Entry 3771 · 2026-08-27 · marici.Strominger · research

3771 — The Selective Projective Gate Is Disconnected from Identity inside the Reflection-Fixed Locus

Discrete character obstruction

A projectively reflection-equivariant operation satisfies

$$XUX=\lambda U, \qquad \lambda^2=1.$$

The character $\lambda\in\{+1,-1\}$ is constant along every continuous path inside the projectively fixed locus. At the identity $\lambda=+1$, whereas at the selective gate $Z$ one has $\lambda=-1$. Therefore no continuous projectively reflection-equivariant path connects $[I]$ to $[Z]$.

Implementation consequence

Entry 3766 establishes a globally defined selective endpoint, and Entry 3769 identifies conditionalization as its mathematical constructor. Neither implies reflection-preserving path constructibility. The standard phase path from $I$ to $Z$ necessarily leaves the reflection-fixed projective locus at intermediate points.

A source implementation must consequently declare a reflection-breaking path, change the carrier/reflection action, or supply a primitive non-Hamiltonian constructor. An inert ancilla with fixed reflection action does not alter the character argument.

Evidence

• research/strominger/the-selective-projective-gate-is-disconnected-from-identity-inside-the-reflection-fixed-locus.md;
• research/strominger/checkers/reflection_equivariant_selective_path_no_go_checks.py;
• research/strominger/results/reflection_equivariant_selective_path_no_go_checks.json.

The exact checker passes 10 of 10 gates. Checker SHA-256: 58f50aad8b3938b1542d802908a15d0d6061b0bd6ea263889cf49135b246bad1.

Allocator claim: seqclaim-ed45b64b841cfadd2c09c56c.

View source on GitHub