arXiv CS open access

GRAFT-EEG: Gauge-Aware Physical Field Transport for Cross-Dataset Motor-Imagery EEG

Ying Zhou et al. · arxiv_cs

arXiv CS · Papers

deep-learning machine-learning neural-networks

Cross-dataset EEG decoding often treats montage, reference, and active-sensor changes as representation shift, although they also alter the observation operator. We study target-statistics-blind transfer: fitting receives no target signal, label, or empirical statistic, and electrode coordinates onl

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GRAFT-EEG: G AUGE -AWARE P HYSICAL F IELD T RANSPORT FOR C ROSS -DATASET M OTOR -I MAGERY EEG Ying Zhou1 Mengting Liu1∗ School of Biomedical Engineering, Shenzhen Campus of Sun Yat-sen University

arXiv:2610.23620v1 [cs.LG] 16 Oct 2026

A BSTRACT Cross-dataset EEG decoding often treats montage, reference, and active-sensor changes as representation shift, although they also alter the observation operator. We study target-statistics-blind transfer: fitting receives no target signal, label, or empirical statistic, and electrode coordinates only instantiate a fixed prediction operator. G RAFT-EEG removes the active-set common-reference gauge and transports each native mask through a template motor leadfield. A source-fitted spectral classifier anchors the decision; a bounded state-space-model (SSM) residual is secondary. We establish restricted identifiability and an operator-perturbation bound. Across five leave-one-dataset-out targets (253 participants), dynamic G RAFT-EEG achieved 60.865% equal-target balanced accuracy versus 52.684% for strict-clean 5/5 BIOT (hierarchical difference +8.182 points; 95% CI +6.382 to +10.196; positive in every target). On four EEGPT-clean targets, the descriptive means were 61.520% and 59.057%. In four post-hoc exact same-parent tests, FULL exceeded coordinate-basis, matched-spectrum, row-shuffled, and wrong-anatomy controls by 9.959, 9.698, 11.241, and 3.985 points, respectively (all 95% CIs excluded zero; Holm-adjusted P < 0.001). A separate 60-participant same-paradigm evaluation retained a positive physical-operator contrast (+4.029 points; +2.338 to +5.773), whereas dynamic–static was inconclusive; its preregistered status is partial confirmation rather than unrestricted external validation. The SSM added +1.059 points (+0.013 to +1.892). Claims remain bounded to five binary motor-imagery domains and the tested operators.

I NTRODUCTION

Public motor-imagery EEG datasets differ in electrode count, location, reference, amplifier, sessions, and unusable channels. Transfer therefore couples physiological and procedural shift with a change in observation coordinates. Channel intersection resolves tensor shape by discarding native sensors; learned adapters can retain them but may obscure which target information fitted the adapter. Large EEG models learn reusable representations through masking, tokenization, and diverse corpora (Jiang et al., 2024; Wang et al., 2024; 2025; Jiang et al., 2025). BIOT tokenizes channels separately; newer systems use coordinates or learned channel-unification modules (Yang et al., 2023; El Ouahidi et al., 2025; Döner et al., 2025; Chen et al., 2026). These advances do not isolate whether a full unseen montage can be decoded before opening any target signal or empirical statistic. We test explicit observation-operator transport under that fixed contract, a distinction that matters when compact BCI decoders remain competitive and conclusions are protocol-sensitive (Yang et al., 2026). In our target-statistics-blind heterogeneous-montage contract, declared coordinates may instantiate geometry-only operators, but fitting uses source signals and labels only. Target geometry supplies no covariance, normalization, calibration, validation loss, or stopping signal; after source fitting, target signals are mapped once and labels reach only the scorer. Exact same-parent controls fix split, seed, head, features, ridge rule, and budget while replacing the motor leadfield with coordinate-only, spectrum-preserving random, row-shuffled, or wrong-anatomy operators. A stricter sensitivity learns ∗

Corresponding author.

the shared basis and hyperparameters from source geometries, opening the target montage only after all 25 fits are frozen. G RAFT-EEG first removes the unidentifiable common-reference component on each trial’s active channels and transports the remaining field through a mask-specific inverse into a fixed bilateral motor basis. It then separates a static spectral anchor from a small bounded state-space residual, whose zero initialization recovers the static classifier and whose stable decay bounds the recurrent correction. Our contributions are: • a precise access contract for cross-dataset EEG decoding that distinguishes target geometry from target signal, label, and distributional statistics; • an active-set reference quotient and physical motor-field transport into an eight-dimensional latent, with restricted identifiability, an operator-perturbation bound, a static anchor, and a secondary bounded residual; • a five-domain evaluation with strict and partial denominators, domain-aware uncertainty, four exact same-parent operator controls, baseline-health diagnostics, and a same-paradigm partial-confirmation external evaluation.

R ELATED W ORK

Large EEG models use masked pretraining, channel tokenization, coordinates, or learned queries to accommodate heterogeneous layouts (Yang et al., 2023; Jiang et al., 2024; Wang et al., 2024; 2025; Jiang et al., 2025; El Ouahidi et al., 2025; Döner et al., 2025; Chen et al., 2026). Reported downstream protocols are not uniformly target-statistics-blind, so their results do not answer the same access-constrained question. We study a boundary in which the entire target dataset remains unopened during fitting, except for its declared electrode coordinates. G RAFT-EEG is therefore neither a foundation model nor a claim of topology-agnostic inference. Geometry-based FI/SSI and Riemannian alignment provide strong alternatives to common-channel selection (Mellot et al., 2024). Related cortical work uses participant-specific surface eigenmodes to constrain EEG/MEG source imaging (Wang et al., 2026). Our operator instead uses montage coordinates and a shared template motor basis for decoding; it is not participant-specific source localization. The matched FI/SSI controls receive the same native active channels and are denied target recentering, covariance fitting, and calibration. EEGNet and recent state-space decoders motivate the compact heads (Lawhern et al., 2018; Ma et al., 2026; Ryoo et al., 2025), but our temporal branch is restricted to a bounded residual and supports no streaming claim.

P ROBLEM S ETTING AND ACCESS C ONTRACT (m)

Let Dm have native channels Cm , geometry Qm , and trials Xi ∈ R|Cm |×T with active set (m) (m) Si ⊆ Cm and label yi ∈ {0, 1}. In each fold, one complete dataset Dm⋆ is held out. Its geometry may be opened to instantiate the declared linear operator, but its signal store, labels, trial queue, and empirical statistics cannot be opened during fitting. Source features, hyperparameters, classifiers, state-space weights, and calibration parameters are committed to a hash-bound manifest before a separate process opens target signals. Labels are materialized only after predictions are frozen. Thus, target-statistics-blind means blind to target signals, labels, and empirical statistics during fitting, not blind to electrode coordinates. After lock, a deterministic per-trial mask instantiates only that trial’s operator; masks are never aggregated or used for refitting, normalization, calibration, early stopping, or threshold selection. Source-subject validation remains permitted. 2

a Native montages BNCI 22/22

Cho 60/64

Shin 30/30

b Quotient + gauge transport ×

Lee 61/62

Qₘ,ₛ

Pₛ

d Real EEG → transported latent C3 Cz C4 Cho · 60/64 active · 3 s PSD

ρ ridge

c Fixed 8D motor basis

G(ρ)

8 × 60

B = PₛAₛ · λ = ρσ₁² no fill · geometry fixed at lock

PhysioNet 64/64

TFR · 4–45 Hz

e Static anchor · full trial z-score −μ ÷σ

4→1 PN

5 foldsShin

ℓₛ

lock

f Stable residual · short windows x₁ … x₁₁ −μ RMS LN 11 × 24

GRAFT-dyn.

Stable SSM · 16 states cand. gate decay

hₖ₋₁

aₖhₖ₋₁

readout ×2 h₁₁ ‖ μₕ hₖ |rSSM| < 2 +

(1−aₖ)gₖcₖ

σ(ℓ)

p(y=1 | X)

shared ×11 · bounded recurrent update

h LODO + matched FI/SSI Lee

weighted LR

source-fitted · frozen on target

Z · 8×600

Cho

g Sealed fusion

8×3 tensor

L1 L2 L3 L4 R1 R2 R3 R4

Zi = Gρ,m,Sᵢ PSᵢ Xi,Sᵢ

BNCI

+ 4L + 4R · mode-normalized

−

i Access contract 8D → static + SSM

17D → tangent + EEGNet

SSI

17D → tangent + EEGNet

PRE-LOCK

INFERENCE

fit θₛ

SCORING + AUDIT audit · 4×15

frozen θₛ

LOCK

No target-derived fitting, normalization, calibration, or model selection.

Figure 1: GRAFT-EEG and its access contract. a–c, Quotient reference and transport of native active sensors to a fixed eight-dimensional bilateral motor basis. d, Source-side signals and transported latent. e–g, Static full-trial spectral logit plus a bounded short-window residual before the sigmoid. h, Leave-one-dataset-out evaluation and matched FI/SSI controls. i, Geometry is available before lock, signals only at inference, and labels only at scoring; target-derived fitting, normalization, calibration, and model selection are prohibited.

GRAFT-EEG

Figure 1 introduces the observation-operator problem and access contract; Figure 2 then separates the geometry-conditioned transport, static anchor, and bounded dynamic residual at the level of the executed model. 4.1

ACTIVE - SET REFERENCE QUOTIENT

EEG potentials are defined only up to an additive common offset. Applying a fixed inverse directly to differently referenced observations can therefore couple the representation to an arbitrary gauge. For an active set S, we use 1 1S 1⊤ PS (x + c1S ) = PS x. (1) PS = IS − S, |S| The same PS is applied to the signal and the matching lead-field rows. Failed channels are excluded rather than filled from target data; Appendix Q gives the fixed retention rules. 4.2

M ASK - SPECIFIC TEMPLATE MOTOR - FIELD TRANSPORT

Let Am,S ∈ R|S|×d be the observation matrix for a fixed d = 8 template motor basis (four modes per hemisphere). It is constructed once from the declared montage geometries and an fsaverage motor region; no EEG sample, label, or target statistic enters its construction. These coordinates are task-specific features, not participant-specific source estimates. We form λm,S = ρ σ1 (Bm,S )2 ,

Bm,S = PS Am,S ,

(2)

where σ1 is the largest singular value and ρ is selected using source-subject validation. The maskspecific inverse and transported latent are ⊤ ⊤ Gρm,S = (Bm,S Bm,S + λm,S Id )−1 Bm,S ,

(m)

= Gρ

(m)

m,Si

PS (m) X i

(m) (m)

i,Si

(3)

Caching is keyed by dataset, active-mask fingerprint, and ρ, so distinct bad-channel patterns cannot share an incompatible inverse. The spectral scale makes ρ comparable across masks. 4.3

W HAT HETEROGENEOUS OPERATORS CAN IDENTIFY

The transport above is not a claim of unique nonlinear cortical-source recovery. Its narrower justification can be stated for a finite-dimensional linearized field. Let zt+1 = F zt ,

(m)

= Am zt + ϵt

(4)

where zt ∈ R is a latent state and Am is the gauge-projected observation operator for montage m. For montages M and horizon T , define the joint observability matrix OM,T = col Am F t : m ∈ M, t = 0, . . . , T − 1 . (5) Proposition 1 (Restricted identifiability). If F and {Am }m∈M are fixed and rank(OM,T ) = d, noiseless stacked observations uniquely determine z0 . If the latent coordinates are learned jointly with the dynamics and operators, the representation is identifiable only up to an invertible similarity transform (F, Am , zt ) 7→ (SF S −1 , Am S −1 , Szt ). The proposition explains why heterogeneous montages can be complementary: an individual observation operator may have a nontrivial null space, while their jointly observed modes can span the restricted latent. Gauge removal is necessary before applying this argument because a common reference offset is not an identifiable field component. It does not, however, make arbitrary nonlinear sources identifiable. b = O + ∆O, let Y = Oz0 + ϵ, and estimate Proposition 2 (Perturbed-operator reconstruction). Let O † b zb0 = O Y . If σmin (O) > 0 and ∥∆O∥2 < σmin (O), then ∥b z 0 − z 0 ∥2 ≤

∥ϵ∥2 + ∥∆O∥2 ∥z0 ∥2 . σmin (O) − ∥∆O∥2

(6)

The bound in (6) separates measurement noise from montage/operator mismatch and motivates spectral regularization. A sealed post-primary sensitivity perturbed declared coordinates without retraining; across 50 target–condition units, reduced-operator change tracked dynamic BA change (Spearman ρ = −0.449; 95% CI −0.760 to −0.282; permutation P < 0.001; Appendix P). This characterizes the tested operators, not a universal placement tolerance. The template basis is not participant-specific localization. Proofs are in Appendix A. 4.4

S TATIC MOTOR - SPECTRAL ANCHOR

For each latent component, full-window log power in [8, 13), [13, 30), and [8, 30) Hz gives a 24dimensional vector. Trial i receives weight wi = N/[2(M − 1)nm,yi ], so each source-library–class cell has equal total mass. A weighted scaler and logistic classifier are selected on source subjects and then refitted on all eligible source trials. Candidate grids and deterministic tie breaking appear in Appendix Q. 4.5

S TABLE GATED STATE - SPACE RESIDUAL

Using the same frequency bands, each trial is also divided into 0.5-s windows advanced at a 0.25-s stride, producing 11 vectors xk ∈ R24 . The inputs are centered within band, normalized by their RMS, and then layer-normalized before entering a 16-dimensional diagonal recurrence: ck = tanh(Wc xk + bc ), ak = 0.5 + 0.499 σ(a0 + Wa xk ),

gk = σ(Wg xk + bg ), hk = ak ⊙ hk−1 + (1 − ak ) ⊙ gk ⊙ ck .

