CALC-090

Figure 5's own intermediate powers say its two rectenna efficiencies are transposed

Supports CLM-0872. Four multiplications, given in full.

SRC-085 Figure 5, PDF p.25, printed p.13, read from a 6x render of the page's lower half by the coordinator. The bottom row prints a power ABOVE each box and an efficiency INSIDE it: 6.58 GW over ATMOSPHERIC LOSSES 0.98, then 5.79 GW over RECTENNA ENERGY COLLECTION 0.89, then 5.15 GW over RECTENNA ENERGY CONVERSION 0.88, then GRID INTERFACES 0.97 into UTILITY BUSBAR 5 GW. The convention that the power above a box is that box's OUTPUT is fixed by the row's own preceding entry: 6.72 x 0.98 = 6.5856, printed 6.58.

One reading reproduces both printed values to the precision they are printed at; the other reproduces neither. Figure 5's arithmetic was performed with 0.88 at the collection box and 0.89 at the conversion box, the reverse of its own labels.

Why this survived every check the document makes on itself

0.89 x 0.88 = 0.88 x 0.89 = 0.7832. Multiplication commutes, so the swap is INVISIBLE in the chain total: Figure 5's MPTS EFFICIENCY = 63.0% and Figure 25's 63 per cent are both correct under either reading, and Figure 25's chain checks out as labelled at 0.85 x 0.9653 x 0.98 x 0.89 x 0.88 = 0.62977. The defect is visible in exactly one place, the intermediate value between the two boxes, and nowhere else. A checker who verifies a chain by its endpoints cannot see it.

Sabotage checks

The script asserts every product above and aborts on any of them. Changing either efficiency, or either printed intermediate, breaks at least one assertion. The discriminating quantity is the 5.79 between the boxes: a reading that does not reproduce it has no support at all.

Provenance, and a digit that was disputed

The value was reported as 5.86 by one stream and as 5.79 by another, and this settles it at 5.79. PDF p.25 was rendered at 6x and read directly. The stream reporting 5.86 reached it by requiring 0.89 to be the collection term - assuming the labels and deriving the intermediate - and recorded at the time that it had been one step from reporting CLM-0869 wrong on that basis. The arithmetic runs the other way: the printed intermediates are the evidence and the labels are what they contradict.

Not established

WHICH IS THE ERROR IS NOW ESTABLISHED, 2026-09-06, AND IT IS THE LABELS. This section originally recorded it as open. A sweep of the document's other efficiency chains found the answer stated outright in a third place, and PDF p.125 was rendered and read directly before this was written.

Figure A-9, printed A-26, "Microwave System Estimated Efficiencies", CURRENT REFERENCE SYSTEM column: DC-RF Conversion 0.85, Transmit Antenna I2R 0.985, Transmit Antenna Mechanical Tolerances 0.98, Average Atmosphere 0.98, RECTENNA ENERGY COLLECTION 0.88, RF-DC CONVERSION 0.89, DC Power Interface 0.97, Overall Efficiency .611. That is the order Figure 5's ARITHMETIC uses and the reverse of what Figures 5 and 25 print in their boxes.

It reconciles exactly: 0.85 x 0.985 x 0.98 x 0.98 x 0.88 x 0.89 x 0.97 = 0.610874 against a stated .611, and the value before the DC interface stage is 0.62977, which is the 63 per cent both other figures state. So all three figures are ONE chain, A-9 carrying a stage the other two stop short of, and nothing is inconsistent between them except the two box labels.

THREE PLACES AGAINST TWO, AND THE TWO CARRY NO ARITHMETIC. 0.88 for collection is given by the p.37 prose, by Figure 5's computed chain and by A-9's stated column; 0.89 is given by the box labels in Figures 5 and 25, which are the two places with nothing to check them against.

AND ALL FOUR A-9 COLUMNS PUT COLLECTION BELOW CONVERSION: JSC .88 against .90, BAC .85 against .89, Rockwell .88 against .90, Current Reference 0.88 against 0.89. Reading the boxes as labelled would make the reference system the only one of four studies where that relation inverts. Note also that JSC's and BAC's collection figures carry an asterisk marking a COMBINED efficiency, with an arrow from the mechanical-tolerances row - the reference column's 0.88 carries no asterisk and lists tolerances separately at 0.98, so it is a collection term alone. Figure 25 and Table B-1 remain untestable by this method and that is a limit, not a pass. Neither prints an intermediate between the two boxes, so only a product-against-total check is available there - and a product is ORDER-INVARIANT, so it cannot detect a transposition at all. Only Figure 5 prints the intermediates that make the test possible, and that is the chain the defect was found in. A-9 settled it not by arithmetic but by STATING the two values in an order the box labels contradict.

