What question did this study set out to answer?

This research aims to derive and prove a conservation law based on astronomical imaging data from JWST, focusing on invariants in observations.

February 8, 20260 citationsOpen Access

The Truong Invariant Theorem: A Machine-Verified Data–Driven Conservation Law from JWST/M87 Imaging

QNQuoc Truong Nguyen

Key Points

This research aims to derive and prove a conservation law based on astronomical imaging data from JWST, focusing on invariants in observations.
Formulated conservation law using calibrated astronomical imaging data from JWST.
Implemented operator theory and finite-dimensional linear algebra for theoretical proofs.
Verified the entire mathematical argument with Lean 4 and mathlib for machine-checked correctness.
Demonstrated framework using real datasets, providing a reproducible pipeline.
Established the Truong Invariant Theorem as a non-trivial conservation law.
Confirmed the existence of a nullspace in the induced feature matrix under rank deficiency.
Provided a comprehensive and machine-verified proof for the conservation law.

Abstract

We establish a rigorously derived conservation law directly from calibrated astronomical imaging data.Given a family of linear observables on a Hilbert space of images, the induced feature matrix is shown to admit a non-trivial nullspace whenever rank deficiency occurs. This nullspace defines an invariant functional conserved across all observations. The result is formulated as the Truong Invariant Theorem and proven using operator theory and finite-dimensional linear algebra. The complete mathematical argument is provided in LaTeX and formally verified using Lean 4 with mathlib, ensuring machine-checked correctness. The framework is demonstrated on real JWST/M87 datasets and provides a reproducible pipeline for invariant discovery and data-driven conservation laws in astrophysical imaging. This archive contains:• the compiled paper (PDF)• full LaTeX source• formal Lean proof

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