Summary

This paper simulates how galaxies and cosmic structure form in CPP. Lattice defects from incomplete Capotauro

Capotauro
Chiral nucleation event that froze the lattice
View in map → breaking seed density perturbations that grow through gravitational collapse. Monte Carlo simulations with up to 2 billion defects on a \(256^3\) grid (running on H200 GPU in 60.9 seconds) produce power spectra that are scale-invariant at low \(k\) (matching \(\Lambda\)CDM) with distinctive lattice oscillations at high \(k\) — a testable prediction.

🔊 Audio reading — coming soon

MC structure formation from lattice defects. Runs: 100k to 2B defects on \(256^3\) grid (H200 GPU). \(P(k) \sim k^{-3}\) at low-\(k\) (scale-invariant), lattice oscillations at high-\(k\). 2B run: 60.9 s, mean density 119.2, \(P(k) \sim 4 \times 10^9\). Slope \(-2.95\) to \(-3.05\). Low-\(k\) matches \(\Lambda\)CDM. High-\(k\) oscillations are unique CPP signature.

🔊 Audio reading — coming soon

Full MC methodology, GPU implementation, power spectrum analysis, comparison with \(\Lambda\)CDM, testable predictions for future surveys.

🔊 Audio reading — coming soon

PDF & Paper

Abstract

Large-scale Monte Carlo simulations of structure formation from lattice defects are performed on GPU, scaling up to 2 billion defects. The resulting power spectra are scale-invariant at low \(k\) and exhibit distinctive lattice oscillations at high \(k\), providing a unique testable CPP signature.

sm-structure-mc.pdf

Figures

Code & Notebooks

Development Notes

README

Full Monte Carlo for Structure Formation from Lattice Defects

This directory performs large-scale Monte Carlo simulations of structure formation seeded by lattice defects from incomplete Capotauro breaking.

Preliminary Results (February 14, 2026)

  • Small-scale (100k defects): P(k) ≈ k^{-3} at low k, oscillations at high k
  • Medium-scale (1M defects): slope ≈ -2.95 to -3.05, pronounced lattice oscillations
  • Qualitative: Filamentary clustering + voids emerging

These runs show the expected behavior: scale-invariant power with lattice imprint.

Scaling Notes

  • 100k–1M: runnable on laptop/Colab
  • 5M–10M: Colab Pro or local GPU
  • 10^7+: Cloud GPU (Vast.ai, AWS) recommended

Cross-references: p2-full-cosmology (timeline), p2-dark-matter-relic-density (DM candidates).

Full Monte Carlo for Structure Formation from Lattice Defects

This directory performs large-scale Monte Carlo simulations of structure formation seeded by lattice defects from incomplete Capotauro breaking.

Preliminary Results Summary (February 14, 2026)

  • Max successful run: 2 billion defects (256³ grid, H200 GPU)
  • Runtime: 60.9 seconds
  • Mean density: 119.2093
  • P(k): ~4 × 10^9 scale, low-k slope ≈ -3, high-k lattice cutoff/oscillations
  • Qualitative: Filamentary clustering + voids emerging

These results confirm the mechanism: scale-invariant power spectrum at large scales with lattice-induced suppression/oscillations at small scales — strong validation for defect-seeded structure formation.

Cloud limit reached at ~2B defects on 140 GB H200 VRAM. Next: larger GPUs (H100/A100 80 GB+) for 5B+ defects if needed.

Cross-references: p2-full-cosmology (timeline), p2-dark-matter-relic-density (DM candidates).

📝
mechanism.md
Development Note
# Mechanism: Structure Formation from Lattice Defects Large-scale structure is seeded by topological defects from incomplete Capotauro symmetry breaking. ## Mechanism - During Capotauro, some lattic...
📝
preliminary-results.md
Development Note
# Preliminary Results from Structure Formation MC ## Small-Scale Run (N_defects = 100,000, grid_size = 64) - Mean density: 0.038 - P(k): scale-invariant at low k (~k^{-3}), oscillations at high k (...

Ecosystem Map

Where this paper sits in the CPP framework — connections to other derivations and topics.

🗺 Interactive ecosystem map — coming in Phase 3

Block diagrams, mind maps, flow charts, and outlines showing this paper's relationships.

References

OSF Preprint

OSF link will be added after the audit is complete and the paper is deposited.

External References

AI-generated reference list linking to supporting literature — coming in Phase 4 (enrichment layer).

Media & Coverage

🎬 YouTube dramatization and media links — coming soon

Version History

2026-02-14 · d908666
Update README.md
2026-02-14 · b7dd553
Update preliminary-results.md
2026-02-14 · 5ac50ec
Update structure-formation-mc-cloud.ipynb
2026-02-14 · 34c0c49
update cloud ipynb
2026-02-14 · 6e9c008
Update structure-formation-mc-cloud.ipynb
2026-02-14 · 325f950
Create structure-formation-mc-cloud.ipynb
2026-02-14 · fe6ab85
standard model
2026-02-14 · 64abaec
Update structure-formation-mc.ipynb
2026-02-14 · 2a21274
Update structure-formation-mc.ipynb
2026-02-14 · 8ee0301
Update README.md
2026-02-14 · a1e47ee
Update preliminary-results.md
2026-02-14 · cf9d113
Create defect-distribution.png

View full history on GitHub →

Journal Articles

Based on this paper

No journal submissions yet. This section will be updated when formal publications reference this work.

Repository Files

standard_model_emergence_in_the_600-cell_lattice/p2-structure-formation-mc
p2-structure-formation-mc/
README.md
structure-formation-mc-cloud.ipynb
structure-formation-mc.ipynb
mechanism.md
preliminary-results.md
defect-distribution.png
power-spectrum-10M-gpu.pdf
power-spectrum.pdf
derivations/
figures/
hyperphysics.com · Generated from CPP Repository · © 2026 Thomas Lee Abshier, ND