The ratios — one plate, many scales

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Seven panels on allometry and dimensionless scaling, drawn only from constants this corpus prints. I draws Kleiber's law as a log–log plot carrying BOTH disputed lines: a 3/4 line tangent to the Kolokotrones quadratic at ~4.2 kg and a 2/3 line tangent at ~160 g — the masses at which each exponent is locally true — with the fitted data bracketed (3.6 g … 460 kg) and everything beyond hatched as extrapolation. A residual strip subtracts the curve so the divergence is visible at all: each straight line touches zero ONLY at its own tangent mass and falls away on both sides. The dispute (Rubner's 2/3 surface law vs Kleiber's 3/4 from n=13) is labelled on the plate, and the cost of extrapolating the 3/4 line down to a 3 g shrew is measured at ×1.95. II plots the local slope — linear in log M, so a straight rising line — crossing 2/3 at ~160 g and 3/4 at ~4.2 kg: there is no exponent, there is a curve. III is rule M2 rendered as a confidence-interval ruler: nine fitted exponents against the 2/3 and 3/4 thresholds, annotated that the nine rows are only FIVE papers. IV shows the claim dissolving on its own spread (51% of Glazier's exponents fall outside 0.7–0.8; the intraspecific mode is 0.667). V draws the Strouhal 0.2–0.4 cruise band with the only per-taxon values this corpus carries — odontocetes and one bat — and prints the gap where the others should be. VI draws the Froude gait transition at 0.5, the inverted-pendulum ceiling at 1, and the measured lunar transition of 1.39 ± 0.45 that broke it. VII carries the key, the numbered caption and what the plate does not claim. Every line carries an evidence-class badge. The vertical datum of I is a stated drafting choice: b₀ is not printed in this corpus, so NO absolute metabolic rate and NO prefactor is drawn or claimed. Marks, not colours — the plate must survive greyscale.

Claims

What this plate does NOT claim

• That metabolic rate scales as M^(3/4). Nor as M^(2/3). Both lines are drawn because both are claimed in the literature; the plate asserts NEITHER. NA-05's position is that the question is malformed as usually asked, because the log–log relation carries curvature — and that THAT position is contested too.
• Any absolute metabolic rate, or any prefactor. The vertical axis of panel I is a difference of logarithms with its datum stated (the 4.2 kg tangent point). b₀ is not printed in this corpus, and a prefactor moves by 1000^b when you change grams to kilograms while the exponent does not move at all. The exponent is the candidate science; the prefactor is bookkeeping.
• That b₁ = 0.5371 is 'the metabolic exponent'. It is the local slope at M₀ = 1 g and changes value if you measure mass in kilograms (b₁′ = b₁ − 2b₂ log k). Only b₂ and the local slope at a NAMED mass survive a change of unit. Quoted as 'the exponent' it is INADMISSIBLE (NA05-08, MacKay 2011).
• That Kolokotrones et al. (2010) settled the dispute, or that the curvature is a law of size rather than a between-Order artifact. That is exactly what is contested — and the reply defending it (Deeds, Savage & Fontana 2011) is by three of the original four authors, a rebuttal by the accused, not an independent corroboration. MacKay's Hayssen & Lacy (1985) receipt and his 70-marsupial fit stand unrebutted.
• Anything to the right of the fitted-data bracket. The 74 t reading is an EXTRAPOLATION ~2.2 decades past the data, hedged twice by its own authors, and is drawn dashed and hatched for that reason. A power law fitted in one range does not extrapolate through a regime change, and the fit will not warn you.
• That St = 0.2–0.4 is a law, that it applies off cruise, or that any animal's St is an adaptation. It is a central tendency at cruise; individual scatter is large (only 44% of 248 odontocete values fall in 0.225–0.275); the modelled optimum is size-dependent (0.15 → 0.8); and one bat's efficient cruise sits BELOW the 0.2 bound.
• Per-taxon Strouhal values for birds, sharks, bony fish or insects. Taylor et al. (2003) NAME those taxa as converging in the band, but this corpus does not carry their individual values, so this plate plots NONE and prints the gap instead of inventing points. Falsifier: read Taylor et al.'s figure and print the per-taxon values it carries.
• That Fr ≈ 0.5 is a universal gait-transition constant, or a mechanical limit. It is scoped to bipeds at 1 g; the mechanical ceiling is Fr = 1; and the measured transition in actual lunar gravity was 1.39 ± 0.45.
• A measured absolute walk→run transition speed. The ~2.1 m·s⁻¹ is computed from Fr and L, not observed; the measured value with its n is NOT-SOURCED in this pass.
• Lunar gravity, or any lunar speed. Only the DIMENSIONLESS lunar result is sourced; converting it to a speed would need a value of g this plate did not source.
• That the trackway application is drawn here. It is not: it is recorded in the caption because a negative that is merely off-topic is still a negative (Alexander's formula ran 1.17×–4.74× measured on guineafowl in mud — Prescott et al. 2025).
• That any exponent, band or threshold here is an OPTIMUM. Per Gould & Lewontin (1979), drift, phylogenetic inertia, developmental constraint, pleiotropy and frozen accidents produce values that optimise nothing — and an exponent is an unusually easy thing to find a story for after the fact. Every number here is a hypothesis generator. Per M7, a design taken from this plate must still beat a TUNED baseline on a PRE-REGISTERED metric with a discriminator that collapses the gain, or it is recorded NEGATIVE.
• That anything here raises any UNI rung. A NATURE CITATION IS NEVER A UNI GATE. This plate contains ZERO UNI claims, and the honest program position is unchanged by it: ~2 of 11+ developmental rungs earned, a developmental active-inference simulation. 'Full human' and 'beyond human' appear nowhere as targets — they are permanent open questions, and reading one into a scaling law would be the exact lane-crossing this wing exists to prevent.

Design fence — {"design_only":"No