CALC-088

The 1978 downlink computed forward, twice, from the document's own design parameters

Supports CLM-0870. A calculation is required: the claim states values computed here.

TWO INDEPENDENT IMPLEMENTATIONS, ONE OF THEM BLIND. Route A was run by an agent given the three stated values and the PDF and nothing else - synthesis/calcs.md, synthesis/beam-profile-adversarial.md, the adversarial and EM staging files and register/claims.md were all named as off-limits, and it reports honouring that. Route B was run by the EM stream, which HAD read CALC-086 and the adversarial pass while verifying CLM-0867 and declared that contamination itself, before being asked; it is a second implementation rather than a second route, and is labelled that way here rather than in a footnote. The working is recorded separately from this body.

What each route reached

The shape is right and only the label is wrong. Route A's ratio of peak to power-inside-5-km is 3.889474e-08 m^-2 against 3.889340e-08 implied by the source's own three numbers, agreeing to 0.003 per cent; and it records that plus or minus one point on the fraction moves that agreement to 1.1 per cent, a factor of 380, so the test is sharp rather than loose. Route B substituted its own 94.14 per cent into the peak-to-mean ratio and got 2.8652 against CALC-086's independently computed 2.8663, agreeing to 0.038 per cent from codes sharing no lines.

The frame question, closed

CLM-0867 recorded an assumption that the region holding the stated collection efficiency is CIRCULAR, and noted it was probably false and worth about 30 per cent. It is true, and the source says so: PDF p.37 reads "88% of its energy within a 5 km radius perpendicular to boresight". Both routes checked it independently. So pi*5000^2 is the right area and the 30 per cent worry does not bite on this term.

Where the routes DISAGREE, recorded rather than resolved

Both agree the collection figure is the odd one out. They give different reasons for it and the difference is not settled here.

- Route A: it is a CHAIN TERM, not a beam-geometry fact. Table B-1 at PDF p.B-68, for the same 1 km, 2.45 GHz, Gaussian-taper, 23 mW/cm2 system, lists "Intercept Efficiency 0.95" as a row SEPARATE from Ideal Beam 0.965, Inter-Subarray Errors 0.956, Intra-Subarray Errors 0.981 and Atmosphere 0.98. Route A's 94.72 per cent is that 0.95. The 0.88 is the chain's "Rectenna Energy Collection" row, being intercept multiplied by the rectenna's own losses that p.41 lists. Its supporting argument is structural: Figure A-9 already carries beam degradation on a separate 0.98 Mechanical Tolerances row, so 0.88 cannot legitimately be doing that job as well. - Route B: it is ERROR-LOADED. Figure 25 prints the conditions directly beneath the box - 10 km rectenna diameter, sigma = 10 degrees, plus or minus 1 dB, 2 per cent tolerances on the transmit array - so the 88 to 89 per cent is the ideal figure after the stated error budget.

Route A's decomposition reaches 0.88 as 0.95 x 0.98 x 0.99 x about 0.955, and the last factor is the one that closes the arithmetic rather than one read off the page, which is why this is recorded as an open disagreement rather than as Route A winning.

A second finding neither route was looking for: the range

SRC-085 NEVER STATES A TRANSMISSION OR SLANT RANGE. Route A searched 322 pages for "slant", "range", "distance", "36,000", "35,800" and "35,786" and found only the geosynchronous ALTITUDE of 35,800 km at p.A-2. Both routes then found that the stated peak requires a range near 37,000 km, not 35,800: Route B computes 248.2 W/m2 at 35,800 km against 230.8 at a 37,125.5 km slant range, and inverting the stated 230 gives 37,190 km. That is a 7.9 per cent effect, LARGER than the 5 to 7 per cent inconsistency this calculation set out to explain, so any recomputation quoting 35,800 km beside this peak is mixing two ranges. Neither route took its slant range from SRC-085, because it is not there.

Sabotage checks

Route A corrupted frequency, aperture, range, taper depth, taper direction, step radii, the integration boundary and the error budget, and every one moved the result. It also recorded two sabotages honestly rather than ticking them: removing the step quantisation moves the fraction by only 0.07 points, so the printed 10-step taper is not what produces the finding and is not claimed as evidence for it; and the 1.2 arc-minute beamwidth agreement is angular and therefore says nothing about range. Route B ran six sabotages, all of which broke their target.

Not done

Neither route modelled the 2 degree mean edge phase error, which is a defocus term that would push the computed fraction DOWN toward 88 and is therefore not conservative in the direction of this finding. Nor the plus or minus 3 arc-minute mechanical alignment, grating lobes, ionospheric phase perturbation, or a Fresnel correction. Route B did not compute the error-loaded collection, so its link from 94 to 89 rests on Figure 25's printed conditions rather than on its own arithmetic. Neither digitised Figure 18.

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