The Erosion of the Metric: Constraint Dynamics in Early Alzheimer's Disease

Within the Constraint Dynamics framework, early Alzheimer’s Disease (AD) is modeled as a primary, predictable failure of the spatial constraint Λ — the entorhinal grid cell lattice that enforces the brain’s internal metric for navigation and self-location.This preprint proposes the Harmonic Collapse mechanism: amyloid-β and tau pathology disrupt PV+ inhibitory microcircuits, causing grid module scale ratios to drift from near-irrational biological optima (~1.42–1.5) toward low-capacity integer harmonics (e.g., 1:2). The resulting premature spatial aliasing collapses Λ(t) → 0, reduces the rank of the cognitive state matrix, erodes self-observability (Mirror, M), and produces sudden global remapping — the phenomenological core of early spatial disorientation (“I’m lost in my own home”).Supported by: Reduced grid-like representations and lower GridScores in human APOE4 carriers years before symptoms (Kunz et al., 2015) Early grid-specific hexagonal symmetry loss, path integration deficits, and compensatory boundary coding in J20 mouse models, with place cells relatively preserved (Ying et al., 2023) This Λ-first cascade explains why spatial symptoms precede widespread episodic memory loss, reframing prodromal AD as an addressing-system disorder rather than primary storage failure.Translational proposals: Diagnostic: Virtual-reality “Dark Loop” path integration stress tests to detect Λ degradation pre-symptomatically Intervention: CETR (Cognitive Entrainment Through Resonance) multi-modal protocol — hexagonal visual flow (Λ support), 40 Hz isochronic tones (Γ stabilization), resonant breathing (Θ metabolic reserve) — designed as a prosthetic scaffold to delay lattice collapse This work builds directly on: Cator (2026). The Outlines of Sanity v10.0 [Zenodo record: insert link/DOI] Related Constraint Dynamics preprints on psychosis (Γ-first) and mechanistic validation Open to replication, critique, modeling extensions, and especially collaboration on CETR pilot studies or Dark Loop biomarker validation.Keywords (add these separately in Zenodo): Constraint Dynamics, Alzheimer’s disease, grid cells, entorhinal cortex, harmonic collapse, path integration, Λ constraint, spatial disorientation, APOE4, CETR entrainmentCC-BY 4.0 | Independent research | January 2026