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20 changes: 16 additions & 4 deletions docs/FARMER_2005.md
Original file line number Diff line number Diff line change
Expand Up @@ -251,12 +251,24 @@ so it is not evidence. **The ratio column and the rank test are the evidence.**
The paper's claim, as conditioned by the paper itself, is **not refuted here**
— it is confirmed in the weak sense available from five stocks:

1. Across the full sample the laws fail, badly, by up to four orders of
magnitude on diffusion.
2. The failure is **monotonic in `dp/p_c`**, the model's own scope parameter
(p = 0.017 for diffusion).
1. Across the full sample the laws fail badly — spread ratios spanning 3.7 to
50, and diffusion ratios spanning 66× on a matched clock. (The raw A4 clock
makes diffusion look like 1,777×, but most of that is the unit mismatch
described above, not model failure.)
2. The stocks separate into **two non-overlapping groups** by `dp/p_c`, the
model's own scope parameter, and the separation survives being re-measured
in all 13 intraday blocks.
3. Where the scope condition holds, the spread ratio is roughly constant.

On the strength of the evidence: the **two-group separation** in point 2 is the
robust claim, with 65 non-overlapping block measurements behind it. The rank
correlation is weaker than it looks — significant for diffusion (ρ = 1.000,
p = 0.0167) but *not* for spread (ρ = 0.900, p = 0.0833), and at n = 5 the
smallest attainable p-value is 0.0167 regardless. The ordering *within* the
small-tick group is not real: GOOG and AAPL swap, persistently and in every
block. So the defensible statement is that tick-constrained stocks behave
categorically differently, not that the error is monotonic in `dp/p_c`.

Ignoring the tick parameter turns a scope condition into an apparent
refutation. That is the substantive lesson, and it is the same mistake in a new
costume as the one at the top of this document: **testing a model outside the
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