CALC-038

The 2.45 to 5.8 GHz ground-intensity ratio, focused against collimated

Supports CLM-0862. A calculation is required because that claim's stated value is arithmetic performed here. Independently reproduced by PyPO 1.2.1 (SRC-358, pinned commit e75c79a, CPU double precision).

Configuration. 1 km circular aperture, 10 dB Gaussian amplitude taper, 6.72 GW radiated, range 35,800 km taken as sub-satellite altitude. Two frequencies, two phase conditions.

Independent reproduction:

FOCUSED    2.45 GHz   248.204  vs PyPO  248.20      +0.002 pct
FOCUSED    5.8  GHz  1391.017  vs PyPO 1391.017     -0.000 pct
COLLIMATED 2.45 GHz   247.582  vs PyPO  247.5812    +0.000 pct
PyPO focused ratio 5.60433153 vs exact 5.6043315285   nine significant figures

Why the collimated case cannot achieve f^2:

Fraunhofer distance 2D^2/lambda:  2.45 GHz  16,345 km    5.8 GHz  38,693 km
R / Fraunhofer at 35,800 km:      2.45 GHz   2.190       5.8 GHz   0.925
residual quadratic phase:         2.45 GHz   0.179 rad   5.8 GHz   0.424 rad

The 5.8 GHz link sits INSIDE its own Fraunhofer distance, so the defocus penalty is larger there and the ratio falls below f^2 by 1.15 per cent. PyPO power conservation 99.904 per cent of 6.72 GW inside 100 km.

A LABEL DEFECT CORRECTED DURING THIS CALCULATION, recorded because correcting it is what isolated the result. An earlier comparison cited PyPO's 247.60 against 248.20 as independent confirmation and called the 0.24 per cent difference agreement. It was not agreement. Those are the COLLIMATED and FOCUSED cases respectively - two different physical configurations. Matched properly, the two implementations agree to six significant figures, about a hundred times better than the figure reported as success.

AN INDEPENDENT CONFIRMATION THAT AGREES TOO LOOSELY IS EVIDENCE OF A CONFIGURATION MISMATCH, NOT EVIDENCE OF AGREEMENT. The corollary is the harder half: agreement is only evidence if you know how closely the two things SHOULD agree. Here that number existed - exact f^2 - and it is the only reason the gap surfaced. This is the eighth instance of METHOD rule VF1's failure mode found on 2026-09-05, and the only one that was inside a confirmation rather than inside a claim.

Origin: EM simulation pass, section 20. Scripts po_beam.py and focused_results.py, PyPO side under pypo-58. Producer-computed and UNVERIFIED: the producer may not verify its own work.

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