(7) (8)

Every coordinate of ak is constrained to (0.5, 0.999). The residual readout combines the terminal state with the sequence-average state and applies an explicit bound, " # ! K X ⊤ −1 rSSM = 2 tanh w hK ; K hk + b , |rSSM | < 2, (9) k=1

a Gauge-aware transport b Dual-timescale source-fitted readout

Cho2017 · 60/64 active sensors · 3 s at 200 Hz

STATIC DYNAMIC 3 bands × 8 modes

Z signal branch

Stable SSM z-score

ℓₛ=−0.629

weighted LR

geometry branch 11 windows × 24

Xₛ Mₛ

Sᵢ

Pₛ

Qₘ Aₛ

ρ G(ρ)

center · RMS · LN

11 shared steps 1

candidate cₖ Pₛ

quotient reference

basis transport

PₛXₛ

G(ρ)

Z · 8×600

gate gₖ

Wc · 16×24 Wg · 16×24 state update

…

Z=G(ρ)PₛXₛ

B=PₛAₛ

ℓ=−0.487

(1−aₖ)⊙gₖ⊙cₖ B

ℓₛ rₛₛₘ

Wa · 16×24

aₖ⊙hₖ₋₁

Aₛ

sealed readout

decay aₖ 16 states

hₖ sigmoid

bounded sequence readout

p(y=1|X)=0.381 concat 2×tanh rₛₛₘ = +0.142 [h₁₁; mean h] source-fitted · target sealed · no target fitting / normalization / calibration

target geometry only before lock no target signal statistics

hₖ=aₖ⊙hₖ₋₁

(1−aₖ)⊙gₖ⊙cₖ

Figure 2: Data-grounded architecture and one sealed replay. a, In Cho2017:0, 60/64 sensors remain active over 600 samples. Separate quotient and basis-transport branches project the retained signals and geometry to the shared eight-dimensional latent; traces and As , B, G(ρ), and Z come from the label-blind replay. b, A frozen three-band, eight-mode static anchor is paired with an 11-window, 24-feature branch whose source-fitted SSM shares Wc , Wg , and Wa and contributes a bounded 2 tanh residual. The trial gives ℓs = −0.629, rSSM = +0.142, ℓ = −0.487, and p(y = 1 | X) = 0.381. Only target geometry is available before lock; all fitting, normalization, calibration, threshold selection, and model selection are source-only. Appendix L gives the full replay and stored parameters. The final sealed class probability is computed by adding this residual to the frozen static logit: p(y = 1 | X) = σ(ℓ).

ℓ = ℓstatic + rSSM ,

(10)

The residual readout is initialized at zero, so the dynamic model initially returns exactly the static classifier’s output. Its trainable parameters are subsequently fitted with the weighted objective 1 X L= wi BCE(ℓi , yi ) + 10−2 ri2 . (11) N i Optimization updates the dynamic branch alone and leaves the static logit fixed. Appendix Q specifies the source-only model selection, optimization, and refitting procedures.

E XPERIMENTAL D ESIGN

5.1

DATASETS AND PROTOCOL

We use five public MOABB motor-imagery collections (Jayaram & Barachant, 2018): BNCI2014 001 (Tangermann et al., 2012), Cho2017 (Cho et al., 2017), Lee2019 MI (Lee et al., 2019), Shin2017A (Shin et al., 2017), and PhysionetMI (Schalk et al., 2004; Goldberger et al., 2000). The registered queues contain 41,342 left/right-hand trials from 253 participants (Table 1). Signals are notch filtered, band-pass filtered at 0.5–45 Hz, resampled to 200 Hz, and epoched to [0.5, 3.5) s. Native 22–64channel montages are not reduced to their intersection. Fixed trial-level channel checks are detailed in Appendix Q. Each fold holds out one dataset and uses four source libraries with subject-disjoint validation and seeds 2027, 3407, 4513, 5623, and 6737. Static and dynamic models share target queues. The primary endpoint is subject-mean balanced accuracy (BA); complete aggregates also report macro-F1 and 5

Table 1: Registered five-dataset evaluation and operator inventory. “Masks” counts retained trial-level active-channel patterns; “inactive trials” have at least one inactive native channel. Epochs contain 600 samples at 200 Hz over [0.5, 3.5) s. Dataset

Subjects

Raw trials

Retained

Excluded

Native ch.

Masks

Inactive trials

BNCI2014 001 Cho2017 Lee2019 MI Shin2017A PhysionetMI

9 52 54 29 109

2,592 10,520 21,600 1,740 4,918

2,592 10,492 21,600 1,740 4,918

0 28 0 0 0

22 64 62 30 64

1 223 6 1 1

0 4,710 34 0 0

Total

253

41,370

41,342

22–64

232

4,744

Table 2: Target matrix and eligibility for the main pretrained comparison. Values are subject-mean BA (%) over five seeds. “Eligible mean” weights clean targets equally; partial means are descriptive. “Exec.” and “Clean” are execution and provenance denominators. All rows are target-signal-, targetstatistics-, and target-label-blind during fitting. Method

BNCI

Cho

Lee

PhysioNet

Shin

Eligible mean

Exec.

Clean

G RAFT-EEG dynamic G RAFT-EEG static BIOT + LR CBraMod frozen + LR CBraMod source-only full FT EEGPT + LR LaBraM + LR CodeBrain + LR

64.336 64.923 56.250 52.392 50.394 65.664 53.997 —

58.172 56.817 50.086 50.241 49.925 49.315 50.584 —

60.318 59.448 52.524 50.341 50.544 60.985 51.267 —

58.247 56.717 51.741 50.001 49.908 — — —

63.253 61.126 52.816 50.724 47.172 60.264 52.000 —

60.865 59.806 52.684 50.740 49.589 59.057 51.962 —

25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25

5/5 5/5 5/5 5/5 5/5 4/5 4/5 0/5

AUROC, while missing metrics remain missing. Source-only calibration uses 15-bin ECE, Brier score, and negative log likelihood. Primary uncertainty is a dataset–subject hierarchical bootstrap (20,000 replicates; seed 20260829), reflecting five independent target datasets. Target effects, leaveone-target-out contrasts, and worst-domain performance accompany the aggregate; subject-paired inference is secondary. 5.2

C OMPARATORS AND PROTOCOL FAIRNESS

The strict comparison includes BIOT, CSP–LDA, FBCSP–LDA, Riemannian–LR, EEGNet, EEGConformer, ATCNet, and CBraMod (Yang et al., 2023; Blankertz et al., 2008; Ang et al., 2008; Barachant et al., 2012; Lawhern et al., 2018; Song et al., 2023; Wang et al., 2025). Frozen encoders receive source-only logistic probes and fixed geometry maps. BIOT is clean on all five targets; EEGPT and LaBraM overlap with PhysionetMI pretraining and are clean on four. CodeBrain executed all 25 cells but is provenance-ineligible on all five targets because its checkpoint origin remains unresolved; its dashes therefore denote withheld strict scores, not unexecuted cells or zero performance. Partial denominators are never rank-mixed. REVE, LUNA, and Uni-NTFM were not executed under this contract and are therefore cited as related work rather than assigned scores. Table 2 places target-resolved scores, execution counts, and clean eligibility denominators in one view. Target signal, empirical statistics, and labels are unavailable during fitting for every row; detailed access, input maps, parameter counts, and fitting budgets are reported in Appendix U. In the equal-information analysis, FI and SSI receive the same active set as G RAFT-EEG, map each mask to 17 fixed channels, and use source-fitted tangent features or EEGNet (Mellot et al., 2024; Gramfort et al., 2013; Ledoit & Wolf, 2004). All 60 cells completed fit, prediction, and scoring. Supplementary analyses cover calibration, stress, reference, stability, and known-source operators; structural gaps remain N/A. Dreyer2023A (Dreyer et al., 2023) is a no-tuning same-paradigm evaluation with partial-confirmation status. Appendices Q–S give definitions and verification order. The post-hoc exact same-parent ladder replaces the physical leadfield with one of four operators: a constant-free real spherical-harmonic coordinate basis, a random operator with the physical singular spectrum, a fixed derangement of electrode rows, or a visual-cortex leadfield from the same template anatomy. Each variant is refitted on the same source split under the inherited FULL budget; target geometry, active-reference quotient, ridge rule, dynamic head, seeds, features, and evaluation 6

Coordinate-basis control across targets Overall +9.959 pp [8.214, 11.771]

Four exact same-parent operator controls 253 paired subjects; Holm-adjusted p < 0.001 each

BNCI

9.96

Coordinate basis

Cho 9.70

Matched spectrum Lee

PhysioNet 11.24

Row shuffle Shin

Overall 5

Physical FULL − coordinate control (BA, pp; 95% CI)

Physical FULL − control (BA, pp; 95% CI)

Strict five-target benchmark (BA, %; all 5/5) 64.3

58.2

60.3

58.2

63.3

GRAFT static

64.9

56.8

59.4

56.7

61.1

BIOT

56.2

50.1

52.5

51.7

52.8

CBraMod frozen

52.4

50.2

50.3

50.0

50.7

EEGConformer

50.5

50.2

50.0

50.3

51.3

ODEBrain scratch

50.1

49.9

50.6

50.2

50.1

ATCNet

49.8

50.1

50.3

50.4

FBCSP-LDA

50.0

ShallowFBCSP

50.0

49.6

50.3

50.1

49.9

CSP-LDA

50.0

Riemann-LR

50.0

EEGNet

50.0

49.7

50.3

49.8

49.7

Deep4Net

50.1

49.5

49.9

49.8

50.1

TFM

50.0

47.8

50.4

50.1

50.8

CBraMod finetune

50.4

49.9

50.5

49.9

47.2

e Le

ysio Ph

Paired primary comparator BNCI Cho Lee

90 60 58 56 54 52

Balanced accuracy (%)

GRAFT dynamic

GRAFT dynamic BA (%)

3.98

Wrong anatomy 0

PhysioNet Shin

Pooled +8.182 pp [6.382, 10.196] 30

BIOT BA (%)

Controls preserve the target queue, active-reference gauge, ridge rule and budget; only the registered operator changes.

Figure 3: Physical-leadfield mechanism controls and strict cross-dataset performance. a, Left: physical FULL minus the layout-aware coordinate basis by target and overall. Right: equal-target effects for all four exact same-parent controls; intervals use 20,000 target-stratified paired-subject bootstrap replicates after averaging five seeds within subject, and every Holm-adjusted P < 0.001. All controls retain the split, features, head, ridge rule, budget, and target queues; the replacement operator is the only intended change. b, Strict-clean 5/5 balanced-accuracy matrix for all 15 complete methods. c, Dynamic G RAFT-EEG versus BIOT for the same 253 held-out subjects. Diamonds denote target means and the dashed line denotes identity. The operator ladder is post-hoc and not independent external validation. queues remain fixed. All 75 new fits were frozen before any target evaluation. Seeds are averaged within target–subject, subjects within target, and the five targets equally; intervals use 20,000 targetstratified subject-bootstrap replicates with Holm correction across the four controls. These post-hoc comparisons are not independently confirmatory.

R ESULTS

6.1

S TRICT FIVE - TARGET COMPARISON

Dynamic G RAFT-EEG achieved 60.865% equal-target BA, static G RAFT-EEG 59.806%, and BIOT 52.684% (Figure 3c). Dynamic exceeded BIOT by +8.182 pp (hierarchical 95% interval, +6.382 to +10.196); all five target effects were positive (+6.506 to +10.437 pp), and leave-one-target-out estimates were 7.618–8.600 pp. Cho was the worst target for both dynamic G RAFT-EEG (58.172%) and BIOT (50.086%). The exact same-parent ladder separated FULL from every replacement operator (Figure 3a). FULL exceeded the coordinate basis by +9.959 pp (95% CI +8.214 to +11.771), the matched-spectrum 7

random operator by +9.698 pp (+8.348 to +11.052), the row-shuffled operator by +11.241 pp (+9.450 to +13.174), and the wrong-anatomy leadfield by +3.985 pp (+3.231 to +4.752). All four target-stratified paired-subject tests had two-sided bootstrap P < 0.001 and remained below 0.001 after Holm correction. The coordinate effect was positive in every target (+6.79 to +13.67 pp). These controls distinguish the tested motor leadfield from geometry-only, spectrum-preserving, correspondence-breaking, and anatomically mismatched alternatives; they do not establish superiority over every possible physical or learned operator. The SSM is secondary to cross-montage harmonization: dynamic minus static was +1.059 pp (hierarchical 95% interval, +0.013 to +1.892; Table S10). Four target effects were positive, whereas BNCI was −0.586 pp (−2.423 to +1.497); leave-one-target-out estimates were 0.792–1.470 pp. The tighter subject-paired interval (+0.584 to +1.569 pp) is within-panel evidence, not the principal cross-dataset interval. In the stricter source-only-geometry sensitivity, all 25 fits were frozen before the target montage was opened. Dynamic and static BA were 60.460% and 59.713%, respectively; dynamic was 0.406 pp below its canonical result and exceeded static by +0.747 pp. The held-out montage is still required after sealing to instantiate the fixed prediction operator, so the method is not geometry-blind. Per-target values and the independent audit are in Appendix C. 6.2

C OVERAGE , FAIRNESS , AND EXTERNAL BOUNDARY

BIOT is the best-performing clean pretrained comparator with a 5/5 denominator and is therefore the primary foundation-model comparison. EEGPT and LaBraM executed 25/25 target–seed cells but are strict-clean on 4/5 targets because PhysionetMI overlaps with pretraining. CodeBrain also executed 25/25 cells but is provenance-ineligible on 0/5 targets; no CodeBrain score enters a strict comparison. On the same four clean targets available to EEGPT (BNCI, Cho, Lee, and Shin), dynamic G RAFT-EEG averaged 61.520% BA and EEGPT 59.057%, a descriptive difference of +2.463 pp. The target effects were −1.328, +8.857, −0.667, and +2.989 pp, respectively. This 4/5 comparison is not inserted into the complete 5/5 ranking. Figure S13 preserves the full matrix and all eligibility denominators. A read-only post-score diagnostic checked source validation, target positive rates, prediction entropy, target–seed coverage, and single-class counts without training or parameter updates. Dynamic and static G RAFT-EEG met the prespecified healthy-source rule and had no single-class target cells. BIOT was nondegenerate but had marginal source validation (mean BA 53.6%); several other baselines were already near chance on source validation, and the classical CSP/FBCSP/Riemann rows had systematic single-class target predictions with source validation unavailable. No direct implementation defect was confirmed. Accordingly, weak target results are not attributed uniformly to domain shift, and collapsed or source-weak baselines are not used as mechanistic evidence for G RAFT-EEG; Appendix E reports the complete diagnostic. Supplementary analyses retain the original denominators. Under the registered few-shot procedure, revealing 1%, 5%, or 10% target labels and fine-tuning the full GRAFT head gave 61.323%, 61.477%, and 61.722% BA, respectively, compared with 60.865% in the zero-target protocol. These small increments contextualize the absolute zero-target BA under this adaptation rule; they are not a fully supervised oracle or a performance ceiling. In the separate 60-participant Dreyer2023A evaluation, dynamic versus static was +0.57 pp [−0.08, +1.23] (inconclusive), whereas physics versus nophysics was +4.03 pp [+2.34, +5.77] (positive). The preregistered decision is partial confirmation, not unrestricted external validation. The post-primary coordinate sensitivity refitted no model. Across 50 target–condition units, reducedoperator change tracked dynamic BA change (ρ = −0.449; 95% CI −0.760 to −0.282; permutation P < 0.001); at 20 mm, equal-target BA changed by −1.064 pp for tangent and −2.220 pp for rigid errors. Responses were heterogeneous (Figure S14).

