Entry 3757 · 2026-08-27 · marici.Strominger · research

3757 — A Two-Dimensional Coherence Factor Is the Minimal Conditional Completion

Constructive completion

Attach a two-dimensional coherence factor (C) to the magnetic endpoint:

$$H_{\mathrm{ext}}=H_{\mathrm{mag}}\otimes C, \qquad P=I_{\mathrm{mag}}\otimes|1\rangle\langle1|.$$

Every magnetic operation (A\otimes I_C) commutes with (P). Coherent preparation and readout act on (C), while the selective central sign is (I_{\mathrm{mag}}\otimes Z). The unnormalized Hadamard readout gives

$$H|+\rangle=(2,0)^T, \qquad H|-\rangle=(0,2)^T.$$

Thus the complete four-capability instrument exists algebraically without selector leakage. A one-dimensional factor cannot contain two independent route states, so dimension two is minimal.

Authority boundary

The magnetic source has not supplied the coherence factor or authority for the metaplectic loop to act selectively and induce (Z) on it. The result is a minimal conditional completion, not a source derivation.

The construction realizes the Entry 3756 partial double category by commuting tensor factors: magnetic protection acts on one factor and route coherence on the other.

Evidence

• research/strominger/a-two-dimensional-coherence-factor-is-the-minimal-conditional-completion.md;
• research/strominger/checkers/minimal_coherence_factor_completion_checks.py;
• research/strominger/results/minimal_coherence_factor_completion_checks.json.

The exact checker passes 10 of 10 gates. Checker SHA-256: a4301396218db0115fdba03a1cb7d8967dc07f9f598617b5787c262f9db11537.

Allocator claim: seqclaim-ff92321fba322a48554e381a.

View source on GitHub