Paper 3 — QNFM Theoretical Framework | Findings

Central Thesis

QNFM proposes that time-series covariance structure — the way variables co-move — carries geometric information that is invisible to methods which flatten or linearize covariance matrices. A quantum circuit with a fixed measurement basis acts as a geometric probe: it reads the directional properties of the covariance manifold without adapting to the data.

Papers 1 and 2 established the first-order invariant (polarity) in EEG data. Paper 3 extends the framework to predict higher-order invariants and cross-domain applicability.

Higher-Order Invariants — Testable Predictions

Shift magnitude: The Bures distance between interictal and ictal covariance matrices. Predicted to correlate with seizure severity.
Ictal trajectory curvature: The curvature κ(t) of the SPD trajectory during seizure onset. Predicted to be higher than interictal baseline.
Inter-patient correlation structure: Whether patients cluster on the manifold by clinical subtype, not just polarity direction.

These are predictions, not findings. Each requires empirical validation with specific falsification criteria defined in the invariant hierarchy.

Cross-Domain Validation Plan

If QNFM is a general framework (not just an EEG trick), the same instrument philosophy should apply to other domains where covariance structure carries signal.

ECG channels in CHB-MIT: Same patients, different modality. CHB-MIT includes ECG alongside EEG. Do ECG covariance matrices show analogous polarity structure?
Financial time series: The E-Gate architecture applies QNFM principles to G10 FX covariance. Different domain, same instrument philosophy.
Metabolic extension: Possible future direction. Covariance of metabolic biomarkers over time — speculative.

Polarity as 1st-Order Invariant

Paper 3 positions polarity (established by Papers 1 and 2) as the foundation of the invariant hierarchy, not a standalone finding. The framework predicts that polarity is the simplest measurable invariant, and that higher-order invariants carry additional discriminative information.

Confirmed: polarity exists and is measurable. Hypothesized: it is the first member of a hierarchy. The distinction matters — the hierarchy is a prediction of the framework, not an established fact.

Status

Drafting. No timeline commitments. The theoretical framework must be mature enough to make falsifiable predictions before submission.

← Paper 2 Findings ↑ Framework →