…As A Falsifiable Test Of The Æ Framework

Introduction

This document defines Version II of the GPS falsification protocol for the Æ framework. It incorporates locked train/test partitions, declared tolerance criteria, observable proxy definitions and explicit revision constraints. The purpose is to determine whether the Æ cascade formalism can predict observable counter drift under disciplined conditions.

The governing constraint remains:

E = mℓ

Observable Surface and Locked Data Regime

1. The observable surface is orbital atomic counter drift relative to a terrestrial reference counter. The measurement target is drift magnitude and sign expressed in microseconds per terrestrial day.

2. Dataset Partition Rule. Training data shall consist of one fixed calendar month of GPS satellite clock correction records from a specified subset of satellites. Test data shall consist of a different month and a different satellite subset. These partitions must be declared before fitting begins and may not be altered during evaluation.

Model Form

Locked Structure

The cascade rate mismatch is defined in proportional form as:

κ_o − κ_g = κ₀ [ α σ(r_o) + β η(Ω_orb, r_o) ]

Observable Proxy Definition for Strain: σ(r_o) shall be defined as a monotonic function of orbital altitude band relative to ground baseline.

Observable Proxy Definition for Twist: η(Ω_orb, r_o) shall be defined as a function of orbital inclination and orientation relative to Earth rotation or magnetic axis.

Pre-Registered Tolerance
and Evaluation Criteria

Tolerance Band shall be fixed prior to evaluation, either as a statistical bound derived from training residual noise or as a declared microsecond per day bound.

Success requires all withheld satellites to fall within the declared tolerance band without additional parameter tuning.

Orbital Modulation Constraint

For eccentric orbits, predicted periodic modulation must be derived using the same α and β coefficients calibrated in training. No new harmonic terms may be introduced.

Versioning and Permissible Revision Rules

Any modification shall be versioned explicitly.

New terms must correspond to observable proxies.

Parameter count must not increase without reduction in residual structure.

Train/test partitions remain fixed across versions.

Failure Conditions

Parameter instability across satellite classes constitutes failure.

Regime-specific retuning constitutes failure.

Residual correlation not captured by declared proxies constitutes failure.

Dependence on propagation delay constitutes failure.

Conclusion

This Version II protocol binds the Æ framework to measurable reality under declared constraints. The model will either predict orbital counter behavior under its own grammar, or it will be revised openly under version control.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams