This insight emerged from an attempt to rigorously test a speculative hypothesis: that gravity might be an information-theoretic constraint rather than a fundamental force.

When we applied strict information resource management principles to the analysis of galaxy rotation curves, a distinct pattern emerged. What was initially a failed attempt to fit a universal constant revealed a consistent scaling law.

This is the documentation of that process—the initial speculation, the data-driven failure, and the resulting discovery.

The Speculative Phase

The initial hypothesis (ISL) proposed that “Dark Matter” effects could be modeled as the “modularity overhead” of a geometric spacetime kernel. We successfully derived the Fine Structure Constant ($lpha$) from this geometry to 6 ppm precision. However, fitting a single galaxy is not proof.

To validate this model, we needed to confront it with the full complexity of galactic dynamics. We chose the SPARC database—175 galaxies of varying mass and structure.

The Failure (Jan 9, 2026)

We initially tested the model assuming a universal modularity parameter ($lpha_{ISL} pprox 0.1$).

AI-assisted analysis immediately exposed the weakness of this assumption. Upon batch-processing all 175 galaxies against ISL, MOND, and Newtonian models, the results were clear.

The Pivot: Data-Driven Refinement

Rather than discarding the framework, we analyzed the source of the variance. We plotted the empirically derived $lpha_{ISL}$ values against galaxy velocity ($V_{flat}$).

The noise resolved into a clear signal.

This implies that geometric overhead is not constant but scales inversely with system complexity. Small galaxies (Dwarfs) exhibit high overhead, mimicking Dark Matter dominance. Giant galaxies exhibit low overhead, appearing nearly Newtonian.

A Unifying Interpretation

This scaling law suggests that the same information-theoretic constraints apply across vastly different scales.

Applying this same logic to the quantum scale, we derived a Collapse Timescale ($ au pprox \hbar/E_G$) that aligns with Penrose’s Objective Reduction threshold. This points toward a unified view where gravity acts as an information resource manager, enforcing bounds at both the quantum and cosmic limits.

Why We Are Publishing This

We believe in transparent, reproducible science. We are publishing the code, the successful fits, and the initial failures.

• Technical Report: Galaxy Scaling Law & Quantum Collapse
• Reproduction Kit: Run the Analysis Tutorial

Whether this interpretation survives further testing remains an open question. We invite the community to review the code and challenge the findings.

— Shri (with AI Assistance)