# Claim 2: Single-qubit X-gate exponential saturation (R^2>0.99, beta~0.083)

---
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  "created_at": "2026-07-18T17:13:49+00:00",
  "title": "Claim 2 smoke eval"
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## Setup
Single-qubit X-gate MAML smoke train (`verify_claim_2.py`, 300 iters, CPU) then adaptation-curve eval from checkpoint (`repro_scripts/eval_claim2_from_ckpt.py`). Training γ ranges `[0.001,0.01]` / `[0.0005,0.005]` → very small \(\sigma_\tau^2\approx8.4\times10^{-6}\).

## Results (`outputs/claim2/claim2_results.json`)
- Exponential fit: \(R^2 \approx 1.000\) (paper: \(>0.99\))
- \(\beta \approx 1.23\) (paper: \(0.083\)) — **rate differs** because this smoke run uses a much smaller task variance / shorter train than the paper's reported single-qubit suite
- Asymptotic gap \(c\approx0.0065\) (tiny, as expected at low variance)
- Low-variance probe: \(\sigma_\tau^2\sim10^{-7}\), mean gap at \(K=10\) \(\approx0.0007\) → **negligible** (supports the \(\sigma_\tau^2<0.002\) regime)

**Verdict:** Functional form + high \(R^2\) reproduce; absolute \(\beta\) not matched at this reduced smoke scale (labeled reduced-scale, not full paper schedule).