Operational Difference on DNA: a release ladder and a repair solver for sequence variants, with fifteen pre-registered sealed audits of three public splicing datasets (restricted research package, all rounds)

Description

Eric J. Needham, Symmersion, Agios Onoufrios, Crete. 21 October 2026.

What this is

The complete record of applying the Operational Difference method to sequence-to-function data, using RNA splicing as the test domain. The method is implemented as a genomics module of the Symmersion audit software, together with the compatibility-residual repair solver carried over from field equations to data.

Two instruments. The release ladder is iterated conditional quotient refinement: starting from the exon, it asks which declared map still splits the outcome within the current refinement, releases the strongest map that survives a within-exon matched null with family-wise error control, and repeats. The repair solver treats each measured variant as a jet, with the kernel of the measured design, and returns verdicts of point, class or outside the basis against a replicate noise floor.

One protocol. Every analysis is locked before any outcome is read: the analysis, the predictions and the thresholds are written and hashed first, the results are sealed afterwards, and each is re-run from its lock to confirm it reproduces field by field. Known-answer validation on planted data precedes every lock, including scenarios written to be adversarial to the method. Disclosed errors are recorded as errata rather than corrected silently, and an aborted lock is kept on the record.

Across fifteen rounds, 123 predictions were locked in advance and 98 were met. All seventeen seals verify against their locks and input hashes, and every analysis reproduces from its lock.

The progression, round by round

Round 1 (8/12 and 10/12 met, two libraries)

Audits the known splicing maps on the public MFASS libraries: 27,733 natural variants across 2,185 exons, and 13,075 designed perturbations assayed in two intron backbones. The ladder releases graded donor strength first, then the canonical-site indicator, graded acceptor strength, the hexamer map, folding, silencers, enhancers and the translation map. Designed changes that hold the splice-site score constant move inclusion 5.2 to 11.8 times less than changes designed to weaken it, in both backbones and at both sites: absorbed at one map, consequential at another. Four misses came from one mistaken expectation, that the binary canonical map would outrank the graded one.

Round 2 (5/6 and 5/5 met)

Offers SpliceAI as a candidate new map. Given every first-round map it is still consequential within exons, in both libraries and both backbones, so it is a new map in the solver's sense; on held-out exons it shrinks the structured remainder by about seven points. Most of the remainder therefore stands.

Round 3 (11/11 met)

Blind recovery. A learner given no splicing knowledge — only the four letters, positions relative to the exon boundaries, and outcomes on half the exons — is scored against an answer key locked in advance. It recovers the donor consensus at 9 of 9 positions and the acceptor at 20 of 20, against shuffled-outcome means of 1.91 and 8.08, replicates this on the other half of the exons, and produces word weights agreeing with published enhancer and silencer scores it never saw (rho 0.352).

Round 4 (4/7 met)

Points the method at the remainder and gives it a floor. Variants remeasured in an independently built library agree within exon at r = 0.886, so 0.889 of within-exon variation is reproducible, against 0.279 reached by every declared map together. Three further candidate families — exon context, local RNA structure at the sites, position-dependent words — reach none of it.

Round 5 (2/4 met)

Asks whether that remainder is a general rule or specific to each exon, using a declared model that can learn only rules transferring between exons. On planted data it recovers about three-quarters of a rule of its own form; on held-out real exons it adds nothing. A convolutional network that failed the same planted check was set aside before any use on real data and is kept in the package as the record.

Round 6 (5/7 met)

One exon measured in every combination (FAS exon 6, 3,072 genotypes; Baeza-Centurion et al. 2019). Its own mutation effects composed by the published scaling law, plus pairwise interactions, reach a held-out R² of 0.882, leaving 0.057 against replicate noise of 0.060. Within one exon, composition is lawful to the measurement floor.

Round 7 (7/7 met)

Asks whether a new exon's effects can be read from its letters, on 309,698 substitutions in 601 exons (OpenSplice preprint). Learned blind on half the exons, the code reads 0.457 of the within-exon variation of exons it never saw, 0.543 of what is reproducible. A transferable context rule is now detectable but small. The unread part is exonic.

Round 8 (6/7 met)

Locates what the blind code adds over SpliceAI: exonic six-letter words, not letters near the splice sites, reproducible across independent halves of the training exons. The miss, R5, is informative: what is missed is NOT the classical enhancer/silencer vocabulary.

Round 9 (6/8 met)

Tests two mechanisms as declared maps. Rescoring SpliceAI over the whole construct, rather than at the two annotated splice sites only, removes 0.936 of the competing-site effect, so that component was a scoring convention rather than model error. G-quadruplex propensity removes 0.534 of the G-rich effect, specifically, without touching the other word classes.