A SECOND TRANSPOSITION FOUND BY THE SAME SWEEP AND NOT RESOLVED. The summer solstice factor is 0.9675 in Figure 5's box and 0.9675 in the p.23 narrative, and 0.9765 in Table B-1 - two digits swapped within one value, two places against one. Which is correct is NOT established, it moves no headline figure, and it is a different kind of error from the rectenna case: that is two values swapped between boxes, this is two digits within one value. Recorded because a sweep that finds one transposition and does not report the second one it tripped over is not a sweep.

THE DEFECT IS LOCALISED. PDF p.23's narrative independently confirms Figure 5's solar side - the summer solstice factor 0.9675, seasonal variation .91, end-of-life concentrator reflectivity 0.83 - and (1 + 0.83)/2 = 0.915 exactly matches Figure 5's REFLECTOR REFLECTIVITY EQUIVALENT box. Figure 5's labels are right everywhere except the two rectenna boxes; it is not a systemically mislabelled figure.

COVERAGE OF THE SWEEP, AND WHAT IT COULD NOT SEE. All 322 pages screened by text layer for three or more decimal factors alongside a power quantity or the word "efficien", giving 8 candidates, of which six pages were rendered and read: 23, 25, 37, 56, 125 and 270. The other 314 pages were not read, and a chain printed as an image with no text layer would never have entered the candidate list; how many such pages exist is not bounded.

Table B-1's braces, read at 600 dpi, and one thing that changes what B-1 means

Added 2026-09-06 after the traceability stream rendered PDF p.270 per block rather than whole. Three braces, three outcomes, and the middle one answers a question that was open against CLM-0870. Every product below re-checked.

Brace 2, printed 0.932: DETERMINED, and it spans TWO rows rather than the whole block. String I2R 0.998 and Bus I2R 0.934 give 0.93213 against a printed 0.932, exact. Cover UV Degradation, Cell-to-Cell Mismatch and Panel Lost Area are OUTSIDE it. This is the brace that had produced a reported 10 per cent discrepancy which the stream declined to call a defect, on the grounds that it could not read the span reliably. It was right to decline: the span was the error, not the subtotal, and the two resistive-loss rows are the grouping that makes engineering sense.

Brace 3, printed 0.86: SETTLED BY ARITHMETIC, and only one combination reproduces it. Ideal Beam 0.965 x Inter-Subarray 0.956 x Intra-Subarray 0.981 x Intercept 0.95 = 0.85976. No contiguous span works: those three alone give 0.90501, plus Atmosphere Absorp. 0.98 gives 0.88691, and all five give 0.84257. The only reading that reaches 0.86 SKIPS Atmosphere Absorp., a row the drawn brace appears to enclose. So the subtotal can only have been computed over those four factors, and the aggregate in Table B-1 comparable to the figures' collection term is 0.86, with 0.95 the GEOMETRIC INTERCEPT ALONE. Whether the document intends that grouping or drew the brace wrongly is not settled. It does not need to be: both readings leave 0.95 an intercept term rather than a collection term, which is the point the reconciliation turns on.

Brace 1, printed 0.151: DOES NOT RECONCILE ON ANY SPAN, and is recorded as a LIMIT rather than a defect. The values are unambiguous at 600 dpi - 0.9765, 0.919, 0.173, 0.97, 0.954 - but the brace is drawn so faintly that only a tick and a vertex survive the scan. All five give 0.14367, 4.9 per cent low; the visible extent gives 0.16009, 6.0 per cent high. Nothing reproduces 0.151, and the brace cannot be read well enough to say the subtotal is wrong rather than the span, which is exactly the position brace 2 has just shown to be the right one.

An appealing dead end is recorded so nobody rediscovers it: substituting 0.182 for the printed 0.173 gives 0.15114, matching to three decimals, and 18.2 per cent is this document's own cell efficiency at 125 C. It is almost certainly a coincidence of arithmetic - see below.

TABLE B-1 IS THE SILICON CHAIN, which nobody had established

Three of its factors are Figure 5's SILICON-branch values exactly: solar cell efficiency 0.173 where GaAlAs is 0.20, temperature degradation 0.954 at 36 C where GaAlAs is 0.908 at 125 C, and panel lost area 0.951 where the GaAlAs array design factor is 0.901. So the printed 0.173 is correct for this table and the 0.182 fit above is coincidence. It also means B-1's Products/Sums 0.0712 must be compared with Figure 5's SILICON overall of 7.06 per cent and not the GaAlAs 6.97 - 0.0712 against 0.0706, 0.8 per cent apart, consistent with different rounding. A comparison against the wrong branch would have shown a discrepancy that is not there.

One piece of evidence on the solstice transposition, and it is not decisive

The 0.9765-against-0.9675 disagreement is re-confirmed at 600 dpi with no ambiguity in any of the three places, and remains unresolved. But Figure 5's silicon branch is arithmetically self-consistent with its own 0.9675: 70.81 x 0.9675 = 68.5087 against a printed 68.51, where 70.81 x 0.9765 = 69.1460. Table B-1 offers no equivalent internal check for its 0.9765. That is evidence toward 0.9675 and not proof - it shows Figure 5 used what it printed, which is a weaker statement than either value being right.

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