# BrainMetastabilityAnalyzerTool — 2026 Reality Audit Status: **discovery-stage research code**. The repository contains a defensible EEG state-space representation, but its historical Alzheimer/FTD language overstates what the existing experiments establish. This document separates **measurement**, **discovery**, **internal robustness**, and **external validation**. ## 1. Core measurement that survives The defensible core is: 1. band-pass scalp EEG; 2. Hilbert phase per electrode; 3. project the complex phase field onto graph-Laplacian eigenvectors built from electrode geometry; 4. choose the dominant spatial mode per frequency band; 5. measure persistence, transitions, and multi-band state occupancy. These are best described as **spatial sensor-phase modes**. The graph is constructed from sensor coordinates, not from diffusion-MRI tracts or a cortical structural connectome. No claim about holography, thought content, consciousness, or a literal brain grammar is required for the measurement to be useful. ## 2. Historical claims reclassified ### KEEP - Spatial sensor-phase mode projection. - Per-band dominant-mode dwell times. - Transition statistics. - Multi-band state words as an exploratory discretization. - `dwell_gradient` as a single frozen candidate for independent replication. ### EXPLORATORY / QUARANTINE - vocabulary size; - entropy; - Zipf exponent; - top-5 concentration; - training perplexity; - PSI / Gerchberg–Saxton convergence; - the `viscosity` interpretation. Several vocabulary metrics summarize the same state-count distribution and should not be presented as independent biomarkers. ### REPAIR / RETIRE **Categorical Pearson coupling.** Dominant mode IDs are labels. Pearson correlation changes under arbitrary relabeling and is therefore not a sound categorical coupling measure. Use a label-invariant measure such as mutual information or continuous coefficient vectors. **Criticality from CV > 1.** Dwell-time coefficient of variation is a legitimate statistic. A threshold of `CV > 1` does not demonstrate a critical phase transition. Use `dwell_cv` unless stronger criticality tests are added. **In-sample bigram perplexity.** The historical Alzheimer analyzer builds and scores the bigram model on the same sequence. This is descriptive training perplexity, not predictive generalization. ## 3. The task-vocabulary result is confounded The historical PhysioNet task analysis compared unequal observation amounts: - REST concatenated two baseline recordings; - TASK concatenated six longer motor-imagery recordings; - whole motor-imagery files were labeled TASK despite alternating `T0` rest and `T1/T2` task blocks. Vocabulary size naturally grows with observation time. Therefore the statement that “task doubles the vocabulary” is not currently established. A clean rerun must use equal-duration event-conditioned T0 versus T1/T2 samples. ## 4. Alzheimer discovery dataset Historical Alzheimer's work used OpenNeuro `ds004504`: - 36 Alzheimer's disease (AD) - 23 frontotemporal dementia (FTD) - 29 cognitively normal controls (CN) - 19 scalp EEG channels - resting eyes closed The strongest later candidate was derived after the original results had already been inspected: ```text dwell_gradient = slope(log(1 + mean_dwell_band)) across delta → theta → alpha → beta → gamma ``` Historical discovery receipt: ```text Kruskal-Wallis across CN/AD/FTD p = 0.0015 AD vs CN p = 0.0003 pooled MMSE Spearman rho = 0.408, p = 0.0001 ``` These are discovery statistics, not confirmation. ## 5. Internal raw-style spectral audit — completed The frozen audit processed all 88 subjects with zero failures and compared dwell gradient with three ordinary spectral baselines. | Feature | AD mean | CN mean | p | |---|---:|---:|---:| | `dwell_gradient` | -0.4469 | -0.4164 | 0.000277 | | alpha relative power | 0.0481 | 0.0755 | 0.004101 | | theta / alpha ratio | 2.6013 | 1.8297 | 0.000993 | | peak alpha frequency | 7.479 Hz | 8.664 Hz | 0.000124 | Internal repeated subject-wise CV: ```text A = age + spectral AUC = 0.729 ± 0.142 B = age + dwell_gradient AUC = 0.756 ± 0.132 C = age + spectral + dwell_gradient AUC = 0.768 ± 0.128 C - A = +0.039 AUC ``` This was interesting but not external validation. The feature was developed on the same cohort. Raw-style receipt: [`INTERNAL_SPECTRAL_AUDIT_RESULT_2026.md`](INTERNAL_SPECTRAL_AUDIT_RESULT_2026.md). ## 6. Internal derivative / cleaned EEG audit — completed The same frozen spatial-phase and dwell transform was recomputed on the dataset's derivative / cleaned EEG, again with 88/88 subjects processed. | Feature | AD mean | CN mean | p | |---|---:|---:|---:| | `dwell_gradient` | -0.3551 | -0.3275 | 0.006175 | | alpha relative power | 0.0494 | 0.0794 | 0.002351 | | theta / alpha ratio | 2.5318 | 1.6045 | 0.0000732 | | peak alpha frequency | 7.493 Hz | 8.681 Hz | 0.000155 | The univariate dwell difference therefore survives preprocessing, although it weakens. The decisive internal comparison changes much more strongly: ```text A = age + spectral AUC = 0.778 ± 0.121 B = age + dwell_gradient AUC = 0.694 ± 0.128 C = age + spectral + dwell_gradient AUC = 0.777 ± 0.118 C - A = -0.00125 AUC ``` Internal classification: `INTERNAL_DERIVATIVE_DWELL_SEPARATION_NO_INCREMENT` This means the disease-associated dwell difference is not simply destroyed by cleaning, but its apparent **incremental diagnostic value beyond ordinary slowing is preprocessing-sensitive and disappears in the cleaned representation**. That substantially weakens the case for Φ-Dwell as a new cheap Alzheimer biomarker on ds004504. The representation may still be scientifically useful as a spatial-dynamical view of disease-related EEG change. Cleaned receipt: [`INTERNAL_DERIVATIVE_AUDIT_RESULT_2026.md`](INTERNAL_DERIVATIVE_AUDIT_RESULT_2026.md). ## 7. Severity claim — not supported The historical pooled MMSE association does not become a reliable within-disease severity effect. Raw-style: ```text within AD: rho = +0.215, p = 0.207 within FTD: rho = +0.121, p = 0.582 ``` Derivative / cleaned: ```text within AD: rho = +0.269, p = 0.113 within FTD: rho = -0.009, p = 0.969 ``` The old pooled MMSE relationship was entangled with diagnostic-group separation. The repository should not claim that dwell gradient tracks cognitive severity. ## 8. Age warning became preprocessing-sensitive The raw-style audit found: ```text within AD: dwell vs age rho = +0.142, p = 0.409 within CN: dwell vs age rho = -0.599, p = 0.000597 ``` After derivative preprocessing: ```text within AD: dwell vs age rho = +0.276, p = 0.103 within CN: dwell vs age rho = -0.100, p = 0.607 ``` The strong control-age relationship therefore does not survive preprocessing and should not be treated as a stable biological finding. Age still remains a frozen covariate for external evaluation. ## 9. The boring baseline: spectral slowing Any Alzheimer's EEG feature must be tested against ordinary spectral slowing. Frozen baselines: ```text alpha_relative_power = power(8-13 Hz) / power(1-45 Hz) theta_alpha_ratio = power(4-8 Hz) / power(8-13 Hz) peak_alpha_frequency = peak frequency in 7-13 Hz ``` The cleaned internal result currently favors the boring explanation for diagnostic performance: spectral features alone reach mean AUC `0.778`, and adding dwell changes that to `0.777`. This does **not** prove dwell and spectral slowing are mathematically identical. It shows that the current dwell feature contributes no additional held-out discrimination in this cleaned cohort under the frozen model. References: - Bruffaerts et al. (2025), *Diagnostic utility of electrophysiological markers for early and differential diagnosis of Alzheimer's, Frontotemporal, and Lewy Body dementias: A systematic review*. PMID 40379988. - *EEG biomarkers in Alzheimer's and prodromal Alzheimer's: a comprehensive analysis of spectral and connectivity features*. PMID 39449097. - Paitel et al. (2025), *Functional and effective EEG connectivity patterns in Alzheimer's disease and mild cognitive impairment: a systematic review*. PMID 40013094. ## 10. PSI status The Phase-Stability Index maps eigenmode power vectors onto an artificial radial canvas and measures Gerchberg–Saxton phase-recovery convergence. Gerchberg–Saxton is a real optimization algorithm. The biological interpretation of its convergence count is currently unvalidated. PSI remains quarantined exploratory work. A historical PSI README also states that `p = 0.006` survives a Bonferroni threshold of approximately `0.003`; mathematically it does not (`0.006 > 0.003`). ## 11. Frozen external validation gate ### Primary question > Does the existing dwell-gradient definition distinguish AD from controls in independent subjects, and does it add held-out information beyond ordinary spectral slowing? ### Frozen primary Φ-Dwell feature ```text dwell_gradient only ``` ### Models ```text A: age + spectral baselines B: age + dwell_gradient C: age + spectral baselines + dwell_gradient ``` Use subject-wise held-out evaluation. The key incremental comparison is **C versus A**. ### No-rescue rule After external labels are inspected, do not change: - frequency bands; - number of graph modes; - graph sigma; - word step; - dwell definition; - log transform; - gradient direction; - primary endpoint; - spectral baseline definitions; - age handling. Other variants become new hypotheses for another held-out cohort. ### External verdicts - `EXTERNAL_DWELL_GRADIENT_NULL` — no reliable external AD/CN signal. - `REPLICATES_BUT_NO_INCREMENT_OVER_SPECTRAL_SLOWING` — representation is interesting, but not a new biomarker. - `EXTERNAL_INCREMENTAL_SIGNAL` — frozen dwell gradient replicates and improves held-out performance beyond the spectral baseline. Even the last verdict would establish a research signal, **not clinical diagnostic utility**. ## 12. Current boundary ```text INTERNAL AUDIT - spectral slowing comparison: DONE - within-AD MMSE: DONE (null) - age parsing: DONE - raw vs cleaned: DONE - cleaned incremental value: NONE under current frozen model - event/duration-matched PhysioNet task analysis: optional mechanism audit EXTERNAL VALIDATION - completely independent AD/control subjects - frozen dwell_gradient - frozen spectral baseline - frozen age handling - subject-wise held-out evaluation ``` The next Alzheimer test should use new people. Do not retune ds004504 to recover the lost `+0.039` increment.