The Invariant Handshake: Stabilizing AI–Legacy Interoperability

This repository provides a C++ implementation of the geometric stability framework detailed in The Invariant Handshake: Stabilizing AI–Legacy Interoperability Through Geometric Normalization by Don M. Feeney Jr.

The Geometric Invariant

Modern computing is a patchwork of architectures separated by decades of design assumptions. Legacy systems operate through deterministic, low-variance pathways, while modern AI accelerators push massive parallelism, probabilistic workloads, and high-frequency stress patterns.

What they share is geometry.

The Invariant Handshake introduces a structural stability condition for evaluating interoperability. It treats legacy binary execution and AI tensor flow as orthogonal stress contributions that must jointly resolve through shared channel capacity.

The invariant is defined as:

$$ i = \frac{a^2 + b^2}{c^2} $$

• a: Binary-side stress (Legacy system contribution).
• b: Tensor-side stress (AI accelerator contribution).
• c: Shared channel capacity (The structural bound).

When the relationship forms a valid right triangle, the invariant $i \approx 1$. If the loads fit the hypotenuse, the combined stress closes within the channel's structural envelope, and the cross-era communication is safe.

“The triangle is not just a metaphor; it is the decision surface... The invariant becomes a universal truth-test.”

The C++ Implementation

The adapter mirrors the mathematics directly inside firmware or embedded environments. As described in the manuscript, this ComputeAdapter is a header-only, zero-overhead C++ structure that acts as a binary gate, normalizing and testing inputs against the invariant boundary.

Note: As detailed in the text, $\pi$ is reserved as a future circular-invariant interpretation for bounded re-expression. This initial gate layer focuses solely on $\Delta AG \to \Delta v$ collapse toward the invariant surface and refrains from evaluating the circular controller.

Build Instructions

This project uses modern CMake. It is structured as a header-only library (InvariantHandshake.hpp), with an executable demonstration (invariant_demo) and a GoogleTest suite (test_invariant).

Prerequisites

• CMake 3.14+
• A C++17 compatible compiler

Build and Run

1. Clone the repository and navigate to the project root:

   git clone <repo-url>
   cd InvariantHandshake

2. Generate the build files:

   mkdir build && cd build
   cmake ..

3. Build the project:

   make

4. Run the demonstration program. This reproduces the canonical "visible boundary condition" example ($a=0.4, b=0.9, c=1.0 \implies i=0.97$):

   ./invariant_demo

5. Run the unit test suite:

   ./test_invariant

Repository Structure

InvariantHandshake/
├── include/
│   └── InvariantHandshake.hpp    # The header-only geometric adapter
├── src/
│   └── main.cpp                  # The canonical demonstration program
├── tests/
│   └── test_invariant.cpp        # GoogleTest suite verifying mathematical stability
├── CMakeLists.txt                # Build configuration
└── README.md                     # Documentation

Reference

Feeney, D. (2026). The Invariant Handshake: Stabilizing AI–Legacy Interoperability Through Geometric Normalization. Zenodo. https://zenodo.org/records/21158238