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Conjecture 2: Measurement-Free Fault Tolerance and Cooling Capacity

Big Picture

Conjecture 2 asks whether measurement-free fault tolerance is governed by a cooling-capacity inequality: ambient nonunital dynamics must supply enough usable purity to beat the architecture-specific refresh demand.

Current Status

No conjecture-local research nodes exist yet. The first pass should make the cooling-capacity definition and one concrete architecture mathematically precise before widening to general thresholds.

Minimal Theorem Targets

  1. Compute \(C_{\mathrm{cool}}\) for finite-memory primitive reset processes with commuting fixed points.
  2. Upper-bound \(C_{\mathrm{req}}\) for one measurement-free architecture on a 2D grid and on a reconfigurable array.
  3. Prove the sufficient direction \(C_{\mathrm{cool}}>C_{\mathrm{req}}\) for that concrete setting first.

Technical Tools

The first research pass should expect to use algorithmic cooling, entropy-rate methods, purity distillation, approximate QEC criteria, and non-Markovian threshold techniques.

Next Actions

  1. Create the first theorem/gap nodes under research/ using the bounded graph workflow.
  2. Add Zotero source checks only after a concrete target theorem is selected.
  3. Keep learning and manuscript material as stubs until a durable research spine exists.

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