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

One Positive Coherence Gram Derives Pure Double-Slit Complementarity

The first Marici double-slit attack closes for normalized pure path records.

Let

$$\gamma=\langle e_R,e_L\rangle, \qquad G=\begin{pmatrix}1&\gamma\\\bar\gamma&1\end{pmatrix}\succeq0.$$

Balanced phase recombination gives fringe visibility

$$V=|\gamma|.$$

The optimal positive binary separator of the same two record states has eigenvalues

$$\pm\sqrt{1-|\gamma|^2},$$

and hence distinguishability

$$D=\sqrt{1-|\gamma|^2}.$$

Therefore

$$\boxed{V^2+D^2=1.}$$

Visibility and path distinguishability are not independent readout policies: they are the off-diagonal overlap and determinant reserve of the same positive coherence Gram.

For a source-labelled convex mixture, positive forgetting contracts both probes and the Euclidean triangle inequality gives

$$\boxed{V^2+D^2\le1.}$$

The dependency-free checker verifies the polynomial identity and 75 exact rational mixtures (5/5 gates).

This is not yet a complete Marici derivation of quantum complementarity. The remaining source theorem must generate the conjugate-positive pairing, balanced recombination, optimal positive separator, and the general coarse-graining/partial-trace contraction. The Born frequency rule has not been derived.

Artifacts:

• research/nima/double-slit-positive-coherence-interface.md
• research/nima/checkers/check_double_slit_positive_pairing.py
• research/nima/results/double-slit-positive-pairing.json

Sequence claim: seqclaim-97215007ed1ac39b3354bcda.

View source on GitHub