retag: logbook.json (verbatim titles)

logbook.json

@@ -1,6 +1,7 @@
 {
   "schema_version": "1.0",
   "title": "Reproduction: Certificate-Guided Pruning for Stochastic Lipschitz Optimization",
+  "emoji": "📏",
   "space_id": "snaykey/repro-graph-alignment",
   "paper": {
     "arxiv_id": "2601.20231",
@@ -10,7 +11,7 @@
     "icml2026-repro",
     "paper-9CqZoRWpoc"
   ],
-  "updated_at": "2026-07-29T12:00:00+00:00",
+  "updated_at": "2026-07-29T00:00:00+00:00",
   "root": {
     "slug": "index",
     "title": "Reproduction: Certificate-Guided Pruning for Stochastic Lipschitz Optimization",
@@ -21,32 +22,32 @@
         "children": []
       },
       {
-        "slug": "claim-1",
+        "slug": "claim-1-certificates",
         "title": "Certificate-Guided Pruning (CGP) maintains an explicit active set A_t of candidate optima using confidence-adjusted Lipschitz envelopes, certifying with high probability that any point outside A_t is suboptimal (Section 3, Algorithm 1).",
         "children": []
       },
       {
-        "slug": "claim-2",
+        "slug": "claim-2-shrinkage",
         "title": "Under a margin condition with near-optimality dimension α (Assumption 2.3), the Shrinkage Theorem bounds the active set volume as Vol(A_t) ≤ C·(2(β_t + Lη_t) + γ_t)^(d−α) (Theorem 4.6).",
         "children": []
       },
       {
-        "slug": "claim-3",
+        "slug": "claim-3-sample-complexity",
         "title": "CGP achieves ε-optimality with probability at least 1−δ using T = Õ(L^d ε^{-(2+α)} log(1/δ)) samples, improving on the worst-case Õ(ε^{-(2+d)}) rate whenever α < d (Theorem 4.8).",
         "children": []
       },
       {
-        "slug": "claim-4",
+        "slug": "claim-4-lower-bound",
         "title": "A matching lower bound shows any algorithm requires Ω(ε^{-(2+α)}) samples under the same margin condition, establishing CGP's minimax sample-complexity optimality (Theorem 4.9).",
         "children": []
       },
       {
-        "slug": "claim-5",
+        "slug": "claim-5-adaptive-l",
         "title": "CGP-Adaptive learns the Lipschitz constant L online via a doubling scheme, adding only an O(log T) multiplicative overhead to the sample complexity (Theorem 5.1, Section 5).",
         "children": []
       },
       {
-        "slug": "claim-6",
+        "slug": "claim-6-cgp-tr",
         "title": "CGP-TR, a trust-region variant, scales to dimension d > 50 via certified restarts that provably never falsely eliminate the region containing the true optimizer x* (Theorem 6.1, Section 6).",
         "children": []
       },