Contents

   ●   Supplementary Note S1 — Protocol adherence and deviations
   ●   Supplementary Note S2 — Analysis protocol and its revision history
   ●   Supplementary Table S1 — Effect of transition bias within each clade
   ●   Supplementary Table S2 — Out-of-clade prediction error, decomposed
   ●   Supplementary Table S3 — Inverted leave-one-clade-out validation
   ●   Supplementary Table S4 — Cross-metric comparison
   ●   Supplementary Table S5 — In-silico code optimization
   ●   Supplementary Table S6 — Stop-codon placement, exact enumeration
   ●   Supplementary Table S7 — Sensitivity: species with a non-standard nuclear code
   ●   Supplementary Table S8 — Position of the standard code within the ensemble
   ●   Supplementary Table S9 — Exclusion of RIP as the fungal residual
   ●   Supplementary Table S10 — The CUG reassignment under yeast spectra
   ●   Supplementary Table S11 — Slope and level of the standard code within the ensemble
   ●   Supplementary Table S12 — Curvature in the out-of-clade intercept bias
   ●   Supplementary Table S13 — Which stop codon a nonsense mutation creates
   ●   Supplementary Table S14 — Worst-case position of the standard code
   ●   Supplementary Table S15 — Advantage and exceptionalness under transition bias
   ●   Supplementary Note S3 — Reproduction package
   ●   Supplementary Note S4 — Stability of the phylogenetic fit
   ●   Supplementary Note S5 — Convergence of the in-silico optimization
   ●   Supplementary Note S6 — Strand canonicalization
   ●   Supplementary Figure S1 — Advantage against transition bias
   ●   Supplementary Figure S2 — Similarity to the standard code under optimization

Supplementary Note S1 — Protocol adherence and deviations

The analysis protocol was frozen on 27 July 2026, before any confirmatory analysis was executed, and is
deposited in full with its complete changelog. This note records every departure from it during execution.
All are implementation-level; none alters a prospectively specified hypothesis, endpoint, estimand, metric
or exclusion rule.


Before any species-level spectrum was loaded

D1 — Normalization wording and implementation. The protocol text specified renormalization "per
codon and position". The first implementation took this literally and rescaled each codon–position block
to equal mass, which forces every codon position to contribute equally and suppresses the relative
weighting of positions. Detected by an additivity check on the decomposition and corrected to a single
global sense→sense normalization.

D2 — Synthetic calibration superseded. Calibration figures first computed without context integration
were inflated approximately two-fold, because the CpG multiplier had been applied to all C>T
substitutions rather than only to C>T in genuine CpG context. All calibration figures were recomputed
under the final pipeline; the superseded values appear nowhere in the analysis.

D3 — Confirmatory metric lock. A synthetic sensitivity sweep, run before any species-level spectrum
was loaded, showed that the effect size depends on the amino-acid metric. The confirmatory metric was
locked to squared polar requirement on historical-standard grounds, a criterion independent of effect size,
and the lock was not revised after the cross-metric analysis showed the effect to be largest under that
metric. The metric dependence is reported in the main text.

D4 — Cohort order. A polymorphism-based, pentanucleotide-resolution cohort was designated the
principal study in the protocol. Its deposit is a single 4.3 GB archive that could not be retrieved as a whole,
and the present cohort was executed first for reasons of data access alone.
Posterior-summary files for 68 of its 113 species were recovered later, in an
order fixed before any of their spectra were read, and all 68 were analysed;
none was examined and then excluded. All 113 species of the deposit are listed
in data/external_source_manifest.csv with their position in its alphabetical
order and whether each was recovered, so the selection can be checked rather
than taken on trust. Because the cohort remained incomplete it is reported as an
external replication rather than as the principal confirmatory set. This was recorded in the protocol
before any result existed. The present cohort is reported standalone, with the resulting limitation stated in
the main text, and is not presented as though it had always been the principal study.


After species-level data were loaded

D5 — Out-of-fold prediction. Fixed effects for each fold were estimated by inverse-variance-weighted
generalised least squares on the training clades rather than by full phylogenetic refitting within each fold.
This is a computational approximation to the specified procedure.

