Quantum R.E.A.P. White Paper Reform, Educational Awareness Program: Structural Diagnostics via the Unified Mathematical Taxonomy (UMT)
Creators: name: Gougouch, Abbey
Publisher: name: Zenodo
Year: 2025
Subjects: subject: Unified Mathematical Taxonomy
subject: Myopathies, Structural, Congenital/diagnosis
subject: Myopathies, Structural, Congenital/diagnostic imaging
subject: Embryonic Structures/diagnostic imaging
subject: Animal Structures/diagnostic imaging
subject: Tertiary Lymphoid Structures/diagnosis
subject: Tertiary Lymphoid Structures/diagnostic imaging
subject: Structural Diagnostics
subject: Quantum Mechanics Reformulation
subject: Projection Logic
subject: Operator Formalism
subject: Entropy Convergence
subject: Relational Encoding
subject: Canonical Equilibrium
subject: Non-Probabilistic Models
subject: Structural Coherence
subject: Scientific Realignment
subject: Diagnostic Framework
subject: Epistemic Misclassification
subject: Cross-Disciplinary Mathematics
subject: Empirical Structural Analysis
subject: Hilbert Space Reform
subject: von Neumann Operator Logic
subject: Entropy Drift
subject: Structural Misalignment
subject: Mathematical Epistemology

description: Quantum R.E.A.P. White Paper: Structural Diagnostics via the Unified Mathematical Taxonomy (UMT)

This is not a theory. It is not a hypothesis. It is a formal, cross-disciplinary diagnostic built on established, empirical mathematics. The Unified Mathematical Taxonomy (UMT) is a structural method, a framework grounded in the foundational mathematics of von Neumann (operator formalism), Boltzmann (entropy), Dirac (algebraic clarity), Hilbert (vector space logic), and Schrödinger (wave coherence).

UMT does not speculate. It realigns scientific models through operator-level structural analysis. It diagnoses failure not in observation, but in structural misread, revealing where misclassifications in projection, entropy, or relational encoding have led to decades of epistemic drift.

Every diagnostic in this document is structurally sourced from five mathematical pillars:





Projection Logic




Structural Operator Dynamics




Entropy Information Convergence




Subspace Relation Encoding




Canonical Equilibrium Constraints



These are not rhetorical. They are factual, organic mathematics, the same that built the machines, systems, and equations we use today.

Across domains including quantum computing, cosmology, thermodynamics, AI, and biochemistry, UMT does not redefine the world. It reveals the structure that’s already holding it together, and reveals where interpretation has failed.

Referenced Framework DOI:Gougouch, A. (2025). “A Unified Mathematical Taxonomy for the Structural Reformulation of Quantum Mechanics”
description: Clarifying the Method, A Projection Analogy

Understanding UMT can feel abstract, until you realise it mirrors everyday interaction. Think of how you select text on a device: simply tapping it does nothing. You must press, hold, highlight, only then can you copy, move, or change it.

That’s projection.

UMT doesn't just observe systems; it highlights the structural region in operator space. Only then do relationships stabilise, and measurements make sense.



Without projection, science has been clicking around the screen, seeing content, but never structurally selecting it.


This is what UMT formalises. Not more theory. Just a method for actually “selecting the right part of the system”, before interpreting what it does.