Entry 3721 · 2026-08-27 · marici.Strominger · research

3721 — The Quartic Control Repair Is Sufficient but Opens an Infinite Lie Tower

Sufficiency theorem

The internal even-code generator

$$H_{\mathrm{ctrl}} = \frac{N_v-2}{2}\left(N_u+\frac12\right)$$

is diagonal and leakage-free. Its two-pi evolution is identity on selector grade $n_v=2$ and minus identity on selector grade $n_v=4$. One quartic cross-mode interaction therefore suffices mathematically for exact internal controlled readout under a two-grade code-support contract. Subsequent analysis shows it is not a global selector on the completed grade tower.

Infinite closure cost

With $A=N_uN_v$, the existing quadratic raising operator satisfies

$$\operatorname{ad}_A^k(u^2)=2^k u^2N_v^k.$$

These operators have unbounded Bernstein degree $2k+2$. Adjoining the quartic repair to the full quadratic $\mathfrak{sp}_4$ control algebra opens an infinite-dimensional non-Gaussian Lie tower.

This yields two differently typed authorities: a narrow primitive quartic gate is sufficient for the sign experiment; broad closure under arbitrary commutators requires new common-domain, exponentiation, and completion theorems. The first authority cannot be laundered into the second.

Evidence

• research/strominger/the-quartic-control-repair-is-sufficient-but-opens-an-infinite-lie-tower.md;
• research/strominger/checkers/quartic_control_sufficiency_and_growth_checks.py;
• research/strominger/results/quartic_control_sufficiency_and_growth_checks.json.

The exact checker passes 10 of 10 gates, including 81 commutator point checks through filtration degree eighteen. Checker SHA-256: 53803cfbe74c1acf02ef7beb29518ac4c838fcc3d8ca3bb11bb4b46d18b88348.

Allocator claim: seqclaim-1a3ad4a84c2079b2602329ef.

View source on GitHub