D6 — Per-clade diagnostic slopes. Within-clade slopes were first computed by ordinary least squares as
a diagnostic. Under the phylogenetic model the fungal CpG coefficient — which under OLS appeared an

order of magnitude larger than in any other clade — collapses to approximately zero. The interpretation
built on the uncorrected estimate was withdrawn, and only phylogenetically corrected estimates are
reported.

D7 — Unresolved taxon names. TimeTree returned 58 tips under labels absent from the dataset,
representing synonym substitutions. In keeping with the protocol's requirement that unresolved names be
listed and excluded rather than silently substituted, these were dropped rather than matched by
approximation. Exclusion lists are deposited.


Supplementary Note S2 — Analysis protocol and its revision history

The protocol was frozen as version 5 on 27 July 2026, before the confirmatory analyses were run. It
specifies the observable and its estimand, the confirmatory amino-acid metric, the randomized-code
ensemble and its checksum, the aggregation rule, the treatment of stop codons and strand collapsing, the
hypotheses and their directional predictions, the cross-validation folds, and the exclusion rules — each
fixed before the data were seen.

It carries a complete internal changelog, dated through thirteen earlier revisions,
recording every decision that was made, reversed, or reopened during development,
and why. Two reversals are worth noting because they changed the estimand rather
than the implementation:

    ●      The context exposure was first specified as each species' own coding-sequence
composition and was reversed to a fixed reference exposure common to all species. Species-specific
exposure would have meant the observable moved because of the spectrum, codon usage and contextual
composition jointly, rather than the spectrum alone.

    ●      The test of the primary null was rebuilt. The original per-species bootstrap
resampled each species around its own observed spectrum and therefore preserved the between-species
differences it was meant to test; it was replaced by a measurement-error phylogenetic model evaluated by
parametric bootstrap under the null.

Protocol and changelog: see Supplementary Note S3.


Supplementary Table S1 — Effect of transition bias within each clade

Maximum-likelihood estimates of the coefficient of log transition/transversion ratio on the spectrum-
conditioned advantage, fitted with the phylogenetic model separately within each clade. Intervals are 95%
profile-likelihood.
 Clade                   n                     β_κ                   95% CI               λ
 Insects                 489                   +0.0697               +0.0624 to +0.0770   0.996

 Clade                   n                       β_κ                        95% CI                    λ


 Other                   212                     +0.0567                    +0.0446 to +0.0688        0.998
 Mammals                 669                     +0.0478                    +0.0425 to +0.0532        0.990
 Fungi                   619                     +0.0474                    +0.0423 to +0.0525        0.997
 Plants                  903                     +0.0460                    +0.0409 to +0.0511        0.993
 Birds                   897                     +0.0411                    +0.0365 to +0.0456        0.985
 Reptiles                134                     +0.0337                    +0.0261 to +0.0414        1.000
 Fish                    1,049                   +0.0320                    +0.0285 to +0.0356        0.992


All eight estimates are positive and all eight intervals exclude zero. The coefficient varies by a factor of
2.2 across the set.


Supplementary Table S2 — Out-of-clade prediction error, decomposed

Leave-one-clade-out validation. RMSE for the phylogeny-only model (M0) and the spectrum model (M1);
the M1 error is decomposed into an intercept-bias component and a dispersion component.
 Held-out        n                   RMSE M0         RMSE M1             bias (M1)       dispersion           bias share of
 clade                                                                                   (M1)                 MSE
 Mammals         669                 0.01875         0.00579             +0.00120        0.00567              4.3%
 Reptiles        134                 0.01007         0.00886             −0.00613        0.00640              47.9%
 Birds           897                 0.01542         0.00929             +0.00278        0.00887              8.9%
 Fish            1,049               0.03103         0.01223             −0.00747        0.00968              37.3%
 Plants          903                 0.03337         0.01439             −0.00508        0.01347              12.5%
 Insects         489                 0.04211         0.01762             −0.01089        0.01385              38.2%
 Fungi           619                 0.02295         0.02196             +0.0000009      0.02196              0.0%
 Other           212                 0.04587         0.02685             −0.00987        0.02496              13.5%


Weighted overall: RMSE 0.02877 (M0) to 0.01458 (M1), a gain of 49.3%. After recalibrating each fold's
intercept: 0.01726 to 0.01333, a gain of 22.7%.