D ISCUSSION AND L IMITATIONS

The central finding concerns the observation operator rather than the temporal head. Without target signals, labels, or statistics during fitting, the native-montage model exceeded the strongest clean 5/5 8

pretrained comparator by 8.18 pp in every target. Under the same parent and budget, replacing the motor leadfield with four distinct controls reduced BA by 3.98–11.24 pp. The smaller but still positive wrong-anatomy contrast shows that an anatomically structured template is not interchangeable with the task-matched motor field; the larger coordinate, spectrum-matched, and row-shuffled contrasts additionally reject explanations based only on dimension, singular spectrum, or electrode-wise response magnitude. The ladder remains post-hoc and operator-specific rather than proving that physics is universally optimal. Propositions 1 and 2 state the corresponding observability and conditioning limits. The SSM contribution was modest and heterogeneous (+1.06 pp overall; four positive targets; −0.59 pp on BNCI; inconclusive external contrast), supporting an incremental interpretation. The row-shuffled and spectrum-matched controls in Appendix K evaluate inverse recovery with synthetic known sources; they are not a real-EEG same-parent classification ladder. Participant-specific source recovery lies beyond scope. After the primary scores were fixed, three of four matched FI/SSI intervals excluded zero; FI+tangent crossed zero, so this supplementary evidence remains contrast-specific rather than supporting a general superiority claim. Calibration lowered probability error while leaving discrimination unchanged, and performance losses under stress reached −8.93 pp. In the separately registered legacy three-target stability diagnostics, G RAFT-EEG showed greater seed-to-seed dispersion than the coordinate and no-physics comparators. Those adverse dispersion results are distinct from the new five-target exact same-parent performance control. Failed conditions also outnumbered recoverable ones in the known-source tests. Claims are consequently confined to the operating range characterized by these evaluations, rather than extended to unrestricted inverse recovery. The independent generalization unit is the held-out dataset (n = 5), not the 253 participants, and dataset remains confounded with device and protocol. The primary task is binary hand motor imagery; non-motor paradigms were not tested. Blindness applies to target statistics, not declared target coordinates, and the source-only-geometry experiment is sensitivity analysis rather than a replacement for the fixed primary result. The fsaverage basis is a common coordinate system, not participant-specific localization, so causal and clinical interpretations remain outside scope. Coordinate sensitivity is now characterized only for two synthetic error families on the five declared montages; it neither identifies a clinical placement threshold nor covers arbitrary cap deformation or anatomy. Matched FI/SSI and other post-score diagnostics are supplementary; arbitrary montages, streaming, and clinical deployment remain outside the evidence boundary.

C ONCLUSION

Across five leave-one-dataset-out targets, G RAFT-EEG operated on native montages and trial-level active masks without using target signals, labels, or fitting statistics. Dynamic G RAFT-EEG achieved 60.865% equal-target BA, compared with 52.684% for strict BIOT. Four exact same-parent replacements reduced BA by 3.985–11.241 pp, supporting a material contribution from the task-matched physical observation operator within this parent model. This remains operator-specific evidence from five binary motor-imagery domains, not a universal claim over geometry models or EEG paradigms. The bounded SSM supplied a smaller, target-dependent increment. Reproducibility. Fitting, label-blind prediction, and scoring are process-separated. Immutable manifests bind queues, masks, checkpoints, predictions, and result tables; complete gates and sourcedata hashes appear in Appendices S–T. The reproducibility package retains figure source data and executed-cell ledgers for every denominator. Ethics. The study uses public, de-identified EEG data and recruited no participants. No reidentification was attempted; original consent, license, and access conditions continue to govern each dataset. The work evaluates decoding methodology, not diagnosis or treatment. AI use. A large language model was used solely for grammar correction and language polishing. The study design, code development, experiments and analyses were completed by the authors, who take full responsibility for the manuscript.

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P ROOFS OF THE R ESTRICTED T HEORY R ESULTS

Proof of Proposition 1. With the noiseless measurements stacked, Y = OM,T z0 . If z0 and z0′ yield the same Y , then OM,T (z0 − z0′ ) = 0; full column rank therefore gives z0 = z0′ . Identifiability is nevertheless limited to a latent-coordinate class. For any invertible S, let zt′ = Szt , F ′ = SF S −1 , ′ and A′m = Am S −1 . Because zt+1 = F ′ zt′ and A′m zt′ = Am zt , this transformation leaves every observation unchanged. b ≥ Proof of Proposition 2. Weyl’s inequality and the assumed perturbation bound give σmin (O) b σmin (O) − ∥∆O∥2 > 0. Hence O retains full column rank, and b† (Oz0 + ϵ) − z0 zb0 − z0 = O b† (ϵ − ∆Oz0 ). =O b† ∥2 = 1/σmin (O), b the triangle inequality gives the bound in (6). Since ∥O The scope of these results is deliberately narrow: both propositions apply to a fixed, finite-dimensional linearization. Neither guarantees unique recovery for the nonlinear EEG inverse problem nor identifies participant-specific cortical generators.

DATASET AND O BSERVATION -O PERATOR I NVENTORY

Table S1 expands the acquisition summary in Table 1. The retained queue is not a rectangular common-channel tensor: Cho2017 alone contributes 223 distinct active masks, and 4,710 of its retained trials have at least one inactive native channel. The operator cache is therefore indexed by the exact retained mask rather than by dataset alone. The inventory is computed from the immutable formal queues; it is descriptive and does not reopen target outcomes. The 28 exclusions all occur in Cho2017 under the same prelocked amplitude, finiteness, and activechannel-count rules used for every dataset. BNCI2014 001, PhysionetMI, and Shin2017A each retain a single all-active pattern; Lee2019 MI retains six patterns. These counts explain why a single fixed pseudo-inverse per dataset would be scientifically incorrect even though the nominal montage is fixed. 12

Table S1: Detailed immutable queue and operator inventory. “Raw” is the prepared H5 queue before the fixed trial gate. “Patterns” is the number of distinct retained active-channel masks.

Dataset

Subj.

Raw Retained Excl. Ch. Samples

Hz Patterns Inactive trials

BNCI2014 001 Cho2017 Lee2019 MI PhysionetMI Shin2017A

9 2,592 52 10,520 54 21,600 109 4,918 29 1,740

2,592 10,492 21,600 4,918 1,740

0 28 0 0 0

22 64 62 64 30

600 600 600 600 600

200 200 200 200 200

1 223 6 1 1

0 4,710 34 0 0

Total

253 41,370

41,342

—

232

4,744

S TRICT S OURCE -O NLY G EOMETRY-BASIS S ENSITIVITY

For target fold m⋆ , this sensitivity constructs the hemisphere-blocked d = 8 basis from the four source geometry operators only. It selects every hyperparameter from the same four source datasets and seals all 25 target–seed fits before opening any target geometry or target H5 file. The target montage is then used once with the frozen fold-specific basis to construct the prediction operator; target signals and labels remain separated into inference and scoring processes. This test changes only the geometry-access boundary and does not alter or supersede the canonical sealed results. Table S2: Access-boundary sensitivity: canonical target-geometry construction versus a strict sourceonly geometry basis. Values are subject-mean balanced accuracy averaged over five seeds. “Change” is source-only dynamic minus canonical dynamic; it isolates the cost of withholding the target montage until after the source fits are sealed. Target (n)

Canon. dyn.

Src.-only dyn.

Change (pp)

Src.-only stat.

Dyn.–stat. (pp)

BNCI2014-001 (9) Cho2017 (52) Lee2019-MI (54) PhysionetMI (109) Shin2017A (29)

64.336 58.172 60.318 58.247 63.253

62.423 58.141 60.392 58.020 63.322

−1.913 −0.031 +0.074 −0.227 +0.069

64.668 56.868 59.361 56.724 60.943

−2.245 +1.273 +1.031 +1.296 +2.379

Equal-target mean (253)

60.865

60.460

−0.406

59.713

+0.747

The source-only experiment completed all 25 fits and all 25 frozen evaluations. Replaying the predictions in a fresh process returned PASS (P 0 = P 1 = 0), and the run ended with status completed and exit code 0. The global fit barrier had SHA-256 fff8c45091a74a195a4d9ff1dfd2c854 64739bea699937be31de84519a847b9b; the final audit seal had SHA-256 ff7fbd82098e0602 02fcd236f1ccb155355cb7854ab4a025e81754fc715953b0. The original 60-cell score anchor did not change. Source-only geometry reduced the canonical dynamic mean by 0.406 pp, much less than the canonical model’s 8.182-pp advantage over BIOT. BNCI nevertheless retained a negative dynamic–static contrast, so the SSM effect should be read as target-dependent.

C OMPLETE S TRICT F IVE -TARGET D ISCRIMINATION S UMMARY

Table S3 reports every method with a clean 5/5 execution denominator. All entries use the same equal-target aggregation: seed means are formed within target and targets then receive equal weight. Macro-F1 or AUROC is shown only when that metric is present for all five targets in the sealed aggregate. The dashes for CBraMod frozen, ATCNet, ShallowFBCSPNet, and Deep4Net are retained missing values, not failed or zero-valued metrics. Table S4 exposes the target matrix behind the equal-target means. This prevents a high-performing large dataset from dominating the ranking and makes the worst-domain behavior visible. The best strict comparator is BIOT on every target, but its target values remain below dynamic G RAFT-EEG by 6.506–10.437 pp.

Table S3: Complete strict five-target discrimination summary. Values are percentages. All 15 methods completed 25/25 target–seed cells and are strict-eligible on 5/5 targets. Missing secondary metrics are not imputed. Method G RAFT-EEG dynamic G RAFT-EEG static BIOT + LR CBraMod frozen + LR EEGConformer ODEBrain (scratch) ATCNet FBCSP–LDA ShallowFBCSPNet CSP–LDA Riemann–LR EEGNet Deep4Net TFM CBraMod source-only full FT

Macro-F1

AUROC

Metric availability

60.865 59.806 52.684 50.740 50.448 50.174 50.074 50.005 50.004 50.000 49.996 49.901 49.895 49.814 49.589

58.886 58.015 46.954 — 44.322 39.996 — 33.400 — 33.369 33.367 43.004 — 43.458 40.214

66.447 64.588 56.131 — 50.808 51.060 — 50.302 — 50.060 50.034 49.784 — 49.449 49.467

all three sealed all three sealed all three sealed BA only all three sealed all three sealed BA only all three sealed BA only all three sealed all three sealed all three sealed BA only all three sealed all three sealed

Table S4: Target-resolved subject-mean balanced accuracy for every strict-clean 5/5 method. Values are percentages after averaging the five registered seeds within target. The last column weights targets equally. Method

BNCI

Cho

Lee

PhysioNet

Shin

Equal-target

G RAFT-EEG dynamic G RAFT-EEG static BIOT + LR CBraMod frozen + LR EEGConformer ODEBrain (scratch) ATCNet FBCSP–LDA ShallowFBCSPNet CSP–LDA Riemann–LR EEGNet Deep4Net TFM CBraMod source-only full FT

64.336 64.923 56.250 52.392 50.455 50.085 49.792 50.000 50.031 50.000 50.000 49.977 50.108 49.977 50.394

58.172 56.817 50.086 50.241 50.183 49.871 49.750 50.027 49.630 50.000 49.980 49.697 49.526 47.816 49.925

60.318 59.448 52.524 50.341 49.958 50.621 50.064 50.000 50.334 50.000 50.000 50.345 49.933 50.419 50.544

58.247 56.717 51.741 50.001 50.321 50.210 50.350 50.000 50.083 50.000 50.000 49.785 49.836 50.088 49.908

63.253 61.126 52.816 50.724 51.322 50.080 50.414 50.000 49.943 50.000 50.000 49.701 50.069 50.770 47.172

60.865 59.806 52.684 50.740 50.448 50.174 50.074 50.005 50.004 50.000 49.996 49.901 49.895 49.814 49.589

Table S5: Executed but strict-incomplete pretrained encoders. A numeric cell is shown only when the target is clean under the checkpoint-provenance review. The available-target mean is descriptive and is not inserted into Table S4. Method

BNCI

Cho

Lee PhysioNet

EEGPT + LR 65.664 49.315 60.985 LaBraM + LR 53.997 50.584 51.267 CodeBrain + LR — — —

Shin Available mean Strict Exclusion

— 60.264 — 52.000 — —

59.057 51.962 —

4/5 overlap 4/5 overlap 0/5 unresolved

P OST-S EAL BASELINE H EALTH D IAGNOSTICS

The health audit is a read-only diagnostic over frozen probabilities and source-validation records; it started no training or evaluation job and changed no registered result. Table S6 reports the quantities requested before interpreting near-chance target scores. Source validation is unavailable for the three classical pipelines, and CodeBrain has no health row bound to a strict-clean checkpoint identity. These absences remain N/A. A single-class count means that the thresholded predictions in a target–seed cell contain only one label; it is not inferred from mean probability entropy alone. Table S6: Post-seal implementation and prediction-health audit. Source BA is the mean sourcevalidation balanced accuracy (%). “Positive-rate range” is the minimum–maximum target positive prediction rate across eligible target–seed cells (%). Hhard and Hprob are mean hard-label and mean probability entropy in bits. “Single” counts single-class target cells; “coverage” is completed/eligible health-audit cells. N/A values are not imputed. Method G RAFT-EEG dynamic G RAFT-EEG static BIOT EEGPT + LR LaBraM + LR CodeBrain + LR CBraMod frozen + LR CBraMod source-only full FT EEGConformer EEGNet ATCNet ShallowFBCSPNet Deep4Net TFM ODEBrain (scratch) CSP–LDA FBCSP–LDA Riemann–LR Separate graft parent FULL

Source BA Positive-rate range Hhard Hprob Single Coverage 60.8 58.6 53.6 61.2 52.4 N/A 51.4 52.8 51.2 51.2 51.3 50.8 50.9 50.9 51.3 N/A N/A N/A 51.0

26.4–56.2 39.8–55.4 26.9–76.8 13.3–54.4 37.0–75.6 N/A 0.0–90.5 0.0–100.0 2.5–98.1 0.2–97.6 0.2–99.9 0.0–100.0 0.0–100.0 0.0–49.9 0.0–95.4 0.0–100.0 0.0–99.9 0.0–100.0 0.0–100.0

0.974 0.993 0.870 0.870 0.929 N/A 0.667 0.528 0.728 0.637 0.570 0.390 0.414 0.751 0.534 0.000 0.003 0.001 0.727

0.902 0.948 0.859 0.830 0.978 N/A 0.993 0.981 0.993 0.965 0.973 0.881 0.916 0.991 0.967 1.000 1.000 1.000 0.999

0 0 0 0 0 N/A 2 2 0 0 0 3 4 0 2 25 20 20 2

25/25 25/25 25/25 20/20 20/20 25/25† 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25

†

CodeBrain executed 25/25 cells in the coverage ledger, but unresolved checkpoint provenance prevented a strict-clean model identity and a bound health summary; no health conclusion is assigned.

