tech/python
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Essay
From Path Tubes to a Near-Critical Domination Bound Revised from 22 July 2026
A first-person, code-heavy companion tracing the near-critical bound that led to The Annealed Critical Window for Growing-Radius Domination in Random Regular Graphs. Rather than reproducing its theorem-and-proof form, this page traces where the problem came from — a cops-and-robbers hypergraph question that collapsed into a domination bound — why the answer carries an unnecessary coupon-collector logarithm, and how a chain of computational detours (a failed concavity conjecture, a catastrophic cancellation, an independent audit that caught a stale constant) repeatedly redirected the proof before it reached its final shape.
Clarified the scope of the tube interpretation, linked the corrected current preprint, and recorded the resolved bounded critical window.