Geometric Origin of Effective Mass from Double-Helix Structure and Phase Synchronization A Defect Model in the Interface Layer Σ

Description
This preprint is published as part of the author’s theoretical series, “Fundamental Being Space (FBS) Theory.” The series introduces a working hypothesis in which the Fundamental Being Space (FBS), an interface layer Σ with effective thickness, and ordinary spacetime S_i form a layered structure. Here, Σ is not treated as a zero-thickness boundary or a purely formal interface, but as an intermediate layer with effective thickness between FBS and ordinary spacetime S_i. The quantity Σ_L denotes this effective thickness, and the normal-direction structure of Σ plays an important role throughout the series. In this paper, mass is treated not as an intrinsic particle property but as an operationally definable effective quantity m_eff emerging from geometric and topological constraints in Σ. Within this interface layer, the double double-helix structure is introduced as an internal geometric configuration, and the defect structures discussed in this paper are understood as localized, stable configurations formed within it. Specifically, the construction is based on localization (phase strain / localized energy), defect self-preservation, and inertial response. A concrete, reproducible double double-helix geometry is specified, together with a self-avoidance constraint and an operational lock-node (defect) criterion based on the minimal separation d(z). The model is organized to be falsifiable: the defect count K is tracked under controlled variations (bonding strength, strong-coupling width, and phase scans within an admissible set).

Start here (fastest reading path): Overview of Paper -> defect definition (d(z) criterion) -> check items (P1-P3). Supplementary Blender scripts are provided to regenerate Figures 1-2 and explore parameter variations directly.

Series links (Paper 1–7)

• Paper 1 — “General Discussion on the Reality of Fundamental Being Space (FBS)”
  We present the overall conceptual framework of FBS theory and introduce the three-tier structure consisting of Fundamental Being Space (FBS), the interface layer Σ, and ordinary spacetime. We also organize the main problems addressed in the series and clarify how the subsequent papers are positioned within this framework.
  Zenodo: https://zenodo.org/records/18220715
  
  
• Paper 2 — “Geometric Origin of Electromagnetism from a Double-Helix Structure in the Interface Layer Σ”
  We derive an effective vector potential A from the geometry and phase difference of a double-helix structure in the interface layer Σ, and show that electromagnetism (E, B) and the Maxwell equations are recovered in the long-wavelength limit.
  Zenodo: https://zenodo.org/records/18232306
  
  
• Paper 3 — “Geometric Origin of Gravitational Weakness from Interface-Layer Filtering”
  We explain the weakness of gravity as a multi-stage filtering (attenuation) effect in the interface layer Σ, and organize a framework in which large hierarchy ratios (e.g., on the order of 10^-36) can emerge naturally.
  Zenodo: https://zenodo.org/records/18240764
  
  
• Paper 4 — “Stabilization of the Light-Speed Hierarchy Ci via Tachyonic Modes”
  We reinterpret “tachyon” not as a particle but as a mode (“tachyonic modes”), and clarify the framework from the viewpoint of stabilizing the light-speed hierarchy Ci and maintaining consistency with dispersion relations.
  Zenodo: https://zenodo.org/records/18327253
  
  
• Paper 5 — “Time Generation via Coherence in the Interface Layer Σ: A Coupled Constraint Between the Velocity Width ΔC and the Time Step ΔT”
  We treat time generation as a constraint/coherence phenomenon in the interface layer Σ, and discuss how observed quantities and the emergence of time follow from a coupled condition between the velocity width ΔC and the time step ΔT.
  Zenodo: https://zenodo.org/records/18327480
  
  
• Paper 7 — “An Experimental and Observational Roadmap for FBS Theory: Testable Predictions and a Minimal Σ-Lagrangian”
  We present a minimal Σ-Lagrangian and organize the experimental and observational roadmap of FBS theory, separating recovery conditions from prediction degrees of freedom and clarifying how testable spectral and correlation signatures can be used for falsifiability.
  Zenodo: https://zenodo.org/records/18908944
  
  

In v1.2, the Zenodo Description has been revised to improve readability and discoverability. The opening paragraph has been optimized to state the operational definition of effective mass (meff) up front and to provide a clear “start here” reading path. In addition, the Description wording has been adjusted to avoid character-encoding issues on Zenodo while keeping the scientific content unchanged.

In v1.1, to improve reproducibility, two supplementary text files containing the Blender scripts used to generate Figures 1 and 2 have been added.

Supplementary files (Blender scripts)

Paper6_Fig1_BlenderScript4.5.4_v1.txt
Blender Python script (provided as a text file) to reproduce Figure 1: the baseline double double-helix geometry (four helices with envelopes R1(z)R_1(z)R1(z), R2(z)R_2(z)R2(z)), including axis/labels and in-figure caption text. Paste into Blender’s Text Editor and run.

Paper6_Fig2_BlenderScript4.5.4_v1.txt
Blender Python script (text file) to reproduce Figure 2: nearest-approach markers for Inner_A–Outer_A and Inner_B–Outer_B pairs, visualizing the minimal separation d(z)d(z)d(z) and the δ\deltaδ cue, with in-figure caption text. Paste into Blender’s Text Editor and run.

Versioning
This preprint may be updated in revised versions. When citing, please specify the DOI and the version.

Author information
Independent Researcher, Japan
ORCID: 0009-0006-8294-5738