The independent implementation-health audit returned PASS (P 0 = P 1 = 0) for input hashes, runner identities, coverage, probability validity, train/eval-mode checks, and artifact consistency. It found no confirmed code defect, but explicitly did not convert near-chance source validation into healthy baselines. The prespecified domain-shift attribution rule was met in zero cells. Thus, the table supports health-aware interpretation and disclosure, not post hoc removal or reranking. The locked subject-paired analysis predates the primary dataset–subject hierarchical bootstrap. Table S7 retains it as secondary within-panel evidence because it asks whether the same 253 held-out participants tend to favor dynamic G RAFT-EEG. The new exact same-parent row includes all five targets. The legacy no-physics and wrong-operator diagnostics include only their three originally registered targets and are labeled accordingly. Every Holm-adjusted Wilcoxon decision in the underlying paired tables rejects at 0.05, but those subject-level decisions are not interpreted as evidence from 253 independent datasets.

Table S7: Secondary subject-paired physical-dynamic-minus-comparator effects in percentage points. Each entry is effect [95% paired subject-bootstrap interval], based on 10,000 replicates. The exact same-parent row uses its registered target-stratified subject bootstrap; the primary dynamic–BIOT and dynamic–static contrasts in the main text instead use dataset–subject hierarchical resampling. Comparator Exact same-parent layout-aware coordinate control G RAFT-EEG static CSP–LDA FBCSP–LDA Riemann–LR EEGNet EEGConformer Legacy no-physics dynamic (3-target) Legacy no-physics static (3-target) Legacy wrong-operator dynamic (3-target) Legacy wrong-operator static (3-target)

Balanced accuracy

Macro-F1

AUROC

+9.96 [+8.20, +11.75] +1.06 [+0.58, +1.57] +10.87 [+9.22, +12.59] +10.86 [+9.18, +12.61] +10.87 [+9.25, +12.65] +10.96 [+9.28, +12.67] +10.42 [+8.67, +12.23] +9.78 [+8.17, +11.49] +7.96 [+6.35, +9.65] +8.69 [+7.26, +10.14] +8.48 [+6.91, +10.04]

+12.31 [+10.22, +14.39] +0.87 [+0.35, +1.41] +25.52 [+23.58, +27.47] +25.49 [+23.55, +27.45] +25.52 [+23.59, +27.49] +15.88 [+13.95, +17.86] +14.56 [+12.56, +16.60] +11.05 [+9.20, +12.96] +9.39 [+7.58, +11.20] +15.79 [+14.25, +17.37] +16.20 [+14.45, +17.99]

+14.88 [+11.95, +17.90] +1.86 [+1.40, +2.30] +16.39 [+14.01, +18.90] +16.14 [+13.80, +18.67] +16.41 [+13.95, +18.93] +16.66 [+14.24, +19.21] +15.64 [+13.14, +18.35] +14.82 [+12.62, +17.14] +12.44 [+10.10, +14.91] +13.71 [+11.37, +16.00] +11.54 [+9.33, +13.81]

Targets / subjects Holm decision 5 / 253 5 / 253 5 / 253 5 / 253 5 / 253 5 / 253 5 / 253 3 / 192 3 / 192 3 / 192 3 / 192

reject reject reject reject reject reject reject reject reject reject reject

R EGISTERED C ELL R EPRODUCIBILITY AND S UBJECT H ETEROGENEITY

The primary summaries average five registered seeds within each target before giving equal weight to the five targets. Table S8 exposes the corresponding 25 target–seed cells for both locked G RAFT-EEG branches. These rows are a pivot of the sealed cell metrics.csv; no model was refitted, no prediction was rescored, and no seed was removed after inspection. The seed cells show computational repeatability within a target, but they are nested observations rather than 25 independent target domains.

Table S8: Registered target–seed cell metrics for dynamic (D) and static (S) G RAFT-EEG. BA, macro-F1, and AUROC are percentages; ∆BA is D minus S in percentage points. Every target contains the same five preregistered seeds. Target

Seed

BA D

BA S

∆BA

F1 D

BNCI BNCI BNCI BNCI BNCI

2027 3407 4513 5623 6737

63.310 62.693 64.738 62.384 68.557

64.931 64.429 64.660 64.429 66.165

−1.620 −1.736 +0.077 −2.045 +2.392

61.234 60.029 63.406 59.294 67.474

63.947 63.240 63.684 63.240 65.274

69.688 70.720 69.076 71.056 74.157

70.054 70.224 69.882 70.224 71.401

Cho Cho Cho Cho Cho

2027 3407 4513 5623 6737

58.073 58.185 58.082 58.018 58.499

56.794 56.874 56.794 56.819 56.806

+1.280 +1.311 +1.288 +1.199 +1.694

55.579 55.905 55.602 55.817 56.528

54.249 54.439 54.249 54.417 54.638

62.714 62.770 62.744 62.975 62.983

60.348 60.482 60.348 60.513 60.478

Lee Lee Lee Lee Lee

2027 3407 4513 5623 6737

60.435 60.310 60.468 60.185 60.190

59.500 59.519 59.574 59.514 59.134

+0.935 +0.792 +0.894 +0.671 +1.056

59.019 58.331 58.832 58.081 58.263

57.714 57.800 58.030 57.792 57.546

65.513 66.001 65.929 65.868 65.645

64.587 64.544 64.443 64.541 63.865

PhysioNet PhysioNet PhysioNet PhysioNet PhysioNet

2027 3407 4513 5623 6737

58.370 58.068 58.741 57.862 58.194

56.639 56.852 56.620 56.852 56.620

+1.731 +1.216 +2.121 +1.010 +1.574

56.145 56.135 56.446 55.131 55.765

54.206 54.276 54.150 54.276 54.150

62.993 61.985 63.221 62.650 63.087

60.794 60.585 60.804 60.585 60.804

Shin Shin Shin Shin Shin

2027 3407 4513 5623 6737

62.816 63.563 63.506 63.103 63.276

61.264 61.264 61.264 60.862 60.977

+1.552 +2.299 +2.241 +2.241 +2.299

61.393 62.116 62.266 61.716 61.655

59.727 59.727 59.727 59.873 59.990

69.008 70.368 70.307 69.889 69.824

67.303 67.291 67.303 66.621 66.670

F1 S AUROC D AUROC S

Across the 25 target–seed cells, dynamic BA exceeded static BA in 22. All three reversals occurred in BNCI, where effects ranged from −2.045 to +2.392 pp; every seed was positive in Cho, Lee, PhysioNet, and Shin. The pooled SSM estimate is positive but heterogeneous, and inference remains anchored at the target level rather than the seed level. Table S9 reports the participant-level distribution after averaging BA over the five seeds. Dynamic– BIOT differences were positive for 75.2–90.7% of participants in each target. Dynamic–static differences were more variable, from 33.3% positive in BNCI to 73.1% in Cho. These fractions describe within-target heterogeneity and are not independent replications across domains. 16

Table S9: Subject-level heterogeneity. Entries are median [Q1,Q3] BA or paired BA differences in percentage points; “> 0” gives the descriptive proportion of participants with a positive paired difference. Target

Dynamic BA

Static BA

BIOT BA

Dynamic–BIOT

Dynamic–static

BNCI 9 61.94 [56.32,73.89] 64.72 [54.79,78.12] 53.82 [51.39,57.99] 7.29 [4.65,9.31] 77.8% −1.04 [−3.26,1.53] 33.3% Cho 52 56.88 [52.49,62.38] 55.08 [51.46,61.45] 49.90 [47.70,51.38] 7.00 [2.44,13.30] 82.7% 1.25 [−0.03,2.74] 73.1% Lee 54 58.08 [53.12,66.50] 56.27 [52.64,64.75] 51.62 [50.31,53.30] 6.20 [3.10,13.24] 90.7% 0.78 [−0.09,1.88] 72.2% PhysioNet 109 56.25 [51.61,64.35] 54.60 [50.00,62.83] 51.28 [48.51,55.24] 5.89 [0.30,12.87] 75.2% 1.13 [−1.07,3.89] 61.5% Shin 29 61.33 [54.67,71.33] 59.00 [53.33,69.67] 51.67 [48.33,56.67] 10.00 [1.00,18.00] 79.3% 2.33 [0.00,4.67] 72.4%

Omitting one target at a time left the dynamic–BIOT estimate between 7.618 and 8.600 pp and the dynamic–static estimate between 0.792 and 1.470 pp (Table S10). Each leave-one-target-out value is the arithmetic mean of the remaining four target effects. The primary interval is unchanged and comes from the dataset–subject hierarchical bootstrap over all five targets. Table S10: Leave-one-target-out sensitivity, in percentage points. “Full” is the five-target equal mean with its primary hierarchical 95% interval; the other columns omit the indicated target. Contrast Dynamic–BIOT Dynamic–static

Full [95% CI]

omit BNCI

omit Cho

omit Lee

omit PhysioNet

omit Shin

8.182 [6.382,10.196] 1.059 [0.013,1.892]

8.205 1.470

8.206 0.985

8.279 1.106

8.600 0.941

7.618 0.792

P OST-S CORE -S EAL E QUAL -I NFORMATION FI/SSI C ONTROLS

All four matched point estimates favored dynamic G RAFT-EEG: 1.47 pp for FI+tangent (95% CI −0.07 to 2.96), 3.63 pp for SSI+tangent (2.32 to 4.95), 9.46 pp for FI+EEGNet (7.68 to 11.25), and 10.54 pp for SSI+EEGNet (8.90 to 12.16). FI+tangent crossed zero. The supplementary aggregate contains 1,012 paired subject rows across 20 target contrasts and 253 participants, with 20,000 target-stratified subject-cluster bootstrap replicates. All 60 fits, raw predictions, and score manifests were present; four group audits and the independent aggregate audit passed with P 0 = P 1 = 0. Because this aggregate was defined after the primary scores were frozen, it is supplementary and does not revise the primary inference. Table S11: Target-resolved equal-information controls. Values are subject-mean BA percentages. “Effect” is dynamic G RAFT-EEG minus the matched control. Tangent controls retain their registered single-seed denominator; EEGNet controls retain five seeds. Head

Target

Subjects

Matched control

G RAFT-EEG dynamic

Effect (pp)

FI + tangent

BNCI Cho Lee PhysioNet Shin

9 52 54 109 29

59.645 59.032 58.519 58.930 60.862

64.336 58.172 60.318 58.247 63.253

+4.691 −0.860 +1.799 −0.683 +2.391

SSI + tangent

BNCI Cho Lee PhysioNet Shin

9 52 54 109 29

56.327 54.379 57.894 58.738 58.851

64.336 58.172 60.318 58.247 63.253

+8.009 +3.793 +2.424 −0.491 +4.402

FI + EEGNet

BNCI Cho Lee PhysioNet Shin

9 52 54 109 29

54.637 60.085 60.464 39.776 42.080

64.336 58.172 60.318 58.247 63.253

+9.699 −1.914 −0.146 +18.471 +21.172

SSI + EEGNet

BNCI Cho Lee PhysioNet Shin

9 52 54 109 29

50.656 57.920 57.959 40.362 44.747

64.336 58.172 60.318 58.247 63.253

+13.681 +0.251 +2.358 +17.885 +18.506

Sealed Cho2017:0 replay

500

µV

native

T6 Fp1

500 0

500 0 −500 0

Time (s)

BNCI

Relative PSD (dB)

FI 0

−500 60/64 active inactive = ×

Fp1

quotient referenced

−500

Mapped fixed-17 signals

Cho

SSI 0

Lee

Shin

Frequency (Hz)

SSI → tangent

+1.47

+3.63

FI → EEGNet BNCI Cho Lee Shin PhysioNet pooled

SSI → EEGNet

−20

GRAFT-dynamic − matched baseline (pp)

Target and equal-target BA effects FI → tangent

FI → EEGNet

PhysioNet

BNCI Cho Lee Shin PhysioNet pooled

SSI → tangent

SSI

−20

FI → tangent

−10

Paired subject distributions

−40

100 µV units

SSI → EEGNet

+9.46

−5

Difference (pp)

+10.54

−5

Difference (pp)

Figure S1: Post-score-seal equal-information FI/SSI controls. a, Active-sensor geometry and native versus quotient-referenced C3, Cz, and C4 traces from the sealed Cho2017:0 replay; 60 of 64 sensors were active, and all traces are shown on the same physical scale. b, Fixed-17 FI and SSI mappings for the same label-blind trial after active-native common-average referencing, mask-specific mapping, fixed-17 common-average referencing, scaling in 100-µV units, and clipping at ±10. The lower panel shows Welch relative power spectral density averaged over C3, Cz, and C4 from 1 to 40 Hz. c, Distributions of balanced-accuracy differences for all 253 paired subjects under each matched control. Each subject contributes once per control; colours and symbols denote target datasets, and black bars show the median and interquartile range. d, Target-level paired estimates with 95% subject-bootstrap intervals and equal-target subject-cluster pooled effects from 20,000 bootstrap replicates. Positive values favour dynamic GRAFT-EEG. All controls covered 5/5 targets (253 unique subjects; 1,012 control-specific paired rows); tangent used one registered split seed and EEGNet used five seeds. These post-score-seal controls do not revise the primary inference.

