v0.3.0: closed-form sigma-curve + 5-algorithm verification + 3.6 self-correction

v0.3.0 — closed-form σ-curve framework + §3.6 self-correction (2026-06-14)

Errata + extension of v0.2.1 (DOI 10.5281/zenodo.20681847).

Summary

The §3.6 boundary-flip + universal direction stochasticity + plateau/overload framework of v0.2.1 is replaced by a single closed form derived from standard phase-noise dephasing of the FFT:

p(σ) = ρ + (p_0 - ρ) · exp(-σ²)
E[K(σ)] = (1 - (1-p)^M) / p

derived from E[|FFT(a·e^{iε})_k|²] = (1-e^{-σ²})/Q + e^{-σ²}·P_0(k).

Cross-algorithm verification (5 classes)

Algorithm	R²
Grover (k iter)	+0.88
Shor pure (b-trick)	+0.95
QPE isolated (no b-trick)	+0.96
Simon (Hadamard + XOR)	+0.99
Hybrid (C)+b-trick (paper §3.6 setup)	+0.91

Positioning

Analytical complement to Yang-Markidis (arXiv:2605.16074, ICS Workshops '26) — their empirical noise-propagation model (1-ε)·P_s + ε·distractors has the same structural form; we provide the analytical foundation ε = 1 - exp(-σ²).

Self-correction (§3.6.bis in paper.md)

Retracted within §3.6:

• "Boundary flip" lexicon as a distinct mechanism.
• "Deterministic flip set within plateau" reading (statistical, not structural).
• "Universal direction stochasticity" as unexplainable — sign(p_0 - ρ) explains it.

Retained:

• All 31,200 raw K-measurements.
• 5/5 regime-map cross-cell predictions.
• The conclusion that SR-based factoring acceleration is precluded (now with closed-form bound).
• Theorems 1–5 (independent of §3.6).

What this is NOT

• Not a new mechanism (exp(-σ²) is standard dephasing).
• Not a refutation of v0.2.1 — data retained, only §3.6 interpretation corrected.

What this IS

• Honest scientific cycle: claim → cross-verification → self-correction.
• Small bridge: Shor-class SR claims ↔ standard dephasing literature.
• Cross-algorithm organizing result.

Citation

Cite both v0.2.1 (theorems 1-5 + raw data) and v0.3.0 (§3.6 self-correction + closed-form framework).

Related work

• Yang-Markidis (arXiv:2605.16074) — empirical recoverability via ML features.
• Tight success bounds (arXiv:2506.20527) — noise-free bounds.
• Coherence/decoherence in noisy Shor (arXiv:2508.11962) — lower bounds.

Files

• paper.md §3.6.bis (self-correction)
• sr_sigma_curve_model.md (unified framework)
• sr_generalization.md (SR generalization scoping)
• release_notes_v0.3.0.md
• arxiv_draft.md (short paper draft, ICS Workshops '27 target)
• experiments/{grover,shor,qpe_isolated,simon,hybrid,shor_n_scaling}_*.py

Companion code

numpy + Python stdlib only. ~3,500 LOC added in this release. Total compute for all 5 R² fits ~1 CPU-hour on 2025 laptop.

python -m experiments.grover_sigma_curve_model   # R²=0.88
python -m experiments.shor_sigma_curve_model     # R²=0.95
python -m experiments.qpe_isolated_sigma         # R²=0.96
python -m experiments.simon_sigma_curve          # R²=0.99
python -m experiments.hybrid_sigma_curve         # R²=0.91