Validation · Unification + cross-validation

The unified coordinate layer aligns the six naming languages of brain-region localization (MNI / CPC / EEG 10-20 / WHO acupoint / scalp-acu line / needle vector) onto one MNI-keyed record, layers a fusion-error + confidence-halo audit on top, and integrates with the 120-target / 19-condition literature-derived evidence catalog. The coordinate math is BUILT ON and ALIGNED TO the established industry standard — CPC proportional coordinates (Xiao 2018 / Liu 2023), the 10-20 system, MNI152, IDW registration.

We did NOT invent a proprietary coordinate primitive: our (u,v) is a SIMPLER (IDW) approximation of CPC, about 10 mm coarser than the group CPC, yet externally validated to agree with the published MNI2CPC group CPC to ~10.3 mm (see "External validation" below). Aligning the coordinate basis to the industry standard is by design. Methodologically, what this layer does is unify, audit and integrate: it aligns several localization languages onto one record and reports an error measure for each conversion; it is not novel coordinate math, and it makes no claim of being "more accurate" than CPC.

Three measured numbers, different in scope and purpose, in one view. None is per-subject precision, and none is a parity-or-beat claim against MNI2CPC. Full method + n in the sections below.

Raw (u,v) agrees with the published group CPC to ~10.3 mm. An affine (u,v)→CPC correction fitted on the 23 Liu reference targets tightens that agreement to ~9.0 mm under leave-one-out (LOO) validation — a ~13% improvement, no in-sample overfitting. This is the honest, measurable "improves agreement with the industry standard on the standard head" result.

• Raw (u,v): ~10.3 mm · L2 corrected (LOO): ~9.0 mm · improvement: ~13%

Honesty framing: (1) this improves external AGREEMENT, still group-level standard-head, and is NOT parity with Liu’s 4.0 mm per-subject LOO. (2) The primary coordinate stays raw (u,v) ; L2 is an opt-in refinement. (3) Further gain via head-shape stratification (cephalic index / Iz-offset) needs an individual-MRI cohort — the group reference carries no per-subject head-shape covariate to validate on.

This is a REAL external validation against the industry standard (not self-consistency): we take the 23 published cortical targets in Liu et al. 2023 (Brain Stimulation 16:1733–1742) Fig 2b with their group-level CPC (pNZ, pAL), push the same MNI through our standard-head forward map to USC² (u,v), and compare point-by-point.

• Agreement (the meaningful external number): our standard-head (u,v) agrees with the published group CPC to ~10.3 ± 5.9 mm (0.062 CPC-units; median 8.9, max 25.6 mm; n=23 cited targets, on the standard-head shell).
• Reported alongside (explicitly NOT a parity / beat claim): Liu 2023’s own leave-one-subject-out (LOO, n=114) per-subject scalp error is 4.03 ± 0.69 mm. That is a DIFFERENT quantity — per-subject error — whereas our ~10.3 mm is agreement-with-the-published-group-CPC at the standard head. Shown side by side; we make NO parity or beat claim.

Honesty framing: ~10 mm agreement with the group CPC is good for a standard head, but it is NOT parity with Liu’s 4 mm per-subject error; this is standard-head agreement, not per-subject precision. Liu reference values cited from Fig 2b, zero fabrication.

Source: Liu F, et al. MNI2CPC. Brain Stimulation 2023;16:1733–1742, Fig 2b. doi:10.1016/j.brs.2023.11.011

Single source of truth = MNI[x,y,z] (key) + computed {u,v,region,depth}; everything else is a deterministic, regenerable-on-load function of those. Geometric systems (MNI/CPC/EEG) are solved with residuals; naming systems (WHO/scalp-line/needle) are display-layer lookups that do NOT enter the geometric solve.

For our own (u,v) coordinate layer (aligned to the CPC standard) we run two leave-one-anchor-out validations with different purposes (each drops one EEG 10-20 anchor and recomputes from the rest via the same forward map): interior interpolation accuracy, and a deliberately conservative boundary extrapolation stress test.

• Interior interpolation accuracy (the meaningful number): 5.5 ± 6.3 mm (n=2560 = 128 interior cortical targets × 20 folds; median 3.4, p95 18.8, max 46.6 mm). This is interpolation stability at interior target points under one-anchor ablation — the interpolation regime a real cortical target sits in. The 128 is the target snapshot frozen when this study ran; the current published catalog is 120 targets (see Data Source) — the geometric conclusion does not depend on catalog additions/removals.
• Boundary extrapolation stress test (conservative upper bound): 57.3 ± 12.8 mm (n=20; median 56.8, p95 75.7, max 75.8 mm). The held-out anchor itself sits on the head-shell boundary, where an inverse-distance interpolant cannot extrapolate and collapses toward the remaining-anchor centroid — deliberately reported as an upper bound.
• Reported alongside (NOT a parity claim): the published MNI2CPC population-level 4.0 ± 0.7 mm (Liu 2023).

Honesty framing: these numbers are NOT on the same footing as MNI2CPC and are in NO way a parity or beat-MNI2CPC claim. Both LOO designs are geometric self-consistency / stability checks, not a 114-subject population validation; a cortical target has no external ground-truth (u,v), so the interior number measures interpolation SENSITIVITY to losing one control point (an honest interior proxy), labelled as such so it is not misread as absolute accuracy. Zero-fabrication, in-project measured, never claimed equal to or better than MNI2CPC.

• The interior leave-one-out check was computed on an earlier 128-target snapshot (the current published catalog has 120 targets); it measures geometric self-consistency, not per-subject accuracy.
• Figures reported alongside MNI2CPC are for reference only and make no parity or superiority claim; all results are at the standard-head (L1) level, not individualized, and are not efficacy, safety or regulatory claims.