{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:FN3W2XZZHPX2MCSDYMT37WCE66","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":"8b8de8cef4032f4890b00561ded88be8927b591afccdc042e114a5e813ae06db","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-06-24T03:53:21Z","title_canon_sha256":"de0db4ff5de950c3d12bc55bb8df7ab70ec8d8df5443fde4e39561aa9321dfbe"},"schema_version":"1.0","source":{"id":"1706.07903","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.07903","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"arxiv_version","alias_value":"1706.07903v1","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.07903","created_at":"2026-05-18T00:41:47Z"},{"alias_kind":"pith_short_12","alias_value":"FN3W2XZZHPX2","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_16","alias_value":"FN3W2XZZHPX2MCSD","created_at":"2026-05-18T12:31:15Z"},{"alias_kind":"pith_short_8","alias_value":"FN3W2XZZ","created_at":"2026-05-18T12:31:15Z"}],"graph_snapshots":[{"event_id":"sha256:aa54ca7f15fc6c9760eed7fda2d591df02877d8cb2cad570d766042d00e5cedd","target":"graph","created_at":"2026-05-18T00:41:47Z","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 and multicasting are two promising methods to support massive content delivery in multi-tier wireless networks. In this paper, we consider a random caching and multicasting scheme with caching distributions in the two tiers as design parameters, to achieve efficient content dissemination in a two-tier large-scale cache-enabled wireless multicasting network. First, we derive tractable expressions for the successful transmission probabilities in the general region as well as the high SNR and high user density region, respectively, utilizing tools from stochastic geometry. Then, for the c","authors_text":"Yang Yang, Ying Cui, Zhehan Cao, Zitian Wang","cross_cats":["math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-06-24T03:53:21Z","title":"Joint and Competitive Caching Designs in Large-Scale Multi-Tier Wireless Multicasting Networks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07903","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":"sha256:32456d05a5f0f643dc5f0832f028e2e588578d3efa6e468b6c7941037539e692","target":"record","created_at":"2026-05-18T00:41:47Z","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":"8b8de8cef4032f4890b00561ded88be8927b591afccdc042e114a5e813ae06db","cross_cats_sorted":["math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2017-06-24T03:53:21Z","title_canon_sha256":"de0db4ff5de950c3d12bc55bb8df7ab70ec8d8df5443fde4e39561aa9321dfbe"},"schema_version":"1.0","source":{"id":"1706.07903","kind":"arxiv","version":1}},"canonical_sha256":"2b776d5f393befa60a43c327bfd844f78cef1cc558d64d4864055e2593869d12","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2b776d5f393befa60a43c327bfd844f78cef1cc558d64d4864055e2593869d12","first_computed_at":"2026-05-18T00:41:47.199292Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:47.199292Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tCQdC7OOXLzw81LCWDZ4GGDjTlPctz5pYlpCPVukam0YwIgOHZvVmNdzuXohiOcIUcSzPfIBVvm/5qwao7QwDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:47.199853Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.07903","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:32456d05a5f0f643dc5f0832f028e2e588578d3efa6e468b6c7941037539e692","sha256:aa54ca7f15fc6c9760eed7fda2d591df02877d8cb2cad570d766042d00e5cedd"],"state_sha256":"4049a8454fa6c4ce5e333ab998a530b0fc9b22ebdad909fd8a62910d9d9ebb6b"}