{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:FY4UNGZXDAZ57BY7PENQYFZUB7","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":"b7050801f981c002d6783d53005d1c025a0d6f0fc74decdaa48df7186a70d5f1","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2013-05-01T12:17:01Z","title_canon_sha256":"f600164b6f364fe4e87360835e5c49cef0a12ff3acb8340795d4760b83c28d32"},"schema_version":"1.0","source":{"id":"1305.0153","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1305.0153","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"arxiv_version","alias_value":"1305.0153v1","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1305.0153","created_at":"2026-05-18T03:26:41Z"},{"alias_kind":"pith_short_12","alias_value":"FY4UNGZXDAZ5","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_16","alias_value":"FY4UNGZXDAZ57BY7","created_at":"2026-05-18T12:27:45Z"},{"alias_kind":"pith_short_8","alias_value":"FY4UNGZX","created_at":"2026-05-18T12:27:45Z"}],"graph_snapshots":[{"event_id":"sha256:a95991601e3fe1f56baf7ab82a8676ca2874193e65707258934c90328e71f45e","target":"graph","created_at":"2026-05-18T03:26:41Z","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":"This paper considers a cross-layer optimization problem driven by multi-timescale stochastic exogenous processes in wireless communication networks. Due to the hierarchical information structure in a wireless network, a mixed timescale stochastic iterative algorithm is proposed to track the time-varying optimal solution of the cross-layer optimization problem, where the variables are partitioned into short-term controls updated in a faster timescale, and long-term controls updated in a slower timescale. We focus on establishing a convergence analysis framework for such multi-timescale algorith","authors_text":"Junting Chen, Vincent K. N. Lau","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2013-05-01T12:17:01Z","title":"Convergence Analysis of Mixed Timescale Cross-Layer Stochastic Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.0153","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:e15a641413dcebe991436d56d5d39eb4d2a027807715c11b2d62472cf9c7494e","target":"record","created_at":"2026-05-18T03:26:41Z","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":"b7050801f981c002d6783d53005d1c025a0d6f0fc74decdaa48df7186a70d5f1","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.SY","submitted_at":"2013-05-01T12:17:01Z","title_canon_sha256":"f600164b6f364fe4e87360835e5c49cef0a12ff3acb8340795d4760b83c28d32"},"schema_version":"1.0","source":{"id":"1305.0153","kind":"arxiv","version":1}},"canonical_sha256":"2e39469b371833df871f791b0c17340fcfbc3e8cc048aea559107d849a8c54c9","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2e39469b371833df871f791b0c17340fcfbc3e8cc048aea559107d849a8c54c9","first_computed_at":"2026-05-18T03:26:41.826073Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:41.826073Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"987tXb5YVwBPAkOGp6iZgbXlS6lDDq71oH0PmCsuJaBNV8/LMzzJDGej+oJjlOhbCVql+QuY63WJ9hch7PvAAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:41.826742Z","signed_message":"canonical_sha256_bytes"},"source_id":"1305.0153","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e15a641413dcebe991436d56d5d39eb4d2a027807715c11b2d62472cf9c7494e","sha256:a95991601e3fe1f56baf7ab82a8676ca2874193e65707258934c90328e71f45e"],"state_sha256":"20a78e09c0c13a5faa410a264745b753d5db11dce3bdb8080a81bcca1f0b9194"}