diff --git a/docs/FARMER_2005.md b/docs/FARMER_2005.md index d21966f..deddfa2 100644 --- a/docs/FARMER_2005.md +++ b/docs/FARMER_2005.md @@ -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