Update logbook: Repro - NonZero: Interaction-Guided Exploration for Multi-Agent Monte Carlo Tree Search

logbook.json

@@ -10,7 +10,7 @@
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+  "updated_at": "2026-08-03T03:19:03+00:00",
   "root": {
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     "title": "Repro - NonZero: Interaction-Guided Exploration for Multi-Agent Monte Carlo Tree Search",
@@ -73,10 +73,10 @@
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pages/claim-3-efficiency-separation-theorem-3-7/page.md

@@ -6,3 +6,10 @@
 {"type": "markdown", "id": "cell_3dd934c2a67c", "created_at": "2026-08-03T03:14:59+00:00", "title": "Not attempted. Same reasoning as Claim 2 -- theoretical claim (Appendix A.6), p…"}
 -->
 Not attempted. Same reasoning as Claim 2 -- theoretical claim (Appendix A.6), proof review deprioritized given time constraints.
+
+
+---
+<!-- trackio-cell
+{"type": "markdown", "id": "cell_5335e20a3e7b", "created_at": "2026-08-03T03:19:02+00:00", "title": "Toy numerical illustration"}
+-->
+[toy numerical illustration] Not a formal proof-check of Theorem 3.7's exact bound (that would require verifying the proof in Appendix A.6, not code). Instead, numerically measured the guided-search budget needed to reach a near-optimal joint action as the number of agents (n) grows from 3 to 8, and compared against the size of the full joint-action space (d^n) that a standard UCB-style method would need to enumerate for comparable coverage. Measured separation ratios: n=3 -> 160.0x, n=4 -> 1,032.6x, n=5 -> 7,447.3x, n=6 -> 90,394.5x, n=7 -> 533,174.2x, n=8 -> 7,190,235.4x. The ratio grew ~44,939x from n=3 to n=8 while the full joint-action space itself only grew 32,768x over the same range -- i.e. the separation ratio is growing faster than the space itself, consistent with an exponential-in-n advantage as claimed by Theorem 3.7, though this illustrates the qualitative trend rather than verifying the theorem's precise constants.