All papers are freely available. Cite via DOI. Each paper is a self-contained contribution — you do not need the full series to read any one paper.
Zenodo · 10.5281/zenodo.19117400
Principia Orthogona, Volume One
The Mathematics of Generative Transitions. Abstract operator algebra, the operator sequence C → K → F → U defined and proved. Singularity classification (Whitney A1–A3), symplectic preservation theorem, curvature threshold κ*. The foundation.
Zenodo · 10.5281/zenodo.19379473
Principia Orthogona, Volume Two
Contact Realization of Generative Transitions. Explicit contact-geometric realization of Volume One. Threshold Equivalence theorem: |κ| ↑ κ* ⟺ μ_max < 0 ⟺ τ ∈ (0,∞). Four dm³ bifurcations ↔ Whitney A1–A3 singularity types. Submitted to IMPA.
Zenodo · 10.5281/zenodo.19122168
Generative Contact Mechanics
A Geometric Framework for Dissipative Systems with Structured Limit Cycles. Complete operator algebra (g-, L-, R-, U-operators). Universal contact normal form (μ_max, ω, β). Stability radius ε₀ = 1/3. Submitted to Journal of Geometric Mechanics.
Zenodo · 10.5281/zenodo.19379385
The dm³ Operator — Explicit Toy Model
Global Dynamic Analysis on contact manifold M = ℝ²×ℝ. Canonical invariant triple (T*, μ_max, τ) = (2π, −2, 2). Global attractor Γ₁₂, four bifurcations, stochastic concentration below embodiment threshold τ = 2. Submitted to SIAM J. Applied Dynamical Systems.
Zenodo · 10.5281/zenodo.19162013
The G6 Crystal
A dm³-derived architectural form for resonance-stable tall structures. Six applications of G yield a hexagonal tower with aspect ratio 66 = 33·τ. Passive Schumann n=4 resonance coupling at 33.516 Hz via Arnold tongue A4:1. Noise tolerance τ·ε₀ = 2/3.
Zenodo · 10.5281/zenodo.19378742
The Collatz Conjecture as a Corollary of Crystal Geometry
Supplement to the Crystal Paper. The coefficient c = 3 in 3n+1 is the fingerprint of triad stabilisation (3×11 = 33). The conjecture is visible from within crystal geometry before it is provable within it. The polar vortex is the empirical certificate.
Zenodo · 10.5281/zenodo.19208015
Biological Transitions as Multi-Agent Realisations of TO/TOGT
Neural oscillations, HPA-axis stress response, circadian regulation, immune adaptation, and protein conformational change modelled as multi-agent realisations of G = U∘F∘K∘C. Fixed-point, contraction, and saturated pitchfork results applied.
Zenodo · 10.5281/zenodo.19210137
Fruit-Fly Connectome Toy Model
Biological Transitions as Multi-Agent Realisations of TO/TOGT: A Drosophila connectome toy model. Neural clusters as coupled agents whose trajectories stabilise under six applications of G. Reproduces neural coherence, oscillatory entrainment, and stress-response switching.
Zenodo · 10.5281/zenodo.19208284
The Swarm Simulator
A Dynamical Systems Model of Collective Intelligence using the TO/TOGT Operator Pipeline. Four collective operators: shared-intent stability It, coordination efficiency Ct, type-propagation multiplier Mt, diffusion factor Ft. All results proved from established theorems.
Zenodo · 10.5281/zenodo.19210058
Mathematical Foundations of Multi-Orbit Identity Theory
Identity orbits defined as operator-generated closed trajectories with invariant structure within the TO/TOGT framework. U-, R-, L-, and B-operator families. Categorical invariants and compositional operator algebra. Mathematically independent of speculative cosmological models.
Zenodo · forthcoming
Additional Papers
GTCT — The Generative Time Circuit Theorem (Ring 5) · Wavenumber 6: Orthogenetic Stability Generator · The dm³ Criticality Principle · The Number 33. DOIs will appear here upon publication.
Links to be added
