# PVD angular correlation figure

Figure. Angular correlation and finite-basis observability of rotated-trench first contacts. (a) Diagonal and anti-diagonal weights on the nine prescribed slope pairs share complete x and y marginals of one third per category. tx and ty are horizontal-to-depth direction ratios; a populated cell carries probability one third. (b) At aspect ratio one, all three distributions give two-thirds bottom contacts for an x-aligned trench, while rotation of the across-direction to (3/5, 4/5) gives diagonal 8/15, anti-diagonal 14/15 and independent-product 2/3. The denominator is all arrivals crossing the opening. (c) Stored bottom-contact fractions at aspect ratios 1, 2, 5 and 10 show the geometry dependence for the rotated direction; connecting lines guide the eye. (d) Cumulative exact ranks of ideal observation matrices are 1, 5, 6, 7, 7, 8, 8 and 9. Open markers identify redundant additions at stages 5 and 7. The stages successively include total probability, complete orthogonal marginals, rotated bottom responses at aspect ratios 1 and 5, rotated right-minus-left imbalance at aspect ratios 1 and 5, orthogonal-rotated bottom response at aspect ratio 5, and its imbalance. The orthogonal direction is (-4/5, 3/5). Rank nine is identification only within the imposed nine-direction noiseless model. Original synthetic study, static first-contact geometry and uniform opening phase; no film-growth or measured-calibration claim.

## Limits

- Nine prescribed directions are a finite basis, not a continuous measured angular distribution.
- No measured data, physical calibration or native SiMTRA execution is represented.
- Static first-contact fractions are not film thickness, deposition rate, sticking, incorporation, reaction yield or device performance.
- No gas scattering, reflection, surface chemistry, evolving shape or process loading is included.
- Observation rows are hypothetical ideal responses; detector acceptance, noise, registration and experimental feasibility remain uncalibrated.
- The rank result does not prove a unique continuous solution, good numerical conditioning or practical measurement identifiability.
- Lines between the four archived aspect ratios guide the eye; no intermediate response was simulated for this figure.
- Ten measurement requirements in the source dossier remain missing, including geometry, source, angular response, footprint, dimensional flux, surface response, growth, loading, electrical linkage and uncertainty.

## Reproduction

Run python -B plot.py --data plot-data.json --out fresh-output with NumPy and Matplotlib. This reuses stored numerical values; no new solver or physical measurement is run.