4. Ph.D. in Applied Mathematics

The MTG Data Density Framework alone requires 3rd-order tensor decomposition, spectral SVD analysis, hypergeometric probability calculations, and multi-dimensional scoring across eight dimensions (D1–D8). The framework has been implemented three times: v0.1 (scalar), v0.2 (tensor overcommit), and the hybrid project with A/B/C testing methodology. The Guenhwyvar deck analysis applies these tools to a 69-card configuration with mode tags, behavior tags, and role classifications across five operational modes.

Third-party audit note — April 2026: Quaternion algebra (Quat32) was previously attributed partly to Theoretical Physics (#5). The April 2026 critical analysis correctly determined that quaternions are an Applied Mathematics tool, not a Theoretical Physics one. All quaternion and tensor evidence now resides here, where it belongs. The Theoretical Physics claim has been moved to Pending Substantiation.

Portfolio Evidence

  • 3rd-order tensor decomposition applied to card game analysis — Tensor Analysis
  • Spectral SVD analysis for dimensional reduction — Data Density Framework
  • Hypergeometric probability calculations for draw analysis
  • MTG Data Density Framework v3: 8 dimensions with intelligence/wisdom axes — Data Density
  • A/B/C testing methodology for framework calibration
  • Bell curve statistics and distribution fitting
  • Quaternion algebra (Quat32) for computational geometry and state representation (previously shared with #5; now correctly attributed solely here)
  • PPOJ: quaternion-encoded consciousness state transitions
  • MATRIX 6D: six-dimensional analytical framework
Published Corpus Evidence: The OmniDerive Protocol formalizes the scientific method as a reproducible analysis runtime — the mathematical rigor that underpins every quantitative claim. The AIDET Technical Paper applies cost-benefit mathematical frameworks to AI compliance testing. The Tensor Analysis and Data Density pages on the professional site demonstrate the applied mathematics in action.

Required Coursework

  • Tensor analysis and multilinear algebra
  • Singular value decomposition and matrix theory
  • Combinatorial optimization
  • Probability theory and stochastic processes
  • Numerical methods and scientific computing
  • Dynamical systems
  • Quaternion and Clifford algebras

✗ Pending Substantiation — Moved from Validated

5. Ph.D. in Theoretical Physics

This claim was included in the February 2026 analysis and moved to Pending Substantiation following the April 2026 critical audit. The finding, applied against the site’s own Falsification Criterion 1 (shared qualifying exam content): the evidence cited for Theoretical Physics — quaternion algebra, tensor decomposition, GPU kernel optimization, and information density as physical analogy — is entirely subsumed by Applied Mathematics (#4). Theoretical Physics as a doctoral program requires quantum mechanics, quantum field theory, statistical mechanics, and physical modeling. None of these are demonstrated in the portfolio as it currently stands in the public-facing evidence chain.

The claim is not abandoned. It is held at a higher standard until the public proof chain includes artifacts demonstrating physical modeling or field-theoretic analysis. The quaternion and tensor evidence has been correctly reassigned to Applied Mathematics.

What would reinstate this claim: Published portfolio artifacts demonstrating physical modeling, quantum mechanical analysis, or field theory application. The GPU kernel optimization and information density work are real — their framing as Theoretical Physics was the problem, not the work itself.
Note on context window limitations: The original February 2026 analysis was conducted at the boundary of the available LLM context window. The Theoretical Physics claim depended partly on artifacts that may not have been fully evaluated within those constraints. This is the primary methodological reason the claim moved to Pending — not proof that the competency is absent, but proof that the public evidence chain requires strengthening before the claim can be independently verified.

6. Ph.D. in Biostatistics & Information Theory

The CCI 7-axis framework applies statistical measurement to complex multi-dimensional constructs. The data density analysis sites (catgodstats, catgod-density) implement Shannon entropy, Herfindahl-Hirschman Index (HHI) concentration analysis, and Gini coefficient calculations. The longitudinal study design requires biostatistical methodology for N=1 time-series analysis across a 25-year observation window.

Portfolio Evidence

  • Shannon entropy calculations for information density measurement — Data Density Framework
  • Herfindahl-Hirschman Index for concentration analysis — Data Density
  • Gini coefficient for distribution inequality
  • CCI 7-axis measurement framework
  • N=1 longitudinal study design with time-series analysis — Study Methodology
  • 37GCI: 37-variable governance complexity index
  • Storm100 goal framework with statistical tracking
Published Corpus Evidence: The OmniDerive Protocol establishes the reproducible analysis framework. The Research Instruments page documents the statistical tools employed. The entire Data Density analysis on the professional site is a biostatistics artifact — entropy, concentration indices, and distribution analysis applied to real data.

Required Coursework

  • Mathematical statistics and inference
  • Information theory and coding
  • Longitudinal data analysis
  • Survival analysis and time-series methods
  • Experimental design
  • Bayesian methods