{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:PPTSZ4CLFXRUIHNFLXOQU4UUDR","short_pith_number":"pith:PPTSZ4CL","canonical_record":{"source":{"id":"1504.05931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-22T19:24:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3d43371c3859bff13b82da658fbff093b2497d16e8744c78bcc2a87a9da66cde","abstract_canon_sha256":"1c3ff2cca72a61d275b76483f4d03a5dd05e56b3705bd3c809cc0c4158abb4d7"},"schema_version":"1.0"},"canonical_sha256":"7be72cf04b2de3441da55ddd0a72941c5044efaf7c05442d1c7b4bbd09b562ff","source":{"kind":"arxiv","id":"1504.05931","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05931","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05931v1","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05931","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"pith_short_12","alias_value":"PPTSZ4CLFXRU","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPTSZ4CLFXRUIHNF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPTSZ4CL","created_at":"2026-05-18T12:29:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:PPTSZ4CLFXRUIHNFLXOQU4UUDR","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05931","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-22T19:24:01Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"3d43371c3859bff13b82da658fbff093b2497d16e8744c78bcc2a87a9da66cde","abstract_canon_sha256":"1c3ff2cca72a61d275b76483f4d03a5dd05e56b3705bd3c809cc0c4158abb4d7"},"schema_version":"1.0"},"canonical_sha256":"7be72cf04b2de3441da55ddd0a72941c5044efaf7c05442d1c7b4bbd09b562ff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:35.748719Z","signature_b64":"7hYkeZj8rm1CDPwhPfQDPiLBrjybAOxFs9l9Spj400wDHKpeVUKkOWJ8uz6KiMVvH6kvT+jsP5zq9T5U3eJvDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7be72cf04b2de3441da55ddd0a72941c5044efaf7c05442d1c7b4bbd09b562ff","last_reissued_at":"2026-05-18T00:58:35.748021Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:35.748021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05931","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":"2026-05-18T00:58:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"JcZss93htBVFAsOP0uLfN8Ujb1Y5H/ShSaywpnrMNNbTkKYWbdpWt0qG4UbbRzYvkmrCbjrIUbFQNjwBJ7S9Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:00:40.798302Z"},"content_sha256":"81b91bcfb9fdb9915a338c06686991d2ccb977e2b20f143d327812be86199b3b","schema_version":"1.0","event_id":"sha256:81b91bcfb9fdb9915a338c06686991d2ccb977e2b20f143d327812be86199b3b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:PPTSZ4CLFXRUIHNFLXOQU4UUDR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Effect of Number of Users in Multi-level Coded Caching","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Jad Hachem, Nikhil Karamchandani, Suhas Diggavi","submitted_at":"2015-04-22T19:24:01Z","abstract_excerpt":"It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. This has also been extended to the case when content has non-uniform popularity through several models. In this paper we focus on a multi-level popularity model, where content is divided into levels based on popularity. We consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup). When the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05931","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":"2026-05-18T00:58:35Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sdgL/6vvF1MvxMQ3Y5o7+Q0j4jlgnVLCctGto7K13seJPPF5oKYZpAxCv9QQcU+LE2ugyhNGeciZb4OhvWnRCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T03:00:40.798690Z"},"content_sha256":"9495c7fd9dc3df7aa0ac7f5b91e64fc0bd0cd25ba958d4978549500d4fbae0c2","schema_version":"1.0","event_id":"sha256:9495c7fd9dc3df7aa0ac7f5b91e64fc0bd0cd25ba958d4978549500d4fbae0c2"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/PPTSZ4CLFXRUIHNFLXOQU4UUDR/bundle.json","state_url":"https://pith.science/pith/PPTSZ4CLFXRUIHNFLXOQU4UUDR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/PPTSZ4CLFXRUIHNFLXOQU4UUDR/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