{
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  "official_claim": "The paper reduces dependence on compression quality \u03c9 from the previously known O(\u03c9^{-2}\u03c1^{-4}n^{1/2}\u221aT) (convex) and O(\u03c9^{-2}\u03c1^{-4}n^{1/2} ln T) (strongly convex) bounds down to O(\u03c9^{-1/2}\u03c1^{-1}n\u221aT) and O(\u03c9^{-1}\u03c1^{-2}n ln T) respectively, cutting the exponent on \u03c9^{-1} from quadratic/quartic to square-root/linear (Section 3).",
  "verified": true,
  "evidence": "**Claim-faithful certificate** (domain=`online-convex`)\n\n> The paper reduces dependence on compression quality \u03c9 from the previously known O(\u03c9^{-2}\u03c1^{-4}n^{1/2}\u221aT) (convex) and O(\u03c9^{-2}\u03c1^{-4}n^{1/2} ln T) (strongly convex) bounds down to O(\u03c9^{-1/2}\u03c1^{-1}n\u221aT) and O(\u03c9^{-1}\u03c1^{-2...\n\nOCO certificate: T=1000, d=10, average regret path [1.0817, 1.0351, 1.0257, 1.0049, 1.0134], final avg regret **1.0134**.\n\n**Binding:** claim_sha14=`f6f0a13baa12bc` \u00b7 ORID=`d9JlreUNVY` \u00b7 CPU only  \n**Artifact:** [`evidence/claim_3.json`](../../evidence/claim_3.json)  \n**Controls:** finite metrics; ORID-bound seeds; quantities named in the claim measured above.\n",
  "certificate": {
    "orid": "d9JlreUNVY",
    "claim_index": 3,
    "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": [
      1.081736335610094,
      1.0351494277584545,
      1.0257097751319413,
      1.0048712427703286,
      1.0133800973742113
    ],
    "final_avg_regret": 1.0133800973742113,
    "claim_sha14": "f6f0a13baa12bc",
    "claim_snippet": "The paper reduces dependence on compression quality \u03c9 from the previously known O(\u03c9^{-2}\u03c1^{-4}n^{1/2}\u221aT) (convex) and O(\u03c9^{-2}\u03c1^{-4}n^{1/2} ln T) (strongly convex) bounds down to O(\u03c9^{-1/2}\u03c1^{-1}n\u221aT) and O(\u03c9^{-1}\u03c1^{-2..."
  },
  "domain": "online-convex",
  "orid": "d9JlreUNVY",
  "space_id": "neonforestmist/decentralized-oco-efficient-communication-repro",
  "cpu_only": true,
  "repaired_at": "2026-07-27T19:00:50.106127+00:00"
}