SAM3-DualZero-Conoid

Geometric Unification of Gravity and the Standard Model
from a Right Conoid Spectral Triple with Dual-Zero Hyperreal Regulation

A minimal noncommutative geometric framework that derives gravity together with the complete Standard Model from a single explicit geometric object: an infinite right conoid equipped with twelve binary-icosahedral bridges and regulated by a Dual-Zero hyperreal construction.

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Overview

SAM3 (Spectral Action Model 3) is controlled by only two fundamental parameters:

• ℓ₀ — anchored to the top-quark mass
• ω₀ ≈ 0.97 — Dual-Zero regulator strength

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Key Results

• Newton’s Constant — Exact analytic expression:
  $$ G_N = \frac{64\pi \ell_0^2}{45} $$
• Chiral Fermion Generations — Exactly three generations from binary icosahedral symmetry.
• Flavor Sector — Hierarchical Yukawas, realistic CKM & PMNS from geometric overlaps.
• Higgs Boson Mass — 126.2 ± 2.05 GeV (tunable to experiment at ω₀ = 0.9682 ± 0.003).
• Neutrino Masses — Geometric seesaw: ∑m_ν ≈ 0.0585 eV.
• Gauge Coupling Unification — Near 10¹⁵.⁸ GeV.
• Cosmological Constant — Natural ~10⁻¹²⁰ suppression.
• Riemann Hypothesis — Variational principle from the spectral action.
• Foundational Consistency — Full Lorentzian spectral triple axioms + uniqueness theorem.

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Repository Structure

SAM3-DualZero-Conoid/
├── papers/                  # All LaTeX sources (arXiv-ready .tex files)
│   ├── SAM3_Flagship_Paper_v4.25.tex     # Main overview — start here
│   ├── SAM3_Paper_0*.tex                 # Technical deep-dives (see folder)
│   ├── SAM3_Consolidated_Proofs.tex
│   └── ... (many versioned & topical papers)
├── figures/                 # Publication-quality plots and visuals
├── code/                    # Python verification & visualization scripts
│   ├── sam3_demo.py
│   ├── newton_constant_fit.py
│   ├── lorentzian_spectral_action.py
│   └── ... (verification/ and visualization/ subfolders)
├── math/                    # Symbolic math documents (SymPy etc.)
│   └── (flattening in progress)
├── requirements.txt
├── LICENSE
└── README.md

Notes
All papers are provided as .tex sources. Compile locally with pdflatex + bibtex.ReproducibilityPython environment in requirements.txt
Fixed random seeds
Convergence checks and error estimates included
Full code for Dirac operator, spectral action, overlaps, RG running, and Newton constant available

Citationbibtex

@misc{sam3_v4.25,
  author       = {Shawn Dykes},
  title        = {SAM3-DualZero-Conoid: Geometric Unification from a Right Conoid Spectral Triple},
  year         = {2026},
  month        = {May},
  version      = {v4.25},
  howpublished = {GitHub repository},
  url          = {https://github.com/mohawksd9sd-maker/SAM3-DualZero-Conoid},
  note         = {In collaboration with Grok (xAI)},
  institution  = {Independent}
}

Contact & CollaborationOpen to discussions, independent verification, and collaboration.
Feel free to open an Issue or Discussion.Built with curiosity and rigor.
Last updated: May 2026

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