Independent Research · 2026

Generative Geometry

A structural framework for how change moves — derived from first principles and tested across