airtime_model_check.py: CR 4/7 is computed as 4/8, overstating ToA by ~14%

[ACETyr]

Summary

reference/airtime_model_check.py — our reference port of SX126x::calculateTimeOnAir(), and the
project's stated authority for airtime — silently maps coding rate 4/7 to 4/8. Every ToA computed
at CR 4/7 is overstated by a factor 8/7 (~14%).

Host-side analysis script, kept in the project folder rather than in this repo; filed here because
this is the project tracker (cf. #5).

Location

reference/airtime_model_check.py:55

cr = cr_wire + 4 if cr_wire < 5 else (cr_wire + 1 if cr_wire == 7 else cr_wire)

The cr_wire == 7 branch adds 1. For cr_wire in {5, 6, 8} the value passes through unchanged, so
the special case is asymmetric and unexplained by the surrounding comment, which states that "a
stored 5..8 is used as-is".

Evidence it is wrong

RadioLib applies the coding-rate denominator directly, with no special case:

.pio/libdeps/Heltec_v3_repeater/RadioLib/src/modules/SX126x/SX126x.cpp:767

uint32_t nSymbol_x4 = (pc.lora.preambleLength + 8) * 4 + sfCoeff1_x4 + nPreCodedSymbols * dr.lora.codingRate * 4;

The symptom is visible directly in the model's own output — the CR7 column is byte-identical to CR8:

 bytes       CR5       CR6       CR7       CR8
    64     529.4     599.0     738.3     738.3
   184    1143.8    1336.3    1721.3    1721.3

Correct values (SF8 / BW 62.5 kHz / preamble 32 / CRC on):

bytes	4/5	4/7 (correct)	4/7 (current, wrong)
16	283.6 ms	324.6 ms	345.1 ms
64	529.4 ms	668.7 ms	738.3 ms
184	1143.8 ms	1528.8 ms	1721.3 ms

Why the selftest did not catch it

--selftest passes 15/15 because every vector uses CR 5. A selftest pinned to a single coding
rate cannot detect a per-CR mapping error by construction. Any fix should add vectors at 4/6, 4/7
and 4/8.

Impact

Low until now, because everything measured so far assumed the AT/EU-narrow preset (CR 4/5), which is
unaffected. It became relevant on 2026-08-22: get radio showed AT-PL-Hofstetten01 running CR 4/7
while KK and the bench companion run 4/5, and the first airtime comparison for that node used the
inflated figures. This is the second CR-related defect in this file after the coefficient fix of
2026-08-17, so the area deserves the extra vectors rather than another point fix.

Suggested fix

Drop the special case, use the denominator as stored, and extend --selftest to cover 4/6, 4/7, 4/8
with hand-computed reference points.

[ACETyr]

Primary-source confirmation of the multiplier, found while chasing an unrelated question.

Semtech SX1276/77/78/79 datasheet, Rev. 4 (March 2015), page 27, Table 14 "Cyclic Coding Overhead":

CodingRate (RegTxCfg1)	Cyclic Coding Rate	Overhead Ratio
1	4/5	1.25
2	4/6	1.5
3	4/7	1.75
4	4/8	2

So the payload-symbol overhead at 4/7 is 1.75, not 2.0 — i.e. the denominator is used as-is, exactly
as RadioLib does at SX126x.cpp:767. The cr_wire == 7 -> 8 branch makes our model bill 4/7 at the
4/8 ratio, which is the 8/7 = ~14% overstatement described above, now confirmed against Semtech rather
than only against RadioLib.

Ratio check: 1.75 / 1.25 = 1.40, matching the payload-symbol part of the corrected table.