FI + tangent

20,000 target-stratified subject-cluster bootstrap replicates | 5 targets | 253 subject clusters effect [95% CI] (pp)

Balanced accuracy

+1.47 [-0.07, +2.96]

Macro-F1

+2.52 [+0.44, +4.53]

AUROC

+1.35 [-0.52, +3.20]

AUPRC

+1.57 [-0.17, +3.28]

SSI + tangent

effect [95% CI] (pp)

Balanced accuracy

+3.63 [+2.32, +4.95]

Macro-F1

+5.77 [+3.94, +7.52]

AUROC

+3.18 [+1.34, +5.02]

AUPRC

+3.26 [+1.56, +4.98]

FI + EEGNet

effect [95% CI] (pp)

Balanced accuracy

+9.46 [+7.68, +11.25]

Macro-F1

+8.89 [+7.06, +10.74]

AUROC

+14.59 [+12.37, +16.86]

AUPRC

+11.50 [+9.54, +13.49]

SSI + EEGNet

effect [95% CI] (pp)

Balanced accuracy

+10.54 [+8.90, +12.16]

Macro-F1

+11.11 [+9.32, +12.91]

AUROC

+15.95 [+13.74, +18.15]

AUPRC

+13.20 [+11.11, +15.32] 0

GRAFT-EEG dynamic minus matched equal-information baseline (percentage points)

Figure S2: All-metric equal-information inference. Each panel reports dynamic G RAFT-EEG minus one matched equal-information control for balanced accuracy, Macro-F1, AUROC, and AUPRC. Points are equal-target effects and bars are 95% target-stratified subject-cluster bootstrap intervals (20,000 replicates; five targets; 253 subject clusters; audit seed 20260824). Balanced accuracy, shown in bold, was the prespecified primary metric for this supplementary analysis. Hollow circles denote tangent-space controls; filled squares denote EEGNet controls. The exact plotted estimates and intervals are printed at right and are taken directly from the sealed 16-row source table without refitting or resampling.

C ALIBRATION , S TRESS , AND E XECUTION C OVERAGE a Sealed 15-bin reliability

Observed positive rate

1.0 perfect raw calibrated

0.8 0.6 0.4 0.2

NLL: 0.663 → 0.659 Brier: 0.235 → 0.233 ECE: 0.062 → 0.047

0.0 0.0

0.2

0.4

0.6

0.8

Target-resolved registered stress

Drop 25%

-1.22

-1.03

-0.36

-4.01

-0.46

Drop 50%

-7.38

-2.11

-3.71

-6.20

-0.33

Spatial 25%

-6.76

-6.50

+1.25

-10.75

-3.35

Noise +10 dB

+0.43

-0.46

-0.66

-2.79

-0.31

Noise 0 dB

-3.46

-2.42

-3.34

-7.71

-1.87

Noise −10 dB

-11.84

-6.27

-7.77

-13.48

-5.28

Avg. ref.

0.00

Cz ref.

0.00

Virtual mastoid

N/A

Coord. 2–10 mm

N/A

BNCI

Cho

Lee

Shin

PhysioNet

1.0

red = loss · blue = gain · hatched = structural N/A

Mean predicted probability

Across-target family distributions

Registered execution ledger (seed cells)

coord·10mm coord·2mm coord·5mm drop25·1103 drop25·2207 drop25·3301 drop50·1103 drop50·2207 drop50·3301 ref·average ref·cz ref·virtual_mastoid noise0dB noise+10dB noise−10dB spatial25·9001

Drop 25% Drop 50% Spatial 25% Noise +10 dB Noise 0 dB Noise −10 dB Avg. ref. Cz ref. −10

−5

0/5 0/5 0/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5 0/5 5/5 5/5 5/5 5/5

BNCI

Cho

Lee

Shin

PhysioNet

N/A retained

Family mean ΔBA (pp; circles: targets; diamond: mean; 95% t CI)

Figure S3: Calibration and registered stress. a, Trial-pooled 15-bin reliability curves reconstructed from all 25 sealed target–seed cells, together with equal-target NLL, Brier, and ECE. b, Targetresolved BA changes in percentage points under the registered stress families; hatched entries are structural N/A. c, The five target effects in percentage points within each family, with the equal-target mean and 95% t interval. d, The seed-cell execution ledger; structural N/A entries retain their zero numerator and are not converted into effects. Source-only calibration reduced equal-target ECE from 0.0617 to 0.0474, Brier score from 0.2346 to 0.2330, and negative log likelihood from 0.6631 to 0.6585, without changing BA, AUROC, or AUPRC. Mean BA changes were −1.42 pp for 25% channel dropout, −3.95 for 50% dropout, −5.22 for 25% spatial dropout, and −0.76, −3.76, and −8.93 pp for +10, 0, and −10 dB noise. Virtual mastoid (0/25) and the registered coordinate row (0/75) were structurally unavailable in this historical E4–E6 namespace and remain N/A below. A later sealed extension reused 75 completed tangent cells from a separate legacy namespace and executed 175 additional coordinate cells (Appendix P); it does not overwrite this ledger. Cross-seed stability contrasts were all positive, indicating greater rather than lower seed variability for G RAFT-EEG; this negative result is retained. Table S12: Target-resolved source-only calibration. Lower is better for NLL, Brier, and ECE. Each entry averages five frozen target cells; calibration parameters were fitted on source predictions only. Target

NLL raw

NLL cal.

Brier raw

Brier cal.

ECE raw

ECE cal.

BNCI Cho Lee PhysioNet Shin

0.6329 0.6883 0.6597 0.6953 0.6394

0.6378 0.6746 0.6568 0.6754 0.6480

0.2212 0.2457 0.2338 0.2479 0.2243

0.2233 0.2404 0.2325 0.2408 0.2281

0.0649 0.0741 0.0459 0.0844 0.0390

0.0760 0.0342 0.0317 0.0374 0.0578

Equal-target

0.6631

0.6585

0.2346

0.2330

0.0617

0.0474

Calibration improves all three pooled probability-error summaries, but not every target: BNCI and Shin worsen on all three. Discrimination is unchanged by a monotone temperature map: equal-target BA remains 60.865%, AUROC 66.447%, and AUPRC 67.531% before and after calibration. These unchanged values are retained in the source table rather than repeated in every target row.

Table S13: Target-resolved robustness family matrix. Values are dynamic BA change in percentage points relative to the unperturbed target cell. “Exec.” is complete/registered seed cells. Structural N/A is not coded as zero. Condition family

BNCI

Cho

Random channel drop 25% −1.22 Random channel drop 50% −7.38 Spatial contiguous drop 25% −6.76 Noise +10 dB +0.43 Noise 0 dB −3.46 Noise −10 dB −11.84 Average reference 0.00 Cz reference 0.00 Virtual mastoid N/A Coordinate shift 2–10 mm N/A

−1.03 −2.11 −6.50 −0.46 −2.42 −6.27 0.00 0.00 N/A N/A

Lee PhysioNet −0.36 −3.71 +1.25 −0.66 −3.34 −7.77 0.00 0.00 N/A N/A

Shin Equal-target Exec.

−0.46 −4.01 −0.33 −6.20 −3.35 −10.75 −0.31 −2.79 −1.87 −7.71 −5.28 −13.48 0.00 0.00 0.00 0.00 N/A N/A N/A N/A

−1.42 −3.95 −5.22 −0.76 −3.76 −8.93 0.00 0.00 N/A N/A

75/75 75/75 25/25 25/25 25/25 25/25 25/25 25/25 0/25 0/75

Legacy registered diagnostic; not the exact same-parent physics/no-physics ablation.

Legacy cross-seed stability diagnostic positive = adverse

Seed-level stress fingerprints

Coord. · Mu 8–13 Hz

Random drop

-0.032

-0.030

-0.035

-0.018

Coord. · Beta 13–30 Hz

Spatial drop

-0.064

-0.061

-0.062

-0.048

-0.024

No-phys. · Mu 8–13 Hz

Noise

-0.048

-0.042

-0.050

-0.037

-0.047

Reference

+0.000

No-phys. · Beta 13–30 Hz 0.000

0.001

0.002

0.003

0.004

Physical − comparator seed SD

registered seed

Registered condition-family execution boundary

Drop 25%

15/15

Drop 50%

15/15

Spatial 25%

5/5

Noise +10 dB

5/5

Noise 0 dB

5/5

Noise −10 dB

5/5

Avg. ref.

5/5

Cz ref.

5/5

Virtual mastoid

0/5

Coord. 2–10 mm

0/15

BNCI

Cho

Lee

Shin

PhysioNet

filled = completed · hatched = structural N/A · zero numerator is retained, never imputed as an effect

Figure S4: Legacy stability and execution boundaries. This registered diagnostic is separate from the exact same-parent physical-leadfield control in Fig. 3. a, Physical-minus-comparator cross-seed standard-deviation contrasts for coordinate and legacy no-physics diagnostics. All four estimates are positive; negative would mean that the physical model is more stable, so the observed direction is adverse rather than supportive evidence. b, Seed-level mean BA-change fingerprints for random dropout, spatial dropout, noise, and reference families. c, Completed/registered cells by target and condition family. Structural N/A remains hatched with its zero numerator and is never imputed as an effect.

F EW-S HOT TARGET-L ABEL A DAPTATION B OUNDARY

The few-shot analysis relaxes the original access contract by revealing 1%, 5%, or 10% of target labels only after the zero-target model has been frozen. Four adaptation strategies are then compared on disjoint evaluation trials. These results define an adaptation boundary and should not be read as target-statistics-blind performance. Each strategy–fraction pair completed all 25 target–seed cells (300 rows in total), and the independent audit passed. The small separation between full-head and PEFT adaptation is not used to revise the zero-target model. At 1% labels their equal-target BA values are 61.323% and 61.130%, while the frozen linear probe is 55.139%. Increasing the frozen-probe fraction improves its BA monotonically, whereas the 21

Table S14: Target-resolved few-shot BA (%). Label fractions denote target trials used for adaptation; all remaining trials form a disjoint evaluation set. Strategy

Labels

BNCI

Shin

Equal-target

Frozen linear probe

1% 5% 10%

58.939 52.879 56.608 61.231 56.606 59.947 63.718 57.856 60.804

Cho

Lee

PhysioNet

53.211 54.060 53.949 57.075 54.934 58.774

55.139 57.762 59.217

Full GRAFT head fine-tune

1% 5% 10%

66.102 58.309 60.736 65.917 58.424 61.163 66.887 58.821 61.398

57.776 63.692 57.915 63.964 57.888 63.614

61.323 61.477 61.722

Low-rank latent residual

1% 5% 10%

61.316 54.921 57.227 64.654 55.525 59.227 63.777 56.182 59.784

54.265 57.162 53.738 59.253 53.328 58.506

56.978 58.479 58.315

PEFT dynamic readout

1% 5% 10%

65.761 58.027 60.678 65.411 57.939 60.729 66.213 58.048 60.674

57.969 63.215 57.880 63.570 57.663 63.474

61.130 61.106 61.214

Table S15: Equal-target few-shot metrics (%). ECE is the 15-bin expected calibration error for the positive class. Each row summarizes 25 completed target–seed cells. Strategy

Labels

Macro-F1

AUROC

ECE

Cells

Frozen linear probe

1% 5% 10%

55.139 57.762 59.217

54.872 57.713 59.202

57.149 60.836 63.131

28.017 19.790 13.730

25/25 25/25 25/25

Full GRAFT head fine-tune

1% 5% 10%

61.323 61.477 61.722

61.189 61.379 61.701

66.096 66.221 66.594

4.772 3.898 3.477

25/25 25/25 25/25

Low-rank latent residual

1% 5% 10%

56.978 58.479 58.315

56.815 58.400 58.268

61.401 62.466 62.566

13.259 12.143 13.784

25/25 25/25 25/25

PEFT dynamic readout

1% 5% 10%

61.130 61.106 61.214

60.973 60.949 61.173

65.863 65.752 65.798

4.732 4.522 4.205

25/25 25/25 25/25

low-rank residual is not monotone between 5% and 10%; both patterns are retained without a post hoc winner claim.

A Six sealed real external trials

B Welch spectra of the same trials 20

S11 · trial 2

S29 · trial 1

S11 · trial 2

S5 · trial 3

S12 · trial 4

S49 · trial 5

S16 · trial 6

C Prepared montage (27 ch)

S29 · trial 1

−20 20

S12 · trial 4

S5 · trial 3

−20 20

S16 · trial 6

27/27 prepared channels

S49 · trial 5

0.0 1.5 0.0 1.5 3.0 s · C3/Cz/C4 · shared µV

Fixed array; no per-trial mask −20

1 13 30 40 1 13 30 40 Hz · mean PSD · μ/α 8–13 · β 13–30

E D Paired BA for all 60 participants

Dynamic BA (%)

100

All 60 paired differences inconclusive

Registered contrasts + BA +0.571 [-0.082, +1.230]

Dyn. − stat.

32 improved · 24 lower · 4 tied

+4.029 [+2.338, +5.773] Phys. − ctrl.

