Neuroscience · Economics · Physics · Mathematics

The Shared

Geometric Structure

Eight formally proven equations in neuroscience, economics, and physics are the same equations. This tool shows the three-faced geometric object they share — not as analogy, but as identical mathematics. A wide-spectrum search across 14 mathematical categories identified 15 additional structures within the same object.

Core Strata

New Candidates

Faces

Calculators

◈UNIFIED OBJECT

Three Faces, One Object

The Unified Stratified Manifold

Neuroscience, economics, and physics are three measurement instruments pointed at the same geometric object. The eight strata below are cross-sections of a single stratified Riemannian manifold governed by one metric, one flow, and one conservation law. The substrate (Level 0) is the generating structure beneath all three faces.

Face A: Neuro-Econ (I–V)(5 strata)

Face B: Physics (VI–VIII)(3 strata)

Level 0: Substrate(Generating structure)

Shared Metric

Fisher Information g_ij(θ)

Same ruler across all 3 faces

Shared Flow

Fokker-Planck ∂ρ/∂t

Same dynamics on all strata

Conservation Law

Wald: E[S_N] = E[N]·E[X₁]

= Noether charge = No-Arbitrage

hover or click a region

Hover over a stratum to see the cross-domain mapping

Formally Proven

Identical Equations

Structural Isomorphism