# A fixed-break mammal benchmark with an unfavorable primary result

## Question and data

Does a continuous hinge fixed at 10 kg predict held-out mammal families better than
a single log–log line? This tests one empirical candidate, not a universal scaling law.
Input: Jones et al. (2009), PanTHERIA WR05 August 2008; DOI 10.1890/08-1494.1.
The original publisher supplement was retrieved through its Figshare record,
10.6084/m9.figshare.3531875.v1. Its archive checksum matched the publisher's MD5.
The dataset has 5,416 rows. Positive BMR-associated mass, positive BMR and a family
identifier retain 573 species in 99 families. All 4,843 exclusions have row-level reasons.
Mass and BMR are separate species medians, not paired individual observations.

Use x=log10(mass in kg), y=log10(BMR in W), with 20.1 J/mL oxygen as a fixed conversion
assumption. A constant oxygen energy equivalent changes the intercept, not slopes;
species-specific metabolism and respiratory quotient can still matter biologically.

## Frozen computational comparison

M0: y=a+b*x. M1: y=a+b*x+d*max(0,x-1). M2: y=a+b*x+c*x².
The 20 kg hinge is a declared sensitivity, not a searched optimum. The local plan
hash is 4f4456046115d896f277eaf5882ae7f0703769853fdbca637144b7a69b7bec41.
Family groups are sorted by median log mass into ten equal-count strata, then selected
with a fixed SHA-256 rule. There are 372 training species in 69 families and 201 held-out
species in 30 families. No family crosses the primary split. This is approximately
70/30 by families, not exactly 70/30 by species. The coverage rule passes: 47 species
above 10 kg, including 35 training and 12 held out, spread across 24 families overall.

| Model | Primary test RMSE (log10 W) | Training AICc |
|---|---:|---:|
| Single line | 0.198095 | -65.7497 |
| Fixed 10 kg hinge | 0.200464 | -95.2869 |
| Smooth quadratic | 0.195600 | -90.9936 |
| Fixed 20 kg hinge, sensitivity | 0.203100 | -95.9304 |

The 10 kg hinge has 1.20% worse primary test RMSE. The predeclared descriptive screen
(coverage, >5% improvement, positive lower interval bounds for improvement and slope
change) fails. Across 2,000 resamples of training and test families, refitting each time,
the 95% percentile interval for MSE(single)-MSE(hinge) is [-0.009464, 0.009020] dex².
The estimated training slope rises from 0.681 to 1.014, with a slope-change interval
[0.169, 0.451]. That fitted curvature does not establish improved held-out prediction.
The interval for MSE(quadratic)-MSE(hinge) is [-0.008564, 0.004336] dex².

AICc is computed on the training Gaussian log-scale likelihood, counting residual
variance as a parameter. Its independence assumption is not fully credible for related
species; it is descriptive and not a phylogenetically corrected decision statistic.
It is never calculated on the test set. The better training AICc and worse primary
test prediction are both disclosed. Akaike weights in JSON apply only to these four
training fits and this approximate likelihood, not probabilities of physical truth.

## Sensitivities and limits

The less restrictive species split gives RMSE 0.186414 for M0 and 0.178941 for the 10 kg
hinge. It permits related families on both sides. Five-fold family CV over all 573
species gives pooled RMSE 0.216684 for M0, 0.211003 for the 10 kg hinge and 0.211458
for the quadratic: a modest hinge improvement of about 2.62%, below the 5% screen.
These checks show split dependence; they do not create another untouched test set.
Raw-watt additive-error fitting changes the target and strongly weights large mammals:
the primary test RMSE is 40.465 W for M0 and 40.669 W for the hinge. Raw- and log-scale
AIC values must not be mixed. All results and predictions are supplied as CSV/JSON.

Family blocking is not tree-based PGLS. Measurement error, body temperature, measurement
protocol and source-study effects remain incompletely modeled. A second compilation
may reuse the same studies; audit overlap before calling it independent replication.
Published candidate crossovers and smooth curvature motivate alternatives but do not
establish a known discontinuity at 10 kg. This release provides no evidence for a
universal NetPhysics breakpoint, and it does not prove that all biological curvature
or breakpoints are absent.

Primary sources: https://doi.org/10.1890/08-1494.1 ;
https://esapubs.org/archive/ecol/E090/184/metadata.htm ;
https://doi.org/10.1006/jtbi.2000.2238 ; https://doi.org/10.1038/nature08920 .