Entry 3773 · 2026-08-27 · marici.Strominger · research

3773 — Every Continuous Selective-Gate Path Fully Unlocks the Reflection Axis

Forced zero-overlap interface

Define

$$s(U)=\frac12\operatorname{tr}(U^\dagger XUX).$$

This continuous reflection-axis overlap satisfies $s(I)=+1$ and $s(Z)=-1$. Every continuous implementation path therefore contains an operation $U_*$ with $s(U_*)=0$. At that interface, the transported reflection axis is Hilbert-Schmidt orthogonal to the original axis.

Lossless saturation

For $U(t)=\operatorname{diag}(1,e^{i\pi t})$, the midpoint $U_*=\operatorname{diag}(1,i)$ remains exactly unitary. Its exact distance from both the commuting and anticommuting projective loci is four in the plus-or-minus Frobenius-squared test.

The forced defect is therefore complete symmetry unlocking, not norm loss, gap closing, or failure of reversibility. A physical contract must identify the source term supporting that unlocked interface and co-transport the detector frame through it.

Evidence

• research/strominger/every-continuous-selective-gate-path-fully-unlocks-the-reflection-axis.md;
• research/strominger/checkers/reflection_axis_midpath_unlocking_checks.py;
• research/strominger/results/reflection_axis_midpath_unlocking_checks.json.

The repaired exact checker passes 10 of 10 gates. Checker SHA-256: b019f349d6cb631da05295df05275dfe9bc222ad1856314c6b4810971bffca62.

Allocator claim: seqclaim-a19ac2f1ddb93c4217f1f505.

View source on GitHub