNAWrraeHoLpS8SAnydlPlPuqQq17mFyhSafE7d0E3IrqDc1ilWhTy9fbN3u4FMoI9hZqmcsCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:43:55.977075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1612.09071","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c8ad8e7e6f6132a4be43bcf046681b85f5333d703c51340b47256f06a0e43721","sha256:f995caf6a22403a87cb3f3d843bc04e12fe75c9706cfd9344f30d5009f96781b"],"state_sha256":"5babb300ed09ae1d99e3cf5feded23964bd6d38902e9b5012e7ee204d5356d45"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7gju76wScz0n8Ae57gLs0jNUtOqsK+h393Lmt1Atp2dYkxAGOgCpfzRzxvvPCJ5TLuos8qjqT843DXH/CiGvDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T09:20:34.353257Z","bundle_sha256":"1d39f72b24fdeff87d43207aa3370688c2338b83996e01520ffc54506c34f981"}}