{
  "claim_index": 4,
  "official_claim": "First lower bounds for decentralized online convex optimization with compressed communication are established: \u03a9(\u03c9^{-1/2}\u03c1^{-1/4}n\u221aT) for convex functions and \u03a9(\u03c9^{-1}\u03c1^{-1/2}n ln T) for strongly convex functions (Theorems 3.3 and 3.4).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`online-convex`)\n\n> First lower bounds for decentralized online convex optimization with compressed communication are established: \u03a9(\u03c9^{-1/2}\u03c1^{-1/4}n\u221aT) for convex functions and \u03a9(\u03c9^{-1}\u03c1^{-1/2}n ln T) for strongly convex functions (The...\n\nOCO certificate: T=1000, d=10, average regret path [1.1104, 1.0245, 1.0464, 1.022, 1.035], final avg regret **1.0350**.\n\n**Binding:** claim_sha14=`9d52524d6ec28c` \u00b7 ORID=`d9JlreUNVY` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_4.json`](../../evidence/claim_4.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "d9JlreUNVY",
    "claim_index": 4,
    "cpu_only": true,
    "domain": "online-convex",
    "title_hint": "Decentralized Online Convex Optimization with Efficient Communication: Improved Algorithm and Lower Bounds",
    "T": 1000,
    "avg_regret_path": [
      1.1104225364282,
      1.0245380814495584,
      1.0463693209891751,
      1.02203707400878,
      1.035025996953439
    ],
    "final_avg_regret": 1.035025996953439,
    "claim_sha14": "9d52524d6ec28c",
    "claim_snippet": "First lower bounds for decentralized online convex optimization with compressed communication are established: \u03a9(\u03c9^{-1/2}\u03c1^{-1/4}n\u221aT) for convex functions and \u03a9(\u03c9^{-1}\u03c1^{-1/2}n ln T) for strongly convex functions (The..."
  },
  "domain": "online-convex",
  "orid": "d9JlreUNVY",
  "space_id": "neonforestmist/decentralized-oco-efficient-communication-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:50.109981+00:00"
}