[qmohsu]

The defect

ch4_rf_point_positioning/example_toa_positioning.py argued the opposite of what the chapter teaches, by juxtaposition:

• Examples 1-2 solve one-way TOA at 0.1 m of range noise and print 0.000 / 0.055 m. The synchronised-clock assumption appeared nowhere in the file — grep -i sync returned nothing.
• Example 5 (RTT, Eqs. 4.6-4.9) uses an honest ns-level timing budget and prints 0.718 m RMSE, 0.704 m of position error.

A reader flipping through sees two-way as 7x worse — a comparison between one protocol's assumptions and another's physics. The RTT math itself was correct and is unchanged.

The three-case comparison (Example 7)

One 20 m array, agent at (8, 12), one number — sigma_t, the agent clock's per-timestamp jitter — and 2000 draws per case, every draw scored:

case	median	RMSE	failed	predicted
A one-way, clocks synchronised	0.2518	0.3018	0	0.3000
B(i) one-way, 20 ns offset, position only	1.7978	1.8416	1	1.7239
B(ii) one-way, 20 ns offset, clock solved (Eqs. 4.24-4.26)	0.2545	0.3039	0	0.3014
C two-way RTT, no sync needed	0.2148	0.2613	0	0.2598

Position DOP 1.0007 (position only) against 1.0053 with the clock as a third unknown — the +0.45% B(ii) pays.

The bookkeeping, derived rather than chosen per case

• One-way: one receive timestamp against a scheduled transmit epoch, so sigma_range = c*sigma_t = 0.2998 m.
• Two-way: two timestamps on the agent's own clock plus the turnaround calibration residual, sigma_RTT = sqrt(2*st^2 + sp^2), halved by Eq. (4.7) — 0.2596 m.

This is the bookkeeping that flatters two-way least: giving the transmit epoch its own sigma_t would make one-way c*sqrt(2)*sigma_t and double the gap. Verified against the simulation rather than asserted — measured range std matches two_way_range_sigma to within 0.5% for sigma_proc from 0 to 3 ns, so both knobs demonstrably reach the measurement.

Reported disagreement with the expected ordering

A <= C was expected; C comes out 13% ahead of A. That is arithmetic, not a thumb on the scale — a round trip puts twice the distance into the interval being timed while the jitter grows only as sqrt(2). The example prints the crossover (sigma_proc = sqrt(2)*sigma_t = 1.414 ns, where the two range equally well) rather than moving a parameter to recover the expected order.

Checks

• Zero-noise sanity: 0.000000 m for all four arms at sigma_t = 0, b = 0, sigma_proc = 0.
• B(i) bias: linearised prediction b*||(H'H)^-1 sum(u_i)|| = 1.1323 m, measured noiseless 1.6976 m. The example shows why: at b = 0.01 m the ratio is 1.001, so the gap is nonlinearity — 6 m of bias on 11-17 m ranges is not a small perturbation. The agent is off-centre deliberately; at a symmetric array's centre sum(u_i) is zero and a common bias is invisible.
• Mutation-checked transcript: perturbing one new digit in the README block turns test_readme_example_output.py red.
• Output reproducible across processes; committed figure byte-identical; no dataset moved.

Also, in passing

Example 5's single-draw positioning number is labelled as one draw with the scale to expect beside it, and its Monte-Carlo RMSE gets the prediction it should match (0.8072 m predicted against 0.7180 m measured over 100 draws).

Documentation

• Chapter README: a clock-requirement table over the four approaches; the RTT section gains the sqrt(2) derivation and an explicit "this does not beat TDOA"; transcript re-pasted from a real run.
• data/sim/ch4_rf_2d_square/README.md: names what toa_ranges.txt assumes, and adds two-way TOA to the equation list.

Test plan

• tests/ch4_rf_point_positioning tests/core/rf — 243 passed
• tests/docs/test_readme_example_output.py -k ch4 alone — 3 passed
• tests/docs/test_readme_code_blocks.py + test_chapter_readme_code_blocks.py — 57 passed, 1 skipped
• repo conventions + console encoding + import-checkout + python-floor + figure gate + black + lint — 806 passed, 8 skipped
• test_repo_validators.py test_semantic_api_debt_only_shrinks.py + lint/mypy/black/doctest trio — 34 passed
• docs guards (flags, paths, module form, file structure, architecture, equation ranges, reader guidance, semantic naming) — 739 passed, 1 skipped
• test_datasets_reproduce_from_their_recipe.py test_examples_answer_help.py — 82 passed

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