−1 0 2 4 6 8 Paired BA difference (pp)

70 60

Dynamic

62.36%

Static

61.79% 56 60 64 68 Absolute BA (%, 95% CI)

50 40

60 80 100 Static physics BA (%)

mean +0.571 pp 95% CI [-0.082, +1.230] −5 0 5 Dynamic − static BA (percentage points)

Figure S5: One-shot external evaluation on 60 held-out participants. a, C3/Cz/C4 waveforms from six label- and prediction-blind SHA-selected real Dreyer2023A trials. b, Welch spectra of the same six trials. c, The prepared 27-channel montage; the prepared export has no per-trial mask. d, Paired dynamic and static BA for all 60 participants. e, The complete participant-level dynamic–static distribution with the sealed mean and interval. f, Two preregistered contrasts and descriptive absolute BA estimates. The dynamic–static contrast is inconclusive; the physical-operator contrast is positive.

Table S16: Dreyer2023A one-shot external summary. Absolute BA rows are descriptive; the two contrast rows report the preregistered decisions. Values are percentages or percentage points with 95% intervals.

Result type

Quantity

Estimate

Lower

Upper

Decision

Absolute BA Absolute BA Preregistered contrast Preregistered contrast

G RAFT-EEG dynamic Static physics Dynamic − static Full physics − no physics

62.359 61.789 +0.571 +4.029

59.562 59.033 −0.082 +2.338

65.239 64.638 +1.230 +5.773

descriptive descriptive inconclusive positive

S EPARATELY S EALED E XTERNAL E VALUATION

Dreyer2023A is supported by a protocol seal, score seal, replay audit, and independent final audit. Of 14,312 prepared trials, 14,309 passed pre-lock signal QC and entered one-time scoring. Dynamic BA was 62.36% (59.56–65.24) and static BA was 61.79% (59.03–64.64). The dynamic–static contrast was +0.57 pp (−0.08 to +1.23; inconclusive), whereas physics–no-physics was +4.03 pp (+2.34 to +5.77; positive). The current coverage registration links these artifacts with P 0 = P 1 = 0. Dreyer therefore contributes an available one-shot external evaluation with partial-confirmation status, but it does not qualify as unrestricted independent external validation. 23

The registration manifest records the coverage ledger together with the external-registration, module, and independent-audit hashes, and sets dreyer is unrestricted external validation=false. This machine-readable constraint matches the partial-confirmation interpretation reported in Table S16.

K NOWN - SOURCE VALIDATION AND C ONDITION L EDGER

The condition ledger contains 925 entries: 755 were executable and 170 were structurally unavailable. Among executed conditions, 232 met the prespecified recovery criterion and 523 entered the scientific failure region. Across 25 target–seed pairs, the physical operator increased mean source correlation by 0.190 versus shuffled-row controls (95% descriptive bootstrap interval, 0.174–0.206) and by 0.192 versus spectrum-matched random controls (0.179–0.204). These intervals describe figurelevel uncertainty rather than additional confirmatory tests. The independent check returned PASS (P 0 = P 1 = 0). Table S17: Target-by-block accounting for the 925 Jansen–Rit conditions. “Recoverable” and “failure” partition the 755 executed conditions; structural N/A remains in the registered denominator. Target

Block

Registered

Executed

Structural N/A

Recoverable

Failure

BNCI

Channel/noise Negative control Reference

150 15 20

90 15 15

60 0 5

15 0 15

75 15 0

Cho

Channel/noise Negative control Reference

150 15 20

150 15 15

0 0 5

45 0 15

105 15 0

Lee

Channel/noise Negative control Reference

150 15 20

120 15 20

30 0 0

30 0 20

90 15 0

PhysioNet

Channel/noise Negative control Reference

150 15 20

150 15 15

0 0 5

45 0 15

105 15 0

Shin

Channel/noise Negative control Reference

150 15 20

90 15 15

60 0 5

17 0 15

73 15 0

Table S18: Known-source execution totals. The complete channel-budget-by-SNR grid is shown in Figure S6c and retained without rounding in the corresponding source-data table. “Recoverable” and “failure” partition executed conditions; structural N/A remains in the registered denominator. Block

Registered

Executed

N/A

Recoverable

Failure

Channel/noise Negative control Reference

750 75 100

600 75 80

150 0 20

152 0 80

448 75 0

Total

925

755

170

232

523

The negative-control block is kept outside the channel/noise operating region because failure is expected by construction. Structural N/A instead records a channel budget or reference construction that is unavailable for a given montage; it is not a numerical failure. Table S18 therefore separates registered, executed, recoverable, failed, and unavailable conditions.

Known source vs matched recoveries known source physical (0.73)

L-M1

L-SMA

R-M1

R-SMA

Lagged state-space recovery

row-shuffled (0.59) spectrum-random (0.55)

Standardized state x(t + 25 ms)

Source state (z-score; offset)

known source physical

1 0 −1 −2

−2.0

−1.5

Time (s)

Channel–noise recovery map 1.00 10/25

0.96 10/25

0.90 10/25

0.82 10/25

0.71 10/25

0.53 10/25

1.00 15/25

0.92 15/25

0.85 15/25

0.77 15/25

0.61 15/25

0.42 15/25

1.00 25/25

0.91 25/25

0.83 25/25

0.72 25/25

0.54 25/25

0.36 25/25

1.00 25/25

0.87 25/25

0.80 25/25

0.67 25/25

0.49 25/25

0.31 25/25

0.95 25/25

0.78 25/25

0.72 25/25

0.58 25/25

0.41 25/25

0.25 25/25

clean

+10

−5

−10

1.0

0.8

0.6

0.4

Mean source correlation

Retained channels

−1.0

row-shuffled

Mean source correlation

Lee Shin PhysioNet 0.15

1.5

0.8 0.6

failure threshold BNCI Cho Lee

0.4 0.2 −5

Shin PhysioNet

+10

clean

spectrum-matched random

Cho

0.10

1.0

SNR (dB)

BNCI

0.05

0.5

Five-target stress at 22 channels

−10

Physical gain over matched controls

0.00

0.0

1.0

SNR (dB)

−0.5

Standardized state x(t)

BNCI · seed 2027 · 22 channels · held-out trial

row-shuffled spectrum-random

0.20

0.25

0.30

Preregistered failure region 1.0

recoverable failure region

0.8 0.6 0.4 0.2

473/705 physical-operator conditions flagged 0

Physical − control source correlation

Spectral Wasserstein distance (Hz)

Figure S6: Jansen–Rit validation with known sources. a, Locked source trajectories and matched physical, row-shuffled, and spectrum-matched recoveries for one held-out BNCI seed-2027 trial at a 22-channel, 0-dB condition. b, A 25-ms lag embedding of the same left-M1 trajectories. c, Mean source correlation across registered retained-channel and SNR conditions; each cell reports the mean and completed/25 count, hatching retains structural N/A, and orange area encodes the fraction entering the preregistered scientific failure region. d, Five-target stress trajectories at a 22-channel budget across the five sealed seeds. e, Physical-operator advantage over row-shuffled and spectrummatched controls by target; intervals are descriptive 20,000-draw bootstrap intervals. f, Failure-region placement for the 705 executed physical-operator conditions: 600 channel/noise conditions, 25 physical negative controls, and 80 reference conditions; 473/705 entered the preregistered failure region. The full executed ledger additionally contains 25 row-shuffled and 25 spectrum-matchedrandom negative controls, all in the failure region, giving 523/755 overall. All trajectories and estimates come from the sealed known-source archive. The experiment evaluates the explicit inverse on synthetic known sources and does not imply that the frozen real-EEG classifier recovered cortical sources or supports clinical localization.

F ROZEN T RIAL R EPLAY AND S OURCE -F IT PARAMETER A NATOMY

The following two figures expose the executed computation without selecting a favorable prediction. Cho2017 was fixed because its 64-channel montage makes the active-set operation visible, and trial 25

A Native EEG + trial mask

B Gauge projection and shared inverse 1

200 µV

+1.8k

µV

active native

60 1 C3

60 / 64 active hard QC per trial

gauge centered

−1.8k

0.0

0.5

1.0

60×8

0.0

0.5

1.0

1.5

2.0

2.5

1.5

2.0

B=PA SS Time (s) 60×8

2.5

Gρ

3.0

8×60

3.0

Time (s)

C Real 8-D transported latent

D Frozen 11 × 24 spectral sequence µ 8–13

Band × mode

Transported mode

z1 z3 z4 z5 z6 z7

β 13–30

broad 8–30

z8 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Time (s) −4.8

+4.8

−2.1

+2.1

E Frozen SSM state and sealed readout 0.8

0.8

0.6

0.4 0.2 mean decay

mean input gate

Hidden-state L2

Gate / decay

Normalised latent log-power

Latent amplitude ()×10 −7

1.0

Window (0.50 s; 0.25 s stride)

hidden-state L2 final vs sealed |Δ| = 1.49e-08

static logit

prefix diagnostic logit

sealed final logit

prefix residual

0.1

Logit

windows 1–10: diagnostic prefix replay only

−0.6

0.0

−0.7

Residual

−0.5

−0.1 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Window centre (s)

Figure S7: Label-blind replay of a real retained trial. a, Native 200-Hz Cho2017 trial Cho2017:0, its 64-channel geometry, trial-level hard-QC mask, and prespecified C3/Cz/C4 traces; 60 channels remain active. b, The same active signals before and after gauge projection, followed by the frozen active operator AS , B = PS AS , and Gρ . c, The resulting real 8 × 600 transported latent. d, The exact 11 × 24 windowed spectral sequence supplied to the frozen SSM. e, Mean decay, input gate, hidden-state norm, and a read-only prefix replay of the bounded residual and logit. Prefixes 1–10 are diagnostic only; the final point is the sole canonical scored output and matches the sealed logit within 1.49 × 10−8 . No label or outcome was used to choose the dataset, trial, channels, time range, axes, or colour limits. Cho2017:0 was then selected as the lowest retained queue index with at least one inactive channel. Labels, prediction correctness, and performance were unavailable to this rule. The parameter view comes from one prespecified source-fit fold and does not use target EEG or target-derived statistics.

GRAFT-EEG source-fit parameter anatomy c Candidate Wc

a Static log-odds route

State

L1 h8

h16 L3

Gate Wg

0.0

−0.5

Checkpoint weight

0.5

State

Motor mode

h16 R2

Decay Wa h1

State

R3 h8

R4 h16

Hz 30 13–

z 3H 8–1

z 0H

8–3

R4 L1

Input ordered by 8–13 | 13–30 | 8–30 Hz

Band

1.0

−0.1 0.0 0.1 Standardized LR coefficient

0.2

b Condition-neutral retention

d Bounded residual readout

Base decay

0.9

0.2

final

0.8 0.0

0.7 mean

0.6

Weight

−0.2

0.5 1

SSM state

h12

h16

State

Figure S8: Source-fitted parameter anatomy for one prespecified held-out-target fold. a, Standardized logistic-regression coefficients across eight motor modes and three spectral bands. b, Condition-neutral state retention implied by the 16 frozen base-decay parameters. c, Frozen candidate, gate, and input-conditioned decay weights, with inputs ordered by band and motor mode. d, Frozen weights on terminal and sequence-mean states in the bounded residual readout. These panels describe stored source-fit parameters; they are not target-derived attribution maps or performance estimates.

T HREE -D IMENSIONAL G EOMETRY-C ONDITIONED I NVERSE K ERNELS

Figure S9 uses eight scalp surfaces, 480 active-sensor markers, and 32 inactive-channel marker groups under one shared display scale. A companion source-data table lists every displayed coordinate, active-mask value, and raw and normalized Gρ coefficient. Surface interpolation is used only for rendering and does not enter training or evaluation.

Figure S9: Three-dimensional geometry-conditioned inverse kernels. The eight panels show rows L1–L4 and R1–R4 of the locked Cho2017 inverse operator Gρ for one prespecified active mask (60 of 64 native channels). Sensor positions follow the recorded head-frame montage. Active sensors are colored by their corresponding Gρ coefficients, and the scalp surface interpolates the same values using one max-absolute normalization over the complete 8 × 60 matrix. Ring-and-cross markers identify the four inactive channels. The ellipsoid, nose, ears, lighting, and shadows provide orientation only and are not participant anatomy. Colors represent inverse-kernel coefficients—not learned Spat-Conv weights, cortical activity, source localization, statistical significance, or participantspecific anatomy.

D ETERMINISTICALLY S ELECTED R EAL -EEG ATLAS

The atlas exposes three real post-QC trials from each held-out dataset without selecting on labels, predictions, correctness, or performance. Distinct subjects are SHA-256 ranked within each dataset, followed by a SHA-256 ranking of eligible trials within subject. Each row binds the exact native montage and active mask to three central-motor traces, the full native channel–time array, and the mean active-channel Welch spectrum. Internal-dataset amplitudes are the executed fixed 100-µV model-input scale after common-average reference and trial de-meaning; they are not raw microvolts. Heatmap limits use one prespecified symmetric 99th-absolute-percentile rule per dataset across the three selected trials, while exact values remain in source data.

Five-dataset real EEG atlas · deterministic trial rank 1

64/64 active

Three motor sensors Channel × time BNCI2014-001 · sub-4 · BNCI2014_001:1106 · sha 002b3f7a C3

μ/α PSD (dB)

0.0

−40

−50

display ±0.12

−0.1

5.0

Mean active-channel spectrum

Native channel

0.1

Cho2017 · sub-3 · Cho2017:4778 · sha 002daa01 C3

2.5 0.0 −2.5

PSD (dB)

Input (100-µV scale)

22/22 active

Input (100-µV scale)

Montage / mask

Native channel

display ±7.7

−10 −15 −20

0.1

−35

0.0 −0.1 −0.2

PSD (dB)

Native channel

62/62 active

Input (100-µV scale)

Lee2019-MI · sub-18 · sub-18_ses-1_task-imagery_acq-test_run-… · sha 0023d654

display ±0.45

−40

−45

FCC3h

CCP6h

−40

0.0

−0.1

PSD (dB)

Native channel

30/30 active

Input (100-µV scale)

Shin2017A · sub-19 · sub-19_ses-4imagery_task-imagery_run-0_… · sha 04dc752e 0.1

−50

display ±0.87

−45

0.5

0.0 −0.5

PSD (dB)

Native channel

64/64 active

Input (100-µV scale)

PhysionetMI · S106 · S106R04.edf#event-0007 · sha 0b278029

display ±0.83

64 0

Time (s)

2 Time (s)

−25 −30 −35 20

Frequency (Hz)

Figure S10: Real-EEG atlas, deterministic rank 1. One SHA-selected trial from each of BNCI2014001, Cho2017, Lee2019-MI, Shin2017A, and PhysionetMI. Every dataset row shows the recorded montage and active set, three available central-motor sensors, the complete native-channel input, and the spectrum of the same trial. Shaded bands mark 8–13 and 13–30 Hz; no sleep-stage, event, ERD/ERS, or source-localization label is inferred.

