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July 15, 2026Open Access

Phase Partition in the First Window of Expansion: From Non-Interacting Planckons to Composite Particles — Sector Ratios, the Acquisition of Mass, and the Proof of Masslessness (ΨD)

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Authors

HBHamdi Barut

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Overview

Randomized trial investigates mass acquisition and non-interaction in planckons, indicating methods for understanding particle composition.

Key Points

  • To explore the nature of mass acquisition and the behavior of non-interacting planckons within the ΨD framework.
  • Utilized three mathematical tools: cubic geometry, energy–potential ledger, and derivative–integral operators.
  • Developed theories based on the dynamics of event-time and partitioning of sectors in dimensional space.
  • Presented numerical analysis with derived thresholds and atmospheric ratios for different particle types.
  • Identified distinct sector ratios: d0, d1, d2, derived from partition dynamics and validated against observational data.
  • Demonstrated that massless behavior is feasible in d3, while features of mass were mapped accurately with zero free parameters.
  • Confirmed fit of observed ratios (dark energy to dark matter) against theoretical predictions with high precision (0.9%).

Cite This Study

Hamdi Barut (2026) studied this question.

synapsesocial.com/papers/6a57245a88b21df875480cf1https://doi.org/10.5281/zenodo.21339412
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Also Consider

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  1. 1Planckon-Based Cubic Structural Phase Theory and Dimensional Flow Cosmology (ΨD)Planckon-Based Cubic Structural Phase Theory and Dimensional Flow Cosmology (ΨD)2026
  2. 2ΨD — Dimensional Flow Cosmology: From the Planckon Fabric to Particles, the Dark Sector and the Endless Cycle — A Unified Derivative Integral Theory on the Folding Cubic Geometry2026
  3. 3Redefining the Dark Sector and Its Two Identities: Pre-Force Matter — the d1 Floor (DE), the d2 Skeleton (DM) and the d0 Isolated Reserve; Derivative–Integral Proofs in Doubling-by-Two Cubic Geometry (ΨD)2026
  4. 4Quantum Interactions of Fundamental Particles: A Physical Model in the Planck Region2026
  5. 5A Planck-Based Unified Framework for Dark Energy and Dark Matter2026