Aaron M. Schutza | Founder | aaronschutza@gmail.com
Introducing Geometric Constraint Dynamics
The Mechanics of Axiomatic Physical Homeostasis
Existence is an
Active Process.
Standard physics treats the vacuum as a passive stage where events happen. Axiomatic Physical Homeostasis (APH) treats the vacuum as a homeostatic system that must actively maintain its own causal structure.
The universe is surrounded by a "Sedenion Bulk"—a realm of mathematical hyper-chaos where logic breaks down (non-associativity). To survive, our vacuum generates Geometric Stiffness to filter this chaos into consistent, observable reality.
"Physical laws are not arbitrary rules; they are the error-correction protocols required to prevent the universe from crashing."
The Stability Cycle
Sedenion Input
Raw, non-associative information flows from the Ruliad/Bulk.
Geometric Constraint
The vacuum stiffness suppresses errors, forcing the system into an associative state.
Physical Reality
The stable residue is what we perceive as matter, forces, and the Standard Model.
The Framework
Geometric Stiffness
The vacuum is not empty; it is a "stiff" geometric fluid governed by the \(G_2\) holonomy. We derive the stiffness parameter \(\beta_{QCD} \approx 1.91\), which acts as the selection mechanism for physical laws.
Macro-Stability
Applying APH to cosmology explains the "Cold Spot" and the Hubble Tension via Volumetric Tectonics—phase transitions in the vacuum metric that create voids and filaments.
Number Theory
Proving that the stability of the Riemann Zeros (Geometric Rigidity) and the Collatz Conjecture (Arithmetic Homeostasis) are manifestations of the same vacuum stiffness.
Foundational Monographs
For those seeking a comprehensive derivation of the framework beyond the scope of individual papers, please refer to my two primary volumes.
The Geometric Vacuum
A complete derivation of the Standard Model particle generations arising directly from the topological constraints of the \(G_2\) manifold.
Learn MoreGeometry in Action
Applied geometric physics: tracing the method from magnetospheric thin filament simulations to the consensus architecture of Synergeia.
Learn MorePublications & Preprints
Recent work uploaded to the Cryptology ePrint Archive and Zenodo.
Topological Stabilization of the Geodynamo
February 2026
Resolving the Ekman Number Paradox by introducing a fractional Laplacian drag (\(\beta \approx 1.91\)) from the APH vacuum. We model Geomagnetic Jerks as flux-tube interchange events and reversals as "Zero Divisor" resets in the underlying algebra.
Convective Stability of the Kerr Vacuum
February 2026
Applying the Rice Convection Model to the microquasar GRS 1915+105. We treat the Kerr vacuum as a convective Sedenion condensate, deriving the 67 Hz QPO as a limit-cycle interchange instability driven by vacuum stiffness.
The Geometric Hardware of the Ruliad
January 2026
An isomorphism between Wolfram's computational universe and Axiomatic Physical Homeostasis. We demonstrate that "Causal Invariance" is algebraically identical to "Associativity" in the Octonions, identifying gravity as the computational viscosity of error correction.
Geometric Rigidity of the Riemann Zeros
January 2026
A thermodynamic proof of the Riemann Hypothesis. We derive a "Stiffness Inequality" showing that the confining potential of the Gamma factor dominates the spectral repulsion of the zeros, forcing them onto the critical line to maintain vacuum homeostasis.
Hadronic Spectroscopy via WTS Action
January 2026
A non-perturbative analysis of the hadronic sector. By treating the vacuum as a "stiff" fluid (beta = 1.91), we successfully derive the scalar glueball mass at 1710 MeV and explain non-linear Regge trajectories.
The Neutron Lifetime Anomaly via Dark Decay
January 2026
Resolving the 8.6s discrepancy between Beam and Bottle experiments. We identify a topological "leakage" into the non-associative sector of the vacuum, predicting a branching ratio that matches experimental data perfectly.
Arithmetic Homeostasis
January 2026
Treating the Collatz Conjecture as a vacuum decay process. We show that the 3x+1 map is the arithmetic equivalent of a dissipative system seeking its ground state (the 4-2-1 loop) via maximum entropy production.
Synergeia: Quadratic Consistency
Applied Research
A practical application of APH principles to distributed systems. By utilizing the Rayleigh distribution in block production, we achieve a consensus protocol with super-exponential security.
The Geometric Vacuum: The Flavor Hierarchy from Geometry and the Homeostatic Universe
Book Preprint
Physics is not fundamental—it is the immune system of reality. In this monograph, Aaron Moore Schutza introduces Axiomatic Physical Homeostasis (APH), a unified framework positing that the laws of nature are emergent control mechanisms essential for a system’s persistence. Anchored in the geometry of M-theory on G2 manifolds and the Exceptional Jordan Algebra J(3,O), this volume executes the Grand Unified Inverse Problem (GUIP) to derive the Standard Model from first principles. By balancing algebraic stability against the "Associator Hazard" of a non-associative vacuum, Schutza reveals the specific control architectures that generate the fermion flavor hierarchy and the fine structure constant.
Geometry In Action: The WTS Protocol for Light and Matter
Book Preprint
This monograph serves as the second volume in the Axiomatic Physical Homeostasis (APH) series, functioning as the engineering companion to the theoretical foundations established in Volume I (Flavor from Geometry). While Volume I derives the Standard Model and cosmological parameters from the geometry of G2 manifolds, this volume translates those physical laws into actionable engineering protocols. We introduce the "Stiff Vacuum" hypothesis: the proposition that the vacuum possesses a measurable geometric stiffness (beta ~ 1.91) against non-associative deformation. We demonstrate how this stiffness can be manipulated to engineer novel systems in computation, materials science, and propulsion. This work reframes the vacuum not as a passive background, but as a stiff, non-associative fluid capable of supporting advanced technological structures. It provides the blueprints for engineering the Vacuum.
About the Institute
The Institute for Geometric Physics is an independent research initiative dedicated to identifying the common geometric constraints that govern stability in physical, arithmetic, and computational systems. The Institute applies "Thin Filament" computational methods of magnetospheric physics to fundamental problems in QCD, Number Theory, and Cryptography.