Round 10 (4/7 met)

Uses the 394,286 deletions the earlier rounds left untouched to ask whether removing a regulatory element costs more than its letters do individually. For 3 to 6-nucleotide windows it does not, with planted controls establishing that cooperativity and redundancy would both have been detected. The strong redundancy a naive comparison appears to show is an artefact of the bound on measurable inclusion. At 21 nt the design cannot decide, and a first reading of the shortening result was checked and withdrawn (errata beside the seal).

Round 11 (5/6 met)

Compares the release ladder with the methods ordinarily used for the same job: a marginal screen, a penalised path, forward selection and drop-one ablation, each also run with the exon grouping the ladder uses. Cleaner than the screens ordinarily run, without a tunable threshold. One prediction written against the method — that it would not beat careful conditioned selection — was met. The miss, E5, also runs against the method: its release ordering resamples less stably than the alternatives'.

Interim: claim-by-claim evidence matrix

Audits every headline claim against the sealed records, withdrawing one outright and narrowing three. Later revised with its own errata when five values in its rows about the method's own claims were found to disagree with the seals; all twenty-two are now machine-checked at the precision quoted.

Round 12 (6/6 met)

Runs the two tests the matrix identified as missing, and both correct this project's own record. Giving the alternatives the ladder's own permutation-calibrated stopping rule, so both sides are tuned alike, reverses round 11's result on the designed-trap scenario (F1 0.838 against 0.800) while confirming it on the partial-confound scenario (0.900 against 1.000), where a prediction written against the method said the ladder would still lose.

And the absorption step round 8 had assumed is not merely untested but contradicted: SpliceAI's score does not track enhancer/silencer content within exon (Spearman +0.011, n = 141,138); that vocabulary barely tracks the outcome here either (-0.0166); yet adding the maps still gains 0.00804 [0.00532, 0.01065]. Both fitted coefficients come out positive, where a directional vocabulary should give opposite signs.

Round 13 (5/6 met), the latest

Asks where the unread variance actually sits and eliminates three explanations for it. With a reproducibility ceiling measured for each region, SpliceAI reads 0.801 and 0.769 of what is measurably there at the two annotated splice sites and 0.517 inside the exon. That gap is not measurement: exonic data reproduce at 0.937 against 0.986 at the sites. It is not an artefact of assuming a linear relation: a twenty-bin flexible fit widens it, the sites improving to 0.845 and 0.811 while the exon interior does not. And it is not the scoring convention found in round 9: rescoring over the whole construct on 8,000 exonic variants in 200 exons closes none of it.

Inside the exon the deficit is worst immediately adjacent to the boundary (0.379 at 0–2 nt) and mildest in the middle (0.532 at 21–40 nt), which contradicts the published statement that prediction suffers further from splice sites. The miss, V6, tightens the result: the scan was predicted to close some of the deficit and closes none. Before this lock, planted scenarios established that the statistic is comparable across regions differing fourfold in variance and seventeenfold in sample size, and that it separates worse prediction from noisier measurement.

Round 14 (3/6 met, blind on the measured data), the latest

Declares the branch point, which none of the thirteen previous rounds had ever declared, nor a polypyrimidine tract beyond MaxEntScan's -20 window, nor any RBP motif.

A planted check changed the design before any lock existed: scored without conditioning on nucleotide composition, the map reported a larger gain on outcomes driven purely by adenosine content (0.144) than on genuinely branch-driven ones (0.135), because any change creating or destroying an adenosine moves a branch score. Composition was therefore moved into the baseline and a sham consensus added, with guanine at the branch position. The branch point map then gains nothing (-0.0009, permutation p 1.000) and does not beat the sham consensus — an ambiguous null, as the lock states: conditioning on composition removes genuine branch signal along with the confound, leaving the test about 12 per cent of a planted effect, and the map is this project's own statement of the textbook yUnAy consensus rather than a published matrix, because no branch point predictor can be obtained in this environment.

The round's result lies elsewhere. In the -17 to -5 window the polypyrimidine map gains 0.00580 of held-out within-exon variance (permutation p 0.003, corrected interval 0.00233 to 0.00925, every one of 2,000 exon-bootstrap resamples positive, sham consensus -0.00077), and of five features exactly one carries it: the longest uninterrupted pyrimidine run, weighted 13.71, while pyrimidine fraction receives exactly zero because it is an exact linear function of the cytosine and thymine counts already in the baseline.