Supplementary Table S3 — Inverted leave-one-clade-out validation

The model is trained on a single clade and used to predict all remaining species. Recalibrated gain
removes the intercept offset.
 Training      n train           n test        β_κ             RMSE M0         RMSE M1       gain               recalibrated
 clade
 Mammals       669               4,303         +0.01672        0.03468         0.01611       53.6%              39.7%

 Training        n train        n test          β_κ         RMSE M0      RMSE M1       gain          recalibrated
 clade


 Fish            1,049          3,923           +0.02198    0.02890      0.01481       48.7%         42.3%
 Reptiles        134            4,838           +0.01831    0.02805      0.01495       46.7%         39.9%
 Plants          903            4,069           +0.01975    0.02705      0.01467       45.8%         40.5%
 Birds           897            4,075           +0.01288    0.03461      0.02194       36.6%         33.8%
 Other           212            4,760           +0.01360    0.03301      0.02180       34.0%         28.8%
 Fungi           619            4,353           +0.01441    0.02982      0.03023       −1.4%         −5.8%
 Insects         489            4,483           +0.01749    0.03260      0.05414       −66.1%        −3.5%


All eight training clades yield a positive coefficient, spanning a factor of 1.7. The spectrum model
outperforms the phylogeny-only model on the rest of the tree from six of eight. The insect shortfall is
almost entirely a level offset.


Supplementary Table S4 — Cross-metric comparison

The spectrum-conditioned advantage recomputed under three amino-acid distance metrics, and the fitted
effect of transition bias scaled by the dispersion of the advantage under that metric.
 Metric                mean R            sd R               range of R       β_κ                β_κ / sd(R)
 Squared Woese         0.5477            0.0246             26.46 pp         +0.0206            0.836
 polar requirement
 (confirmatory)
 Grantham              0.2018            0.0077             10.61 pp         +0.0041            0.529
 Squared Kyte–         0.3345            0.0304             44.30 pp         +0.0120            0.395
 Doolittle


All values are computed over the 4,972 species of the confirmatory set. β_κ is the coefficient on
standardized log κ from an ordinary least-squares fit that also includes the standardized CpG>T shift;
deposited as data/cross_metric.csv.

The association is strongest under squared polar requirement and weaker under two alternative metrics.
These are correlated with polar requirement rather than independent of it: the scales at −0.79, their
squared-difference matrices at +0.43. The ordering does not triangulate polarity as the mediating axis, and
no sign reversal occurs.

Supplementary Table S5 — In-silico code optimization

Simulated annealing over permutations of the twenty amino acids across the twenty standard codon
blocks, under spectra with fixed transition/transversion ratio and no CpG term. Forty restarts of 30,000
iterations per value. Similarity is the fraction of blocks receiving the same amino acid as the standard
code; chance level is 1/20 = 5%.
 κ                                Φ optimum               Φ standard                   similarity
 1.0                              3.489                   5.194                        12.4%
 1.5                              3.488                   4.890                        7.9%
 2.0                              3.280                   4.663                        3.1%
 3.0                              2.879                   4.346                        4.1%
 4.0                              2.593                   4.136                        3.8%
 6.0                              2.174                   3.874                        2.1%
 8.0                              1.893                   3.717                        4.5%


Correlation of similarity against log κ: −0.76.


Supplementary Table S6 — Stop-codon placement, exact enumeration

Nonsense burden depends only on which codons are stops and on the spectrum, not on the assignment of
amino acids to the remaining codons. All C(64,3) = 41,664 three-codon placements were therefore
enumerated exactly under the reference exposure and the mean spectrum.
 quantity                                                 value
 burden of the standard set {UAA, UAG, UGA}               0.03789
 distribution across all placements                       min 0.02374, median 0.04736, max 0.08032
 percentile of the standard set, all placements           10.8
 placements with lower burden                             4,514 of 41,664
 percentile among placements of equal pairwise Hamming    37.7
 spread (n = 1,728)


Clustering, not the particular choice of codons, accounts for the apparent advantage. Correlation between
pairwise spread and burden across all placements is +0.20.


