Appendix A — Universal morphogenesis: the γ gene-clock from DNA to body

The same R19 switch and the same measured stiffness γ that read DNA in this paper also grow a body. A gene-clock application schedules morphogenesis by spinodal(γ): the order of structural features is a deterministic γ readout [V], but a falsifiable test finds γ is orthogonal to developmental timing [O]. γ fixes what and in what order, not when.

This applied volume runs the paper's Layer-1 machinery forward into form. One bistable switch, spinodal(γ)=2(γ/3)^1.5, is bit-identical (max|Δ|=2.2e-16) to the body engine and the neural-emergence engine, and the same NCBI→SantaLucia γ (corr(γ,GC)=0.994–0.998) drives it — never fitted. The emergence order of features equals argsort(spinodal(γ)) and resorts when a γ is perturbed [V]; a direct test against locked, cited Carnegie staging returns an honest null at three resolutions, sharpest inside the heart's own cascade (Spearman ρ=+0.071, permutation p=0.882) [O]. A composition axis then splits form into a genetic fraction H²=0.51 inside the published twin band and an environmental envelope, never tuned to the anchor.

A.1 · One switch across DNA, neurons, and the body

The application introduces no new physics: it reuses the paper's R19 switch unchanged. The spinodal that schedules each feature is asserted at run time to equal the body engine's morpho_core.spinodal and the neural-emergence engine's functional_spinodal to 2.2e-16, so the one primitive that writes DNA, fires neurons, and folds the body is literally the same here.

Every per-gene γ enters through the identical NCBI→SantaLucia measurement used throughout this paper, with corr(γ,GC) between 0.994 and 0.998 across the gene tables. γ is measured and read-only [L]; only each gene's pro-storage or satiety sign is a declared forced label [F]. Two independent runs are byte-identical (2× sha256).

A.2 · DNA → form: the deterministic core

Form is grown in layers from the same switch. Layer 1 reads two opposing morphogen gradients through the fold to give sharp body-plan registers, a segmentation clock whose somite count scales with axis length and with γ, and a faster distal clock that yields the urodele four-finger / five-toe formula — all reproduced bit-for-bit.

Layer 2 fills the body with tissue-typed anatomy; Layer 3 grows the generic form onto a scanned target coordinate-by-coordinate, with surface error driven to zero (RMS ≈ 0.05–0.11, Chamfer → 0 on fish, bird, quadruped, and a human face). Re-coupling Layer 3 to the switch, each feature switches on at a time τ_on set by its gene's spinodal, so the emergence order equals argsort(spinodal(γ)) exactly and re-sequences when a γ is moved [V]. This is the DNA-fixed core of form.

A.3 · The central falsifiable result — γ is orthogonal to timing

The order being a clean γ readout raises the paper's own kind of question, and the volume tests it rather than asserting it: does promoter stiffness predict when a feature actually appears? The schedule is scored against a locked, cited, γ-independent Carnegie-staging table (O'Rahilly & Müller; Larsen's; the UNSW Hill atlas), frozen by sha256, by rank correlation with an exact permutation null.

The answer is a null at every resolution tested, and it sharpens as the staging gets cleaner: seven master features give ρ=−0.018 (p=0.99); eight visceral organs give ρ=−0.414 (p=0.36); the heart — the textbook gold standard for crisp developmental staging — gives ρ=+0.071 (exact p=0.882) on its own eight sub-stage cascade. The cardiac master NKX2-5, the first specifier in vivo, is ranked near-last by γ while a late-septation gene ranks first.

The apparatus is provably not blind: a synthetic γ ordered to the stages recovers ρ=+1.000 exactly and a shuffle collapses it, so the null is real, not a broken test. The order claim is therefore graded a measured [O] — tested and not matching — which is a stronger, more honest position than an untested hedge. This is the same lesson as the main paper in the time axis: γ is the threshold scale, not the locus of difference.

A.4 · gene × environment: the envelope, and how much of form is DNA

The single largest source of variation in an individual's external form is composition, and the volume adds that axis with the same fold in the energy variable. One genome is made lean or heavy by an energy drive read through the R19 set-point, with the lean reference preserved bit-for-bit, so the Layer-3 convergence proof is never disturbed.

On that gated machinery, body shape decomposes into a genetic fraction H²=0.51 — inside the published twin band — and a substantial environmental fraction; the fraction is population-dependent, rising to 0.84 under narrow environmental variation and falling to 0.10 under wide, reproducing a published fact rather than a tuned decimal. For one genome the lean core is bit-identical between twins, while two lives add +37% body volume and +25% lower-face roundness. Form has a first cause in DNA but is not wholly fixed by it.

A.5 · Honest scope — open items and their obstacles

Each open claim names the measured input that would close it, none of which the package contains. The timing null is for promoter composition only; a different measured modality (expression-onset or chromatin accessibility at the master loci) could still carry order but needs an external developmental atlas as a locked input [O].

Absolute organ and body sizes are a crude canvas pending anthropometric data [O]; the model's facial bone has no non-adiposity environmental axis, so it cannot represent aging, gravity, or sun [O]; the decomposition is an exact property of the measured-γ model, not validated against paired genotype–morphometry scans [O]; and a single canonical H² would require fixing a population's environmental distribution [O]. Layers 2–3 are a coarse-to-fine geometric read-out, a principle demonstration, not an HPC-scale continuum tissue-mechanics simulation grown from cells [O]. The full register is aggregated in IRREPRODUCIBILITY_LEDGER.md.

Reproduction is one command: verify_all.py returns PASS 20/20 — twelve morpho and five emergence gates, a source pin over 87 governed files with drift 0, and the fidelity baselines matched leaf-for-leaf. The applied volume lives in full under repro/dna/ax-a-universal-morphogenesis-gene-clock/ and imports the paper's switch as a single pinned source, so nothing in §1–§13 is modified.