Authors: NanoCERN Team (Chief Experimenter: Shrikant Bhosale)
Date: January 6, 2026
Target Journal: Physical Review Letters (PRL) / Nature Astronomy
Abstract
We present observational evidence for a binary phase transition in galactic gravitational dynamics, challenging the standard paradigm of continuous dark matter halos. Analyzing 165 rotation curves from the SPARC database using the Inverse Scaling Law (ISL) framework, we identify two distinct gravitational states: a Newtonian “bare metal” state () governing dwarf galaxies (
km/s), and a Saturated state (
) governing massive spirals (
CDM assumes a continuous distribution of cold dark matter, while MOND proposes a universal modification of law at low accelerations. Both assume a smooth, analog universe. We propose a third possibility derived from Information Theory and the Inverse Scaling Law (ISL): that “Dark Matter” is a manifestation of strictly quantized modularity overhead in the universe’s computational structure.
2. Methodology
We utilized the SPARC database (Lelli et al., 2016), a sample of 175 galaxies with high-quality rotation curves. We fit each galaxy’s rotation curve using the ISL potential correction:
where represents the “modularity overhead” coefficient. We then performed K-Means clustering (
) on the resulting
distribution to test for quantization.
3. Results: The Binary Universe
Our analysis reveals a stark bimodal distribution in , falsifying the initial hypothesis of a universal
.
3.1 Two Distinct States
The clustering algorithm identified two stable centroids:
* State 0 (Newtonian Mode): (
). Predominantly low-mass dwarf galaxies.
* State 1 (Saturated Mode): (
). Predominantly high-mass spiral galaxies.
3.2 The Phase Transition
We observe a clear phase transition correlated with the maximum rotational velocity (), a proxy for total dynamical mass/complexity:
* km/s: Systems remain in State 0 (
).
* ).
* Transition Zone: A scarcity of stable intermediates suggests a rapid phase change, analogous to a thermodynamic phase transition (e.g., water boiling).
4. Discussion: The Complexity Tax
The data implies that the universe does not apply dark matter phenomenology universally. Instead, it optimizes. Small systems (“Dwarfs”) are computationally cheap to evolve and render, requiring minimal overhead (State 0). As systems grow in complexity (mass/scale), they breach a critical threshold (), forcing the spacetime metric to switch to a higher-overhead, “saturated” mode (State 1) to maintain causal consistency.
This “Digital Gravity” framework resolves the tension between LambdaCDM (good for large scales) and MOND (good for spirals) by introducing scale-dependent switching. It also explains the “Diversity of Dwarfs” problem, as dwarfs near the threshold may flicker between states.
5. Conclusion
Gravity is not an analog slider; it is a digital switch. We have inverted the ISL paradigm from a small universal correction to a binary state machine. Future work will focus on deriving the theoretical value of and predicting the behavior of galaxy clusters, expected to be locked in State 1.
Data Availability
All analysis code and data are available in the NanoCERN repository.