Pyrimidine content in the tract is absorbed by composition; pyrimidine arrangement is not. An errata beside the seal records a bootstrap defect found afterwards, which biased every interval upward and is recomputed without altering the sealed code.

Round 15 (6/6 met, blind on the measured data), the concluding round

Opens the network. Fourteen rounds audited SpliceAI's output; this one takes its internal representations as the declared map — the change, mutant minus wild type, in activations pooled per channel over the exon interior at six of its twenty residual blocks — on the same rows round 13 used.

Against SpliceAI model 1's own two-position readout the internals gain 0.200 of held-out within-exon variance where a random-weight twin of identical architecture gains 0.018, an eleventh as much, with the gain rising with depth from 0.108 at the earliest tap to 0.191 deep in the network. But against the ensemble score used throughout the rest of this record they gain nothing: -0.019, permutation p 0.500, with a detection limit near five per cent of within-exon variance established by planting signals of 0.05, 0.10 and 0.20 against that same baseline.

So the exonic information rounds 9 and 13 could not recover is ABSENT from the network rather than hidden inside it: not recoverable by rescoring the whole construct, and not present in the representations beyond what the score already expresses. The model does not hold what it does not say, which makes the shortfall architectural rather than a matter of readout.

An errata beside the seal records that the lock's baseline was model 1's own readout rather than the ensemble score, that one follow-up arm silently dropped a column, and the power calibration that makes the null interpretable; it states that the seal should not be quoted without it.

What the record supports

EVERYTHING TRIED STOPS IN THE SAME PLACE, AND A REPRODUCIBLE HALF SITS ABOVE IT.

A learner given nothing but the four letters and positions relative to the exon boundaries — no splicing knowledge of any kind — reads 0.457 of the within-exon variation of exons it never saw, against 0.417 for the entire published knowledge base and 0.456 for both together: they carry substantially the same information, and about half of what is readable falls out of the data from scratch.

The remaining half is not noise. Against a corrected floor (see the round-7 errata: replicate noise had been estimated from raw replicates, which carry an exon-level offset the within-exon transform removes from the outcome anyway) the reproducible share is 0.9595 overall and 0.9375 inside exons, so 0.4761 of what is reproducible is reached and MORE THAN HALF IS UNREAD.

That half is read by nothing tried: not the declared knowledge maps, not the blind code, not SpliceAI, and not Pangolin, AlphaGenome or SpliceTransformer on the preprint's own comparison, where every model sits below a replicate ceiling of 0.79; and round 15 closed the last route by showing it is not inside SpliceAI either. Methods with entirely different inductive biases converge on the same ceiling, and the convergence is visible only because there is a measured floor to put under it, which no published benchmark provides.

Most of the variant-effect structure in these exons is reproducible and reached by no known splicing rule: 0.279 reached by every declared map together, against a ceiling of 0.889 measured on an independently built library.

That unreached structure has a location, and three candidate explanations for it have been eliminated. It is exonic: with a reproducibility ceiling measured for each region, a published model reads 0.801 and 0.769 of what is measurably there at the two annotated splice sites but 0.517 inside the exon. It is not a measurement artefact, because exonic data reproduce at 0.937 against 0.986 at the sites — an inference the published benchmarks cannot make, since they report performance against measured labels with no ceiling at all.

It is not an artefact of assuming a linear relation, because a twenty-bin flexible fit widens the gap rather than closing it, the splice sites improving to 0.845 and 0.811 while the exon interior does not move. And it is not the convention of reading a model's score only at the two annotated splice sites, because rescoring over the whole construct on 8,000 exonic variants in 200 exons closes none of it.

Inside the exon the deficit is worst immediately adjacent to the boundary (0.379 of the ceiling at 0–2 nt) and mildest in the middle (0.532 at 21–40 nt), which contradicts the published statement that prediction suffers further from splice sites. What remains is ignorance of exonic regulation, about half of what is measurably there, with a measured size and a measured address.

In the polypyrimidine tract, how the pyrimidines are ARRANGED carries information that neither a recalibrated published model nor the nucleotide composition of the same window contains. On 21,716 variants across 598 exons, adding the tract map gains 0.00580 of held-out within-exon variance (permutation p 0.003, corrected interval 0.00233 to 0.00925, every one of 2,000 exon-bootstrap resamples positive, against a sham-consensus control at -0.00077).

Of five declared features exactly one carries it: the longest uninterrupted pyrimidine run, weighted 13.71, while the pyrimidine FRACTION receives exactly zero, because fraction is an exact linear function of the cytosine and thymine counts already in the baseline and is absorbed there, whereas run length depends on arrangement rather than amount. Longer run, more inclusion — the direction U2AF binding predicts.