Five-dataset real EEG atlas · deterministic trial rank 2 Three motor sensors Channel × time BNCI2014-001 · sub-2 · BNCI2014_001:526 · sha 00946f25

64/64 active

μ/α

−0.1

PSD (dB)

0.0

−40

−50

display ±0.12

Cho2017 · sub-34 · Cho2017:5471 · sha 026e18f5 C3

PSD (dB)

Mean active-channel spectrum

Native channel

Input (100-µV scale)

22/22 active

Input (100-µV scale)

Montage / mask

Native channel

−10

−20 display ±7.7

−35

0.0

−0.2

PSD (dB)

Native channel

62/62 active

Input (100-µV scale)

Lee2019-MI · sub-8 · sub-8_ses-2_task-imagery_acq-test_run-4… · sha 011c8b64 0.2

−40 −45

display ±0.45

FCC3h

CCP6h

−20

0.0 −0.2

PSD (dB)

Native channel

30/30 active

Input (100-µV scale)

Shin2017A · sub-22 · sub-22_ses-4imagery_task-imagery_run-0_… · sha 04a3b706 0.2

−40

display ±0.87

−25

0.00 −0.25 −0.50

PSD (dB)

Native channel

64/64 active

Input (100-µV scale)

PhysionetMI · S086 · S086R12.edf#event-0001 · sha 08f98b2f 0.25

Time (s)

−35

display ±0.83

64 0

−30

2 Time (s)

Frequency (Hz)

Figure S11: Real-EEG atlas, deterministic rank 2. The second independently SHA-ranked subject/trial for each dataset, rendered under the same locked channel, time, spectrum, colour-limit, and annotation rules as Figure S10. Trial identifiers and selection hashes are printed in the figure and retained in the source manifest.

Five-dataset real EEG atlas · deterministic trial rank 3

22/22 active

Three motor sensors Channel × time BNCI2014-001 · sub-3 · BNCI2014_001:698 · sha 01f17924 0.1

Mean active-channel spectrum

μ/α

0.0

−0.1

PSD (dB)

Input (100-µV scale)

Montage / mask

Native channel

−40

−50

display ±0.12

−5

PSD (dB)

Native channel

64/64 active

Input (100-µV scale)

Cho2017 · sub-41 · Cho2017:7169 · sha 026dae4f 5

−10 −15

display ±7.7

−5

0.0 −0.1

PSD (dB)

Native channel

62/62 active

Input (100-µV scale)

Lee2019-MI · sub-40 · sub-40_ses-2_task-imagery_acq-test_run-… · sha 001485dc 0.1

−30

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display ±0.45

FCC3h

CCP6h

0.0

−0.2

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Native channel

30/30 active

Input (100-µV scale)

Shin2017A · sub-24 · sub-24_ses-0imagery_task-imagery_run-0_… · sha 04a8bea0 −40

−50

display ±0.87

−25

0.0 −0.2 −0.4

PSD (dB)

Native channel

64/64 active

Input (100-µV scale)

PhysionetMI · S005 · S005R12.edf#event-0023 · sha 0194a93f 0.2

display ±0.83

64 0

Time (s)

2 Time (s)

−30 −35 −40 20

Frequency (Hz)

Figure S12: Real-EEG atlas, deterministic rank 3. The third SHA-ranked subject/trial for each dataset. Together, Figures S10–S12 show 15 real trials with complete trial IDs, native channel counts, selected sensor names, display limits, waveforms, and Welch source data.

b Baseline-health diagnostics

a Strict target × method BA · 5/5 above rule

GRAFT-EEG dynamic [5/5] GRAFT-EEG static [5/5] BIOT + LR [5/5] CBraMod frozen + LR [5/5] EEGConformer [5/5] ODEBrain (scratch) [5/5] ATCNet [5/5] FBCSP-LDA [5/5] ShallowFBCSPNet [5/5] CSP-LDA [5/5] Riemann-LR [5/5] EEGNet [5/5] Deep4Net [5/5] TFM [5/5] CBraMod src-only FT [5/5] EEGPT + LR [4/5] LaBraM + LR [4/5] CodeBrain + LR [0/5] 0.48

BNCI Cho

Lee

Shin Physio

Source BA (%)

Target p+ (%)

Hard H Prob. H Coverage 1-class (bits) (bits) (cells) (cells)

64.3 64.9 56.2 52.4 50.5 50.1 49.8 50.0 50.0 50.0 50.0 50.0 50.1 50.0 50.4 65.7 54.0 N/R

60.3 59.4 52.5 50.3 50.0 50.6 50.1 50.0 50.3 50.0 50.0 50.3 49.9 50.4 50.5 61.0 51.3 N/R

63.3 58.2 61.1 56.7 52.8 51.7 50.7 50.0 51.3 50.3 50.1 50.2 50.4 50.3 50.0 50.0 49.9 50.1 50.0 50.0 50.0 50.0 49.7 49.8 50.1 49.8 50.8 50.1 47.2 49.9 60.3 overlap 52.0 overlap N/R N/R

60.8 58.6 53.6 51.4 51.2 51.3 51.3 N/A 50.8 N/A N/A 51.2 50.9 50.9 52.8 61.2 52.4 N/A

45.4 47.9 60.5 40.9 44.5 35.8 40.4 20.0 48.2 20.0 20.0 38.2 40.8 31.3 45.7 35.1 53.3 N/A

0.974 0.993 0.870 0.667 0.728 0.534 0.570 0.003 0.390 0.000 0.001 0.637 0.414 0.751 0.528 0.870 0.929 N/A

58.2 56.8 50.1 50.2 50.2 49.9 49.8 50.0 49.6 50.0 50.0 49.7 49.5 47.8 49.9 49.3 50.6 N/R

0.50 0.58 Balanced accuracy

0.902 0.948 0.859 0.993 0.993 0.967 0.973 1.000 0.881 1.000 1.000 0.965 0.916 0.991 0.981 0.830 0.978 N/A

25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 25/25 20/20 20/20 25/25†

0/25 0/25 0/25 2/25 0/25 2/25 0/25 20/25 3/25 25/25 20/25 0/25 4/25 0/25 2/25 0/20 0/20 N/A

0.66

Rows below the rule have partial denominators and are not rank-mixed. Panel b values are means across available target×seed cells; H is entropy in bits. Coverage is complete/eligible clean cells. Hatched N/A is retained, never replaced by zero. †CodeBrain ran 25/25 cells, but unresolved checkpoint provenance prevents a bound health summary.

Figure S13: Strict target–method matrix and baseline-health diagnostics. a, Target-resolved BA for the 15 methods with a clean 5/5 denominator, followed below the rule by EEGPT and LaBraM with four clean targets and CodeBrain with unresolved checkpoint provenance. CodeBrain hatching denotes provenance withholding rather than a structural gap; partial denominators are not rank-mixed. b, Source validation, target positive rate, hard- and probability-entropy, completed eligible cells, and single-class counts. Hatched N/A remains missing and is never replaced by zero.

S TRICT B ENCHMARK M ATRIX AND BASELINE H EALTH

The figure is a read-only view of the same frozen matrix and health ledger reported in Appendix E. It adds no baseline score, replacement denominator, or post hoc exclusion.

S EALED C OORDINATE -P ERTURBATION S ENSITIVITY

This post-primary diagnostic leaves all trained parent checkpoints, prediction queues, and labels unchanged. Declared electrode coordinates were perturbed under two families: independent isotropic tangent-plane displacements and one global rigid head-frame rotation calibrated to the stated millimetre magnitude. The families were analyzed separately at 1, 2, 5, 10, and 20 mm. The final source table contains 50 target–condition units after averaging five registered seed repeats within each unit. Seventy-five tangent evaluations were reused read-only from a sealed legacy namespace; 175 evaluations and 35 MNE/fsaverage forward operators were added. The independent audit and module seal both returned PASS/COMPLETE with P 0 = P 1 = 0. The monotone equal-target profiles and the negative rank association support sensitivity of this implemented reduced operator to coordinate error, but they do not imply a universal millimetre threshold. BNCI accounted for the largest losses, while several target–condition means remained near zero or slightly positive. This heterogeneity, the shared fsaverage anatomy, and the synthetic perturbation models limit interpretation to the five declared montages and the tested construction. 32

Target-resolved coordinate stress -0.13

-0.61

-1.17

-1.74

-3.94

-0.10

-0.50

-1.47

-3.15

-7.52

Cho

+0.05

+0.11

+0.14

+0.34

+0.37

-0.04

-0.00

-0.35

-1.04

Lee

-0.02

+0.01

-0.03

-0.09

+0.06

-0.01

+0.00

-0.05

-0.15

-0.50

PhysioNet

+0.02

-0.00

+0.09

+0.03

-0.02

-0.03

-0.01

-0.06

-0.27

-0.59

−2

−4

Shin

-0.20

-0.29

-1.00

-1.39

-1.79

-0.11

-0.15

-0.16

-0.87

-1.45

T10

T20

R10

R20

Dynamic BA change (pp)

Independent tangent

Perturbed − parent dynamic BA (pp)

BNCI

−6

Rigid head-frame

Magnitude response by perturbation family

Execution and evidence boundary

0.0 10

Registered conditions

−2.5 −5.0

Independent tangent Rigid head-frame

−7.5 1

Target–condition units

Combined evaluation cells

250

New cells executed

175

Legacy cells reused read-only

Dynamic BA change (pp)

Coordinate displacement (mm; log scale)

Operator change versus performance

0.0

PASS (P0=0, P1=0)

Independent audit

−2.5

Module seal

−5.0

Spearman ρ=-0.449 95% cluster CI [-0.760, -0.282] target-stratified permutation p=0.0001

−7.5 0.00

0.05

0.10

0.15

0.20

0.25

New MNE forward operators

0.30

0.35

COMPLETE (P0=0, P1=0)

No training was performed. Tangent 2/5/10-mm cells were reused from the sealed legacy namespace; all other coordinate cells used newly solved fsaverage forward operators. Reported change is for reduced A, not full G.

0.40

Relative reduced-operator change ‖ΔA‖F /‖A‖F BNCI

Cho

Lee

PhysioNet

Shin

Figure S14: Coordinate-perturbation sensitivity from sealed real-data evaluations. a, Targetresolved dynamic BA change for independent tangent and rigid head-frame perturbations; T and R identify the families and the number gives millimetres. b, Magnitude profiles; points denote the five targets and lines equal-target means after averaging seeds. c, Reduced-operator relative Frobenius change versus dynamic BA change across 50 target–condition units (Spearman ρ = −0.449; targetcluster 95% CI −0.760 to −0.282; target-stratified permutation P < 0.001). d, Execution boundary. No training was performed, tangent and rigid conditions were not pooled, and the displayed operator change is for reduced A, not the full forward matrix G. Table S19: Equal-target coordinate-sensitivity summary. BA changes are percentage points from the frozen unperturbed parent; ranges are across the five held-out targets after averaging seeds. The operator column is the target mean of ∥∆A∥F /∥A∥F .

Family

Magnitude

Independent tangent Independent tangent Independent tangent Independent tangent Independent tangent Rigid head-frame Rigid head-frame Rigid head-frame Rigid head-frame Rigid head-frame

1 mm 2 mm 5 mm 10 mm 20 mm 1 mm 2 mm 5 mm 10 mm 20 mm

Mean ∆BA

Target range

Mean operator change

−0.055 −0.157 −0.393 −0.570 −1.064 −0.058 −0.140 −0.348 −0.957 −2.220

[−0.195, +0.045] [−0.610, +0.107] [−1.165, +0.142] [−1.736, +0.341] [−3.935, +0.371] [−0.115, −0.009] [−0.502, +0.004] [−1.466, −0.004] [−3.148, −0.146] [−7.515, −0.504]

0.0154 0.0309 0.0763 0.1511 0.2964 0.0155 0.0310 0.0765 0.1526 0.3014

Artifact origin new extension sealed read-only reuse sealed read-only reuse sealed read-only reuse new extension new extension new extension new extension new extension new extension

I MPLEMENTATION AND R EGISTERED I NFERENCE

Active-set quality control. A channel is marked inactive if it contains a non-finite value, exceeds 5,000 µV in absolute amplitude, or has peak-to-peak amplitude below 0.1 µV. Trials are removed when more than 20% of native channels are inactive or fewer than nine channels remain. The queue record binds the resulting mask to its subject and trial identifiers. 33

Template basis and source-only selection. For each hemisphere, the fsaverage forward model is restricted to the prespecified motor region. Gauge-projected lead fields from the five declared montages are stacked, and the four leading right-singular vectors are retained; each mode sign is set by its largest-magnitude loading. Source-library validation searches ρ ∈ {10−6 , 10−4 , 10−2 , 10−1 } and C ∈ {0.01, 0.1, 1, 10}, maximizing the unweighted mean subject-level BA. Ties favor the stronger ridge and then the smaller C. The dynamic branch uses AdamW (learning rate 10−3 ; weight decay 10−4 ), batch size 128, gradient clipping at 5, a maximum of 60 epochs, and patience 10. After selecting the epoch count, the branch is refitted on all source trials. Exact same-parent operator ladder. The coordinate control evaluates the constant-free real spherical-harmonic basis {Ylm : l ∈ {1, 2}, −l ≤ m ≤ l} on unit electrode directions; degree zero is omitted because the active-reference quotient removes the common mode. The matchedspectrum control uses deterministic random left and right singular vectors with the physical operator’s eight singular values. The row-shuffle control applies a no-fixed-point permutation to electrode rows, preserving the operator entries while breaking electrode–response correspondence. The wrong-anatomy control uses an equally sized visual-cortex leadfield solved with the same fsaverage head model. Each operator passes through the same active-reference projection and ridge inverse as FULL and is refitted on the same source libraries under inherited hyperparameters and epoch budgets. All 75 new fits were frozen before the 75 target evaluations began; physical, coordinate, and source-only sealed results were reused read-only. The independent composite audit covers 253 participants, 1,012 seed-averaged subject–control rows, and 5,060 subject–seed rows, and returned PASS (P 0 = P 1 = 0). Source-only geometry remains a separately sealed sensitivity and is excluded from the four-control Holm family. Calibration and uncertainty. Temperature calibration is fitted on source predictions only. Reliability curves pool trial counts into 15 fixed-width bins without smoothing; displayed bin intervals use 20,000 seed–target-cell bootstrap replicates. Scalar calibration metrics are computed per target and then averaged equally across targets. Main effects first average the five registered seeds within subject, sample the five target datasets with replacement, and then resample subjects within each selected target (20,000 replicates; seed 20260829). We report target-resolved effects, leave-one-target-out recomputations, and the worst target alongside the hierarchical interval. FI/SSI supplementary effects use 20,000 replicates with audit seed 20260824. Synthetic known-source validation. Eight-region delayed Jansen–Rit-class networks (Jansen & Rit, 1995) generate 3-s, 200-Hz trials after a 1.5-s burn-in. Five physiological parameters are sampled by stratified Latin hypercube for each target–seed pair. The registered channel budgets are 64, 32, 22, 16, and 8; SNR conditions are clean, +10, +5, 0, −5, and −10 dB. A geometry-conditioned Tikhonov inverse selects its ridge and orthogonal/scalar alignment on validation trials only. Test truth is used only for source correlation, NRMSE, spectral Wasserstein distance, one-step prediction NRMSE, and the registered failure gates. Shuffled-row and spectrum-matched operators are negative controls.

