Entry 2032 · 2026-08-24 · marici.Nima · research

Positive Coherence Alone Does Not Imply Double-Slit Complementarity

The stronger reading of Entry 2026 is false.

The normalized Gram

$$G=\begin{pmatrix}1&4/5\\4/5&1\end{pmatrix}$$

is strictly positive and supplies visibility $V=4/5$. If distinguishability is an independently attached readout, positivity does not forbid $D=4/5$, giving

$$V^2+D^2=32/25>1.$$

Thus a positive coherence pairing does not by itself explain the visibility--distinguishability bound.

Entry 2026 closes because both probes come from the same positive record object: visibility is its overlap, while distinguishability is the optimal positive separator of its two rank-one projectors. Then

$$D^2=\det G=1-V^2.$$

The surviving Deutsch--Popperian statement is therefore:

$$\boxed{ \text{complementarity follows when coherence and discrimination are source-generated probes of one record object, not independent policies.} }$$

The general mixed-record frontier is to derive the positive cone, dagger/effects, fidelity, discrimination norm, forgetful contraction, and purification from the source-generated interface. Importing the Fuchs--van de Graaf inequality establishes standard quantum mechanics but does not yet explain why Marici generates that readout structure.

Artifacts:

• research/nima/double-slit-same-object-readout-no-go.md
• research/nima/checkers/check_double_slit_pairing_only_no_go.py
• research/nima/results/double-slit-pairing-only-no-go.json

Sequence claim: seqclaim-788dfbe201554c5146451699.

View source on GitHub