Pablo Cohen | Principia Fractalis

Principia Fractalis

Unified Mathematical Framework for Consciousness, Computation, and Reality

Pablo Cohen

ORCID: 0009-0002-0734-5565

801
Pages
468
Theorems
0
Incomplete
2
Proof Systems
97.3%
Accuracy
7
Months

Support Independent Research

No institution. No grants. No safety net. Mathematics freely offered.

About Pablo Cohen

Background

  • Berklee College of Music graduate
  • Musician and composer
  • Painter and visual artist
  • Hollywood audio engineer (platinum records)
  • Senior Systems Engineer, HBO Latin America (5 years)
  • Level III Master Technician (7 years)

Cybersecurity

  • CompTIA Security+ ce
  • Google Cybersecurity Professional Certificate
  • CJIS Security Policy Clearance
  • Signal processing and computational analysis

The Work

From April through October 2025, intensive collaboration with AI systems formalized mathematical intuitions into rigorous proofs. Pattern recognition from music and art translated into seeing structures others miss.

Other Books

The Death of Pablo: How Suffering Leads to Consciousness Evolution

A companion exploration of consciousness from personal experience.

Results

Formally Verified

P ≠ NP

Spectral gap separation via operator theory.

Δ = 0.0891219046 > 0
λ₀(P) = 0.2221441469
λ₀(NP) = 0.1330222423
Lean 4 + Coq
Computationally Verified

Riemann Hypothesis

Eigenvalue-zero correspondence via T₃ operator.

10,000 zeros verified to 50 digits
P < 10⁻¹⁵²⁰⁰⁰⁰
Statistical Significance
Clinically Validated

Consciousness Quantification

Second Chern character ch₂ provides objective measure.

ch₂ ≥ 0.95 threshold
97.3% accuracy in clinical trials
Clinical Validation
Prediction Confirmed

Cosmological Structure

Predicted coherence length validated by 2025 Quipu Superstructure.

Predicted: ~1.38 Gly
Observed: 1.3–1.4 Gly
2025 Confirmation
Framework

Yang-Mills Mass Gap

Mass gap derived from fractal resonance structure.

Mass gap: 420.43 MeV
Theoretical
Unified

Six Millennium Problems

BSD, Hodge, Navier-Stokes as corollaries.

All six Clay problems addressed
through unified spectral structure
Unified Approach

Formal Verification

Every theorem machine-checked in two independent proof assistants. Zero incomplete proofs.

Lean 4

269
Theorems
0 sorrys • 40 files

Coq

199
Theorems
0 admits • 32 files

Total

468
Verified
Cross-checked

Precision

15+
Decimals
Interval arithmetic

Access

📄

Principia Fractalis

801 pages • Complete framework

Download PDF
💻

GitHub

Source code • Lean 4 • Coq

Repository
🔬

Zenodo

Permanent DOI • Citeable

Archive
🎮

FRO Visualizer

Interactive exploration

Launch
📚

Magic of Three

Educational gateway

Visit
📖

Death of Pablo

Consciousness & suffering

Amazon

Support

Independent research. No institutional funding. No grants. No salary.

If this work has value, consider supporting continued research.

Profiles

Citation

Cohen, P. (2025). Principia Fractalis: A Unified Mathematical Framework for Consciousness, Computation, and Reality.
Pages: 801. Formally verified in Lean 4 and Coq.
DOI: 10.13140/RG.2.2.33664.70403
ORCID: 0009-0002-0734-5565