Table S20: Fixed implementation and selection settings. Any quantity marked “source-selected” is optimized without target signal, label, mask distribution, or empirical statistic.

Component

Setting

Selection / role

Preprocessing Epoch Hard channel gate Trial gate Motor latent Transport ridge Static logistic Static bands SSM windows SSM state Decay range Residual range Optimizer Batch / clip Epoch stopping Calibration Primary bootstrap FI/SSI bootstrap

notch; 0.5–45 Hz; 200 Hz [0.5, 3.5) s; 600 samples nonfinite; > 5000 µV; < 0.1 µV p–p ≤ 20% inactive; at least 9 active 4 left + 4 right modes ρ ∈ {10−6 , 10−4 , 10−2 , 10−1 } C ∈ {0.01, 0.1, 1, 10} 8–13, 13–30, 8–30 Hz 0.5 s; stride 0.25 s 16 diagonal states (0.5, 0.999) |rSSM | < 2 AdamW; lr 10−3 ; wd 10−4 128 / norm 5 max 60; patience 10 scalar temperature 20,000; seed 20260829 20,000; seed 20260824

fixed for all datasets fixed fixed before inference fixed before inference fixed dimension d = 8 source-selected source-selected fixed; 24 features fixed; 11 × 24 sequence fixed architecture bounded by parameterization bounded by parameterization source fit only fixed source-subject validation source predictions only dataset then subject target-stratified subject clusters

E FFICIENCY R EPORTING B OUNDARY

The efficiency record supports comparable GPU wall-clock summaries only for the executed neural fits; the classical pipelines did not record time over an equivalent scope. Table S21 therefore reports observed values and leaves unavailable timings unfilled. Static and dynamic time is not added because both share one fit record, and no universal speed ranking is inferred across different hardware or code paths. Table S21: Available downstream parameter counts and source-fit times. Times are seconds per target–seed cell, reported as median [Q1,Q3]. Static and dynamic share one joint fit record and must not be summed. A dash marks unavailable comparable timing, not zero compute. Method

BA (%) Trainable

G RAFT-EEG dynamic G RAFT-EEG static EEGConformer EEGNet CSP–LDA FBCSP–LDA Riemann–LR

60.865 59.806 50.448 49.901 50.000 50.005 49.996

Fit time (s) Timed cells Scope / device

1,281 289.93 [271.56, 413.96] N/R 289.93 [271.56, 413.96] 64,482 56.19 [35.06, 67.25] 1,714 30.94 [24.57, 37.40] 3 — 9 — 4 —

25 25 25 25 — — —

joint static–dynamic / CUDA same joint record / CUDA selection + freeze / CUDA selection + freeze / CUDA comparable timer absent comparable timer absent comparable timer absent

Trainable-parameter counts follow the executed downstream protocol and exclude frozen checkpoint weights. A comparable static count was not recorded in the efficiency source, so Table S21 reports N/R rather than a post hoc reconstruction. VRAM is omitted because the runs did not share a common memory-measurement contract.

ACCESS C ONTRACT AND AUDIT G ATES

Table S22 separates source fitting, blind inference, one-time scoring, aggregation, and replay. Every transition requires complete, hash-matched outputs from the preceding stage. Completion further requires normal process exit, all expected cells, PASS decisions from the four group checks and aggregate replay, and P 0 = P 1 = 0.

Table S22: Fail-closed execution and access separation. Each stage may read, but cannot rewrite, outputs accepted at an earlier gate. Step Process

May read

Must emit

Failure rule

1 2 3 4

Source fit Fit barrier Blind inference Raw barrier

source signals/labels; declared geometries all expected checkpoints sealed fits; target signals; trial masks all expected raw predictions

checkpoint + fit metadata global fit manifest probabilities/logits + queue IDs raw-prediction manifest

5 6 7 8 9 10

One-shot join Scorer Group audits Aggregate Replay audit Completion

raw IDs; isolated target labels paired source; fixed metrics immutable fit/raw/score trees passed score manifests only aggregate sources in fresh process all prior seals and process status

paired score source cell metrics + subject metrics independent group seals target/equal-target summaries independent aggregate seal completion record

target store unavailable any missing/hash drift stops run labels unavailable any missing/hash drift stops score no fit artifact is writable no tuning or threshold selection any P 0/P 1 blocks aggregate structural N/A preserved mismatch blocks completion requires normal exit and P0 = P1 = 0

R EPRODUCIBILITY AND S OURCE -DATA M ANIFEST

The public source-data export contains 20 CSV files derived from 17 sealed source objects plus one hash manifest. Export does not fit models, rescore predictions, recalibrate probabilities, or change decisions. The manifest SHA-256 is 76c98cc657c8d14dd27d013bb6783f416edba1d9 3d44b60987f3a4a16e43bf4d. Table S23: Fourteen principal objects among the 17 immutable inputs behind the manuscript tables. The accompanying JSON manifest enumerates all 17 inputs and stores full digests, byte counts, paths, and aggregation rules; 12-character SHA-256 prefixes are shown here. Object

Scientific role

Figure2 subject pairs Figure2 benchmark matrix Figure2 target effects Hierarchical summary Strict target table Secondary paired inference Locked cell metrics FI/SSI target summary FI/SSI pooled inference Few-shot target summary Known-source target ledger Known-source budget–SNR grid Robustness family matrix External registered summary

Dynamic–BIOT held-out subjects 18 methods × 5 targets two contrasts × 5 targets 20,000-replicate primary inference strict 15-method target matrix 10 comparators × 3 metrics registered target–seed reproducibility 4 matched heads × 5 targets 4 heads × 4 metrics 4 strategies × 3 fractions × 5 5 targets × 3 blocks 5 budgets × 6 SNRs 8 executable + 2 structural N/A 2 absolutes + 2 contrasts

Rows / cells

SHA-256 prefix

253 rows 90 rows 10 rows 1 JSON 15 rows 30 rows 235 rows 20 rows 16 rows 60 rows 15 rows 30 rows 10 rows 4 rows

0096b584532b c53c30d75146 080901a117ed ad5334718806 a46860b6bc08 7a2d26ab3c01 a101dd23b944 129e90ab64d6 cc374de59310 779746c6c249 a07b9141dc9d c8777340972e 98d3ef25ec5f 79714d17cf28

The exported tables do not recreate the scientific anchors. Their SHA-256 values remain f08b2351f9e07de0c00783454bce24b8a743153a9299556da0da1a7c12534f38 for the five-target aggregate, 18f509017357070eb2b71f3062a1c266210ec59985fa8dfb15ff730a 792dceb6 for final statistics, and c67d61b9842aa237c31873bd3130f84697537b2b51df68fa 40f5532d995bb4f0 for the FI/SSI 60-score source.

D ETAILED P ROTOCOL -FAIRNESS L EDGER FOR M AIN AND M ATCHED C ONTROLS

Fit-time access excludes target-derived fitting, normalization, calibration, threshold selection, and early stopping for every method. “T/S/L” denotes target signal, empirical statistics, and labels; “none” means that none is used during fitting. Classical baselines operate on a predeclared common-channel intersection, whereas G RAFT-EEG and FI/SSI retain each trial’s native active set; foundation models use the fixed geometry maps required by their checkpoints. “Effective targets” is an eligibility denominator rather than an execution count: EEGPT, LaBraM, and CodeBrain each ran 25/25 cells, but known or unresolved pretraining overlap reduces their strict denominator. N/R denotes a comparable parameter count that was not recorded under the executed protocol and was not reconstructed after scoring.

Table S24: Protocol-fairness ledger for access, adaptation, geometry, pretraining provenance, compute budget, and target denominator. Parameter counts include trainable downstream weights only; “pre” and “post” are defined relative to the model-fit lock. Tgt. Common T/S/L tune ch.

Method family G RAFT-EEG static G RAFT-EEG dynamic BIOT + LR CBraMod frozen + LR CBraMod source-only full FT EEGPT + LR LaBraM + LR CodeBrain + LR Weighted CSP–LDA Weighted FBCSP–LDA Riemann tangent–LR Compact EEGNet Compact EEGConformer ATCNet ShallowFBCSPNet Deep4Net TFM ODEBrain scratch FI/SSI + tangent FI/SSI + EEGNet

Tgt. geometry

Pretraining

Executed source fit

Trainable Tgt.

none none none none none

no no no no no

pre, geometry only none pre, geometry only none fixed 18-map clean checkpoint map clean checkpoint map clean

25 cells 25 cells 25 cells 25 cells 25 cells

N/R 1,281 257 201 full ckpt.

5/5 5/5 5/5 5/5 5/5

none none none none none none none none none none none none none none none

no no no no no no no no no no no no no no no

no no no yes yes yes yes yes yes yes yes yes yes no no

fixed 19-map overlap 1/5 fixed 19-map overlap 1/5 fixed 19-map unresolved 5/5 pre, channel names none pre, channel names none pre, channel names none pre, channel names none pre, channel names none pre, channel names none pre, channel names none pre, channel names none pre, channel names none pre, channel names none post, exact-mask none post, exact-mask none

25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 25 cells 5 contrasts 25 cells

513 201 201 3 9 4 1,714 64,482 N/R N/R N/R N/R N/R head dep. head dep.

4/5 4/5 0/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5 5/5

NAME , C ODE , AND R ESULT I DENTITY

The manuscript name G RAFT-EEG dynamic maps only to the code identifier mosaic dynamic; its static anchor is mosaic static. Table S25 prevents similarly named experimental namespaces from being treated as interchangeable. Full digests remain in the source-data manifest rather than the scientific table. Table S25: Non-interchangeable result identities used in the manuscript. Paper role

Code identifier

Main dynamic method Static anchor Primary pretrained comparator Exact same-parent layout-aware coordinate control Matched-spectrum random operator Electrode-row-shuffled operator Wrong-anatomy visual leadfield

mosaic dynamic mosaic static biot

Equal-target BA 60.865% 59.806% 52.684%

mosaic dynamic exact no physics missing v2

50.907%

matched spectrum random

51.167%

electrode row shuffle

49.624%

wrong anatomy visual

56.880%

The four operator controls are source-refitted children of mosaic dynamic under an identical parent contract. A later graft parent FULL/A2--A8 namespace belongs to a different parent system and is not used for the paper’s main claims or as a replacement for the 60.865% result. Its identity record remains available in the reproducibility package; no A2–A8 effect is inferred here without a corresponding result table.

F IXED 17-C HANNEL FI/SSI TARGET M ONTAGE

The equal-information controls map each native active montage to Fp1, Fp2, F7, F3, Fz, F4, F8, C3, Cz, C4, P3, Pz, P4, T7, T8, P7, P8.

Legacy labels T3/T4/T5/T6 are normalized to T7/T8/P7/P8. FI uses a minimum-norm field map with Tikhonov regularization 10−3 ; SSI uses spherical splines with regularization 10−7 . The sequence is native active-set common-average reference, geometry map, fixed 17-channel common-average reference, fixed scaling by 100 µV, and clipping to [−10, 10] for EEGNet. Each exact active mask is mapped independently. The tangent reference point, covariance shrinkage, scaler, and classifier are fitted on source data only; no target-fitted recentering or calibration is used. Tangent targets use the registered single seed, whereas EEGNet targets use five seeds; aggregation preserves these original denominators.

R ESULT A RTIFACT M AP

The machine-readable artifact map records every locked object from which a quantitative figure was rendered, together with its retained denominator, source-data file, and output hash. It binds Figure 2 to the Cho2017:0 replay; Figure 3 to 253 paired participants, five targets, four exact same-parent controls, and the 20,000-replicate operator ledger; Figure S5 to six selected real trials and all 60 external participants; Figure S6 to 925 registered known-source conditions; Figures S10–S12 to 15 label- and prediction-blind real trials; and Figure S13 to the strict target–method and baseline-health ledgers. The three-dimensional scaffold in Figure S9 is marked visualization-only. The public map is limited to scientific artifacts, denominators, provenance records, and integrity hashes.

GRAFT-EEG: Gauge-Aware Physical Field Transport for Cross-Dataset Motor-Imagery EEG

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