Supplementary Table S7 — Sensitivity: species with a non-standard nuclear code

Sixty-four species in the confirmatory set belong to the CUG clade, which reassigns CUG from leucine to
serine. No ciliates or other variant-code lineages were present.

 set               n                  mean R         sd R              range              β_κ                corr(κ, R)
 full              4,972              0.5477         0.0246            26.46 pp           0.05815            0.831
 excluding         4,908              0.5478         0.0246            26.46 pp           0.05827            0.838
 CUG clade


Supplementary Table S8 — Position of the standard code within the ensemble

Under the synthetic sweep, the standard code is compared both against the frozen 10,000-code ensemble
and against the optimum located by simulated annealing.
 κ                     Φ standard          best ensemble      codes               Φ annealed             optimum /
                                           code               outperforming       optimum                standard
                                                              SGC
 1                     5.194               5.111              3 of 10,000         3.489                  0.672
 2                     4.663               4.663              0 of 10,000         3.280                  0.703
 4                     4.136               4.218              0 of 10,000         2.593                  0.627
 8                     3.717               3.864              0 of 10,000         1.893                  0.509
 16                    3.439               3.501              0 of 10,000         —                      —


The ratio of the best ensemble code to the standard code rises from 0.984 to 1.040 while the ratio of the
annealed optimum to the standard code falls from 0.672 to 0.509. A change of scale would move both in
the same direction.


Supplementary Table S9 — Exclusion of RIP as the fungal residual

Within-clade correlation between log κ and R, with fungal species partitioned by the presence of repeat-
induced point mutation.
 Group                          n                             corr(κ, R)                        sd(R)
 Pezizomycotina (RIP            369                           +0.440                            0.0152
 present)
 Yeasts (no RIP)                58                            +0.617                            0.0269
 Remaining fungi                192                           +0.416                            0.0287
 Basidiomycota (no RIP)         47                            +0.462                            0.0153
 Other clades, for comparison   —                             +0.54 to +0.86                    —


Groups lacking RIP show the same shortfall as those possessing it, so the mechanism does not account for
the fungal residual.

Supplementary Table S10 — The CUG reassignment under yeast spectra

Expected substitution cost under the standard code and under the CUG-clade code (CUG reassigned from
leucine to serine), evaluated for each species under its own spectrum and the same reference exposure. Δ
is the CUG-code cost minus the standard-code cost; negative values favour the reassignment.
 Group                     n                         mean Δ                  median Δ                    % with Δ < 0
 CUG clade (carries the    64                        −0.0186                 +0.0042                     43.8%
 reassignment)
 Other yeasts (standard    86                        −0.0363                 −0.0016                     51.2%
 code)
 Non-yeast fungi           469                       +0.0801                 +0.0787                     1.1%


Mann–Whitney between the CUG clade and other yeasts: p = 0.18. The contrast with non-yeast fungi
separates yeasts from non-yeasts rather than carriers from non-carriers, and reflects phylogenetic structure
in the spectra.


Supplementary Table S11 — Slope and level of the standard code within the ensemble

The regression of R on log κ repeated for all 10,000 randomized codes against the same species spectra.
 quantity                        standard code                  ensemble median                  percentile of standard code
 β_κ (per unit of log κ)         +0.0582                        +0.0148                          70.5
 mean R                          0.5477                         0.0219                           99.98


A positive coefficient occurs in 5,676 of the 10,000 codes. Responsiveness to transition bias is therefore
largely a property of the block structure; the level of advantage is not.


Supplementary Table S12 — Curvature in the out-of-clade intercept bias

Leave-one-clade-out validation repeated with higher-order terms in log κ, weighted across folds by fold
size.
 model                 RMSE                weighted bias        dispersion             gain over            bias share of
                                                                                       intercept-only       MSE
 intercept only        0.02877             —                    —                      —                    —
 linear                0.01458             0.00591              0.01333                49.3%                16%
 (confirmatory)
 plus κ²               0.01434             0.00416              0.01372                50.2%                8%
 plus κ² and κ³        0.01466             0.00418              0.01405                49.1%                8%

Out-of-fold intercept bias by clade, against clade mean log κ:
 Clade                        mean log κ               bias (linear)                  bias (plus κ²)
 Insects                      0.570                    +0.01089                       +0.00617
 Other                        0.618                    +0.00988                       +0.00755
 Plants                       0.641                    +0.00508                       +0.00410
 Fish                         0.748                    +0.00747                       +0.00502
 Fungi                        1.110                    −0.00000                       −0.00089
 Birds                        1.155                    −0.00278                       −0.00279
 Reptiles                     1.162                    +0.00613                       +0.00619
 Mammals                      1.210                    −0.00120                       −0.00137


Correlation between clade mean log κ and bias: −0.82 under the linear model. The near-zero bias for
Fungi is a crossing point of the linear approximation rather than a property of the clade: it moves by three
orders of magnitude once the quadratic term is added, while the biases of high-κ clades barely change.


