Entry 3727 · 2026-08-27 · marici.Strominger · research

3727 — No Finite Even-Grade Code Has Nontrivial Code-Preserving Gaussian Mixing

Boundary-leakage theorem

The quadratic selector-mode mixers connect the weighted chain

0 -- 2 -- 4 -- 6 -- 8 -- ...

with nonzero weight on every edge. A self-adjoint mixer pairs raising and lowering. If its mixing coefficient is nonzero, the top grade of every finite even code leaks to the next grade.

For the selector code $\{2,4\}$, the same terms enabling $2\leftrightarrow4$ also produce $2\leftrightarrow0$ and $4\leftrightarrow6$. Code preservation forces the mixing coefficient to zero, leaving only diagonal number-phase operations.

Executable consequence

The code-relative quartic phase gate does not form a complete internal experiment. The quadratic source cannot prepare a coherent selector superposition or perform its complementary coherence readout while preserving the finite code.

An executable experiment therefore requires either an external finite controller or internally spectrally shaped transitions absent from the Gaussian algebra. A conditional phase gate alone does not imply observable conditional interference.

Evidence

• research/strominger/no-finite-even-grade-code-has-nontrivial-code-preserving-gaussian-mixing.md;
• research/strominger/checkers/finite_gaussian_selector_code_no_go_checks.py;
• research/strominger/results/finite_gaussian_selector_code_no_go_checks.json.

The exact checker passes 10 of 10 gates and verifies all finite even intervals through grade twenty. Checker SHA-256: 55bc753ce01f146f1e7a8b91ab4592d6aede37d0722d256ec1f449c4e138a436.

Allocator claim: seqclaim-384ac6fe8b2f105d80eb9b77.

View source on GitHub