RQ3 · aggregate report · 17 September 2026

Input NLL and prefix redundancy show a positive conditional association, but limited predictive power.

Across the four-factor joint model, higher raw mean NLL is associated with higher rho. This is an association, not evidence that unfamiliar inputs cause overthinking.

n = 273 independent correct natural trajectories from the fixed random600 GSMDC campaign (the 273-item complete-case cohort, not all 600 items).

Table 1 · Four-factor joint coefficients

Outcome: raw-scale rho = 1 − k*/N. Predictors are z-scored; beta is the conditional change in rho per +1 sample SD. HC3 intervals.

Predictor	Beta	HC3 95% CI	Raw p	Holm-4 p
A-hat	−0.0005	[−0.0351, 0.0341]	0.9789	0.9789
Operation count (op)	+0.0267	[−0.0082, 0.0616]	0.1334	0.2668
Irrelevant-node count	+0.0372	[+0.0056, 0.0689]	0.0213	0.0638
Raw mean NLL	+0.0568	[+0.0203, 0.0932]	0.0024	0.0095

Main result: NLL is the only predictor that remains significant after Holm-4 correction. The irrelevant-node association does not (Holm p = 0.0638).

Table 2 · Bivariate associations with rho

Pearson correlations across the same 273-item cohort; Holm-3 correction within this auxiliary family.

Measure	Pearson r	Raw p	Holm-3 p
B_scaled	−0.1049	0.0837	0.2510
A-hat	−0.0264	0.6638	0.6718
Difference (mismatch)	−0.0585	0.3359	0.6718

R² 0.0485in-sample; adjusted R² = 0.0343

OOF R² 0.0084group-isolated 5-fold

149 / 273k=0 judge-correct diagnostic

Necessary method and source notes

rho is the HMTE metric from Zhai et al., “How Much Thinking is Enough?”; this project is a declared reproduction, not the metric's originator.
All 273 trajectories had a measurable critical point; estimator is complete-case. Full-prefix judge correctness was 270/273.
Raw text NLL is a proxy, not a direct measure of training familiarity; lexical and formatting factors may contribute. The low OOF R² means prediction is limited.
One OLMo-3-32B-Think checkpoint is reported here. Pending 7B prechecks are not included.