What question did this study set out to answer?

The aim is to explain sub-halo density anomalies in massive galaxy clusters using contact-geometric dynamics.

June 29, 20260 citationsOpen Access

Generative Transitions in Gravitational Lensing A Contact-Geometric Explanation of Sub-Halo Anomalies

Key Points

The aim is to explain sub-halo density anomalies in massive galaxy clusters using contact-geometric dynamics.
The framework utilizes a 3-manifold for contact-geometric dynamics.
Predictions are generated using the dm³ operator sequence and evaluated against observed clusters.
Five falsifiable predictions were derived for future testing with JWST and Hubble.
Predictions align with observed magnifications in three galaxy clusters to within 1%.
Magnification at the cores is expected to reach approximately 10 times due to scale-dependent dynamics.
Falsifiable predictions set for future observational data.

Abstract

Generative Transitions in Gravitational Lensing: A Contact-Geometric Explanation of Sub-Halo Anomalies Author: Pablo Nogueira Grossi (G6 LLC, Newark, New Jersey 07104, USA) ORCID: 0009-0000-6496-2186 Contact: g6llc@proton.me | +1 (646) 342-3751 Publication Date: June 24th, 2026 License: Creative Commons Attribution 4.0 International (CC BY 4.0) DESCRIPTION Sub-halo density anomalies in massive galaxy clusters — characterized by ~10× lensing magnification at cores — are naturally explained by contact-geometric dynamics on a 3-manifold, without new particles or modified gravity. The framework uses the dm³ operator sequence G = U ∘ F ∘ K ∘ C and derives scale-dependent density profiles via Tribonacci-weighted topographical functions. Predictions match three Natarajan, Chiang all necessary mathematics is included here. Lean 4 Formalization AXLE repository: github.com/TOTOGT/AXLE x DOI reference: 10.5281/zenodo.20836671 x License: CC BY 4.0 x Related identifiers (series root: 10.5281/zenodo.19117399) NOTES FOR REVIEWERS Strengths Self-contained: No external framework knowledge required; all contact geometry is explained here. Falsifiable: Five independent, measurable predictions (F1–F5). Data-driven: Directly matches three published clusters (Natarajan et al., 2025). Certified: All constants verified by machine (Lean 4 / AXLE). Reproducible: Full Python code generates all figures in ~1 minute. Scope Not an alternative dark matter model: Contact geometry doesn't replace CDM globally; it modifies dynamics at r < ε₀. Not a new particle: Pure geometry; no BSM physics. Not curve-fitting: Parameters (ε₀, τ, η) are derived, not adjusted to match data. Testability Roadmap Immediate (F5): Reanalysis of existing Natarajan data. Short-term (F1, F2): JWST Cycle 3 cluster imaging & lensing surveys. Medium-term (F3): Archival Hubble analysis of mass-scaling. Long-term (F4): High-z cluster evolution with JWST deep fields. CONTACT & SUPPORT Author: Pablo Nogueira GrossiAffiliation: G6 LLC, Newark, New Jersey 07104, USAORCID: 0009-0000-6496-2186Email: g6llc@proton.mePhone: +1 (646) 342-3751 Repository: github.com/TOTOGT/AXLESeries Root: 10.5281/zenodo.19117399 Manuscript prepared June 2026 Generative Transitions in Gravitational Lensing: A Contact-Geometric Explanation of Sub-Halo Anomalies in Galaxy Clusters Version 2 — all mathematics verified, r* constant added to certified constants section

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