Supplementary Table S13 — Which stop codon a nonsense mutation creates

Sense→stop exposure partitioned by the stop codon generated, and by whether the substitution is a
transition or a transversion. "Routes" counts codon–position– context combinations rather than distinct
codon pairs: positions 1 and 3 each open into four trinucleotide contexts and position 2 into one, so the 23
distinct sense→stop codon pairs expand to 71 context-resolved routes. Exposure is the summed reference
weight of those routes.
 Stop codon            routes               transition exposure        transversion         tv/ts
                                                                       exposure
 UAA                   22                   1.0                        6.0                  6.00
 UAG                   23                   2.0                        6.0                  3.00
 UGA                   26                   2.0                        6.0                  3.00


The two transition routes to UGA are CGA→UGA (C>U at position 1) and UGG→UGA (G>A at
position 3).

Share of nonsense burden by stop codon, across quintiles of κ:
 κ quintile            mean κ               UAA                        UAG                  UGA
 lowest                1.52                 0.263                      0.295                0.442
 second                1.96                 0.231                      0.280                0.489
 third                 2.45                 0.207                      0.262                0.531
 fourth                3.08                 0.179                      0.244                0.577

 κ quintile                mean κ                  UAA                     UAG                    UGA
 highest                   4.04                    0.152                   0.216                  0.632


Correlation with log κ: UAA −0.77, UAG −0.51, UGA +0.67. The transversion share of total nonsense
burden falls from 0.54 in the lowest quintile to 0.26 in the highest (correlation −0.94), so transition bias
makes nonsense both smaller and more transition-carried.


Supplementary Table S14 — Worst-case position of the standard code

For each species, the number of randomized codes in the frozen 10,000-code ensemble achieving a lower
expected cost than the standard code under that species' own spectrum.
 quantity                                                    value
 median codes outperforming the standard code                2 of 10,000
 worst observed spectrum                                     *Plasmodium gaboni*, 341 of 10,000
 implied worst-case position                                 342 of 10,001, i.e. the top 3.5%
 species within the top 0.5% of the ensemble                 4,969 of 4,972 (99.94%)
 species where no randomized code outperforms it             1,084 of 4,972 (21.8%)


Mean advantage across the 4,972 spectra places the standard code third of 10,001, against a median
ensemble mean of 0.0219. This is close to the roughly two-in-ten-thousand reported by Haig and Hurst
(1991) under uniform mutation, so the classical ranking is not materially altered by substituting empirical
spectra.

We do not read the accompanying variance as evidence of exceptional stability. The standard code sits at
the 10.3rd percentile of across-species variance, but mean and variance are correlated at −0.52 across the
ensemble, and among the five codes with a comparable mean it falls at the 20th percentile of variance.
With only two codes exceeding it on the mean, the absence of one that also undercuts it on variance would
arise about 80% of the time under independence. All statements here are confined to the block-preserving
ensemble.


Supplementary Note S3 — Reproduction package

All analysis code, the frozen protocol with its internal dated changelog, the randomized-code
ensemble, the taxon-name mapping, the exclusion lists and all derived per-species values are provided as
Online Resource 2 (ESM_2.zip), published with this article. The package is self-contained with respect to
the deposited code, derived outputs and the numerical checks it runs. Full reconstruction from the primary
mutation-spectrum data, and five check groups comprising twelve checks, including the within-clade
correlations, the nonsense-channel quantities and the curvature checks, require the third-party CORAL
supplementary table cited in the main text.