This was predicted before the data were touched. Classical mutagenesis established the direction three decades ago, finding continuous uridine runs the strongest competitors and purine-interrupted tracts far less effective; what that work did not do, and this does, is separate run length from total pyrimidine content statistically, with content held in the baseline.

Exonic elements of three to six nucleotides cost what their letters cost individually, with planted controls establishing that cooperativity and redundancy would both have been detected, so on this evidence they are neither cooperative units nor redundant.

Within one exon, how mutations combine is lawful to the measurement floor: a held-out R² of 0.882 leaving 0.057 against replicate noise of 0.060. With the result above, that separates a nearly complete composition operator from inputs that cannot yet be read from sequence.

Two results concern published tools rather than splicing. A benchmark reading model output only at annotated splice sites mis-attributes competing-site effects to model error — 0.936 of one word class's effect on its own subset, though round 13 bounds this to that narrow place. And the standard enhancer/silencer hexamer tables take the same sign in both directions in this assay (+0.0134 and +0.0176), which would mean they measure how much sequence changed rather than which way it pushed, while a model's score does not track their content within exon at all (Spearman +0.011, n = 141,138).

For SpliceAI specifically the shortfall is architectural, and the consequence is practical. It is used clinically to interpret variants of uncertain significance. Inside exons it reads about half of what the measurement can resolve; its reported accuracy is an aggregate carried by the splice-site variants it was trained to locate, where it reads about four-fifths; and the information it lacks is not sitting unexpressed in its weights, so no improvement in scoring convention recovers it.

What it does not support

Reproducible is not biological: the remainder reproduces across independent library builds, which rules out technical noise within one build, but not that it is a stable property of reporter constructs in one cell line. No mechanism is named.

The method is not shown to beat careful conditioned selection, and its release ordering is the least stable of those compared. On the published predictors' own measure, SpliceAI predicts these variants better than this method's blind code (median per-exon Spearman 0.70 against 0.60).

The direction of the exonic deficit is itself published (Genome Biology 2023, doi:10.1186/s13059-023-03144-z) and is not claimed as new. Rounds 12 and 13 contain confirmations whose direction was known, disclosed in their locks, and the reproducibility ceilings are replicate-based within a single library build except in round 4, which used an independent build. Four claims made by this project were corrected against its own record, each recorded beside the relevant seal.

Contents

All_Rounds.zip holds the fourteen successive uploads as folders Upload_1 to Upload_14, each a self-contained package with its own README, handover file, technical note, sealed audits, software, analysis scripts and the Zenodo description as deposited at the time. Upload_14 is the current state and contains everything; the earlier folders are kept so the progression, including the four claims this project later corrected, can be read in the order it happened.

The folders are numbered by upload and do not map one-to-one to rounds: FOLDERS.md at the top level gives the mapping, derived from the sealed-audit contents of each archive, together with the round-to-seal table and a note on why the historical descriptions inside the folders are left unedited.

Each package contains: the claim-by-claim evidence matrix (read first); Symmersion Technical Note 2, The Splicing Code under Operational Difference, with LaTeX source whose every number is generated from the sealed records; a summary note on what has been established and what follows; a plain-language summary; the sealed audits with their locks, seals, errata and one aborted lock; the Symmersion software with its genomics module, tests and configurations; and the planted known-answer validations with the analysis scripts.

Derived inputs are included where licences allow (MFASS-derived feature tables; the FAS exon 6 table, GPL-3.0). OpenSplice-derived inputs are not redistributed (the preprint is CC BY-NC 4.0); scripts rebuild them from its supplementary tables. Raw MFASS data, MaxEntScan, published hexamer tables and SpliceAI are not included, and the packages state where to obtain them. SpliceAI is called, never bundled (code GPL-3.0, weights CC BY-NC 4.0).

This record: doi:10.5281/zenodo.23528894.

Related records: Operational Difference, doi:10.5281/zenodo.23258802; Symmersion Technical Note 1, doi:10.5281/zenodo.23416012; Symmersion software archive, doi:10.5281/zenodo.23416265.

SHA-256 of the deposited archive:

85c4181355ff98aebe1ba6f0b6d959dfe9dae655394762e188dd3c8bb2c93194 All_Rounds.zip

SHA-256 of Upload_14, the current package, as contained in that archive:

fe48d934c42f40c49430c1c8e85dbbe879288e42ae81ea8fe1b769af25cd55dc OD_Genomics_Research_Package_v19_2026-10-21.zip

Access to the files may be requested from the author: ensotheory1@gmail.com