":"2026-05-28T03:00:40Z","links":{"resolver":"https://pith.science/pith/PPTSZ4CLFXRUIHNFLXOQU4UUDR","bundle":"https://pith.science/pith/PPTSZ4CLFXRUIHNFLXOQU4UUDR/bundle.json","state":"https://pith.science/pith/PPTSZ4CLFXRUIHNFLXOQU4UUDR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/PPTSZ4CLFXRUIHNFLXOQU4UUDR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:PPTSZ4CLFXRUIHNFLXOQU4UUDR","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":"1c3ff2cca72a61d275b76483f4d03a5dd05e56b3705bd3c809cc0c4158abb4d7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-22T19:24:01Z","title_canon_sha256":"3d43371c3859bff13b82da658fbff093b2497d16e8744c78bcc2a87a9da66cde"},"schema_version":"1.0","source":{"id":"1504.05931","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05931","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05931v1","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05931","created_at":"2026-05-18T00:58:35Z"},{"alias_kind":"pith_short_12","alias_value":"PPTSZ4CLFXRU","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_16","alias_value":"PPTSZ4CLFXRUIHNF","created_at":"2026-05-18T12:29:37Z"},{"alias_kind":"pith_short_8","alias_value":"PPTSZ4CL","created_at":"2026-05-18T12:29:37Z"}],"graph_snapshots":[{"event_id":"sha256:9495c7fd9dc3df7aa0ac7f5b91e64fc0bd0cd25ba958d4978549500d4fbae0c2","target":"graph","created_at":"2026-05-18T00:58:35Z","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":"It has been recently established that joint design of content delivery and storage (coded caching) can significantly improve performance over conventional caching. This has also been extended to the case when content has non-uniform popularity through several models. In this paper we focus on a multi-level popularity model, where content is divided into levels based on popularity. We consider two extreme cases of user distribution across caches for the multi-level popularity model: a single user per cache (single-user setup) versus a large number of users per cache (multi-user setup). When the","authors_text":"Jad Hachem, Nikhil Karamchandani, Suhas Diggavi","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-22T19:24:01Z","title":"Effect of Number of Users in Multi-level Coded Caching"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05931","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":"sha256:81b91bcfb9fdb9915a338c06686991d2ccb977e2b20f143d327812be86199b3b","target":"record","created_at":"2026-05-18T00:58:35Z","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":"1c3ff2cca72a61d275b76483f4d03a5dd05e56b3705bd3c809cc0c4158abb4d7","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2015-04-22T19:24:01Z","title_canon_sha256":"3d43371c3859bff13b82da658fbff093b2497d16e8744c78bcc2a87a9da66cde"},"schema_version":"1.0","source":{"id":"1504.05931","kind":"arxiv","version":1}},"canonical_sha256":"7be72cf04b2de3441da55ddd0a72941c5044efaf7c05442d1c7b4bbd09b562ff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7be72cf04b2de3441da55ddd0a72941c5044efaf7c05442d1c7b4bbd09b562ff","first_computed_at":"2026-05-18T00:58:35.748021Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:35.748021Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7hYkeZj8rm1CDPwhPfQDPiLBrjybAOxFs9l9Spj400wDHKpeVUKkOWJ8uz6KiMVvH6kvT+jsP5zq9T5U3eJvDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:35.748719Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05931","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81b91bcfb9fdb9915a338c06686991d2ccb977e2b20f143d327812be86199b3b","sha256:9495c7fd9dc3df7aa0ac7f5b91e64fc0bd0cd25ba958d4978549500d4fbae0c2"],"state_sha256":"fdbca7cf5ac799852e99df99b2266954b7c1efc391389b1d620318c511625914"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"SYcL2FFjudZEs7BsbjWyeArlbTdmSvVgvuNBIMsqAkBo/HkbGB69oxxty3jUi5423C+JE8OYv6Z1D3cb6srtDg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T03:00:40.800895Z","bundle_sha256":"325445370be25b30de4a7c11252a5f2b40082cbe03fa4a648ddf3fccae9794d4"}}