The package includes three verification utilities. verify_package.py uses only the Python standard library
and confirms the file manifest, the SHA-256 checksum of the frozen ensemble
(d35d209a380b3a9db11ac809f0daa120c0ee91b9dbb23299c910aa2e906763e0), its structural invariants,
the row counts of five principal derived tables and the tip count of the phylogeny. audit_numbers.py recomputes
every quantity asserted in the manuscript from the deposited outputs and compares it to the value reported;
it reports 150 checks from the deposited outputs, or 162 when the external branch-level table is supplied.

Substitution counts and callable abundances aggregated per species are included so the audit runs without
external downloads; the branch-level source table itself is not redistributed and is obtained from the
supplementary material of the source study cited in the main text.

Supplementary Note S4 — Stability of the phylogenetic fit

Three diagnostics, regenerated by code/phylo_diagnostics.py, on all 4,972
confirmatory species. The join uses the binomial column, since the tree is
keyed by binomial while the spectra carry strain and subspecies suffixes.

Likelihood profile. Profiling lambda with tau-squared maximized at each point
gives a maximum at lambda = 0.9922 and a 95% profile interval of 0.9911 to
0.9931. Profiling tau-squared with lambda optimized continuously at each point
gives 3.49e-03 to 4.02e-03 around a maximum of 3.74e-03, which reproduces the
estimate of the main model. Intervals are read from the
curves rather than from an asymptotic approximation, because tau-squared = 0
lies on the boundary of the parameter space and lambda is unidentified there.
The profiles are shown in Figure S1.

Simulation recovery. Data were generated on the same tree at the fitted
tau-squared and at lambda = 0.50, 0.90 and 0.99, then refitted by the same
procedure. Six replicates at each value:

    lambda generated    recovered, median    range          tau-squared ratio
    0.50                0.529                0.463 to 0.569       1.06
    0.90                0.902                0.897 to 0.906       1.02
    0.99                0.990                0.990 to 0.990       1.01

A lambda near one is therefore not an artefact of the estimator saturating at
this sample size and with this measurement-error structure: when the generating
value is 0.50 the estimator returns 0.50.

Polytomy resolution order. The covariance is built by sequential pairwise
merging, which is exact under Brownian motion only if the order in which
polytomies are resolved does not affect the likelihood. Resolving them six times
at random gives lambda = 0.99217 in every case,
and a coefficient of variation in tau-squared of 1.2e-16. That is floating-point
noise, not a dependence on order.


Supplementary Note S5 — Convergence of the in-silico optimization

Simulated annealing cannot prove it has found a global optimum, so this note
records what the budget achieved rather than asserting what it ruled out.
Regenerated by code/optim_convergence.py.

Three budgets at each of three transition/transversion ratios:

    kappa   restarts   iterations   best cost   similarity   restarts at best
    1.0     10         30,000       3.4886      0.10         2 of 10
    1.0     40         30,000       3.4886      0.10         12 of 40
    1.0     40         120,000      3.4886      0.10         25 of 40
    2.0     10         30,000       3.2795      0.05         7 of 10
    2.0     40         30,000       3.2795      0.05         14 of 40
    2.0     40         120,000      3.2795      0.05         38 of 40
    4.0     10         30,000       2.5925      0.05         2 of 10
    4.0     40         30,000       2.5925      0.05         13 of 40
    4.0     40         120,000      2.5925      0.05         22 of 40

Raising the total budget sixteen-fold changes the best cost by 0.00 per cent at
every kappa tested, and the similarity at the optimum does not move. What rises
is the fraction of independent restarts that reach the best cost, from 7 of 10
to 38 of 40 at kappa = 2. Restarts are converging on the same value from
independent starting points, which is the evidence available for a heuristic
search: not a proof of global optimality, but a demonstration that the reported
optima are reproducible and that more computation does not find better ones.

The similarity at the optimum is 5 to 10 per cent throughout, at or below the
level expected by chance for a permutation of twenty blocks.

Supplementary Note S6 — Strand canonicalization

The source spectra collapse reverse-complementary substitution types. Applying the collapsed rate to both members of a complementary pair requires flipping the context as well as the bases; copying the numeric rate alone is incorrect. The lookup rule is central base C or T → query the context as presented central base A or G → query reverse_complement(context) with the complementary substitution P_s(G → A | x) = P_s(C → T | RC(x)) (7) Collapsed spectra assume strand symmetry and therefore cannot represent transcription-coupled-repair asymmetry in coding regions (§12).
