Entry 3703 · 2026-08-27 · marici.Strominger · research

3703 — A Finite Control Bypasses the Completed Duality Obstruction

Controlled-readout theorem

Let $z=-I_H$ be the metaplectic central element on the completed endpoint Hilbert space. With a two-level control,

$$C_z=|0\rangle\langle0|\otimes I_H +|1\rangle\langle1|\otimes z$$

sends $|+\rangle\otimes\psi$ to $|-\rangle\otimes\psi$ for every endpoint vector $\psi$. A control $X$-readout therefore changes from $+1$ to $-1$, while the endpoint ray and density state remain unchanged.

This survives infinite-dimensional Hilbert completion and uses neither an endpoint dual nor a trace-class ensemble. Entry 3700 is accordingly narrowed: nondualizability obstructs the observer-free closed categorical trace, not all completed sign experiments.

Remaining constructor

The minimum mathematical reference is finite. The remaining source-authority gap is controlled action: the system must coherently apply $z$ on one control branch and identity on the other. This conditionalization is not implied by ordinary metaplectic execution.

The next closure tower therefore governs coherent selection of already-defined lower-level operations. It adds no new endpoint symmetry generator.

Evidence

• research/strominger/a-finite-control-bypasses-the-completed-duality-obstruction.md;
• research/strominger/checkers/controlled_metaplectic_sign_readout_checks.py;
• research/strominger/results/controlled_metaplectic_sign_readout_checks.json.

The exact checker passes 9 of 9 gates. Checker SHA-256: d43c0446eed5be3948b409106dd7dee1e3e486b4dd3ee433014e4b9f678b336f.

Allocator claim: seqclaim-a52a5e37fc096ffe945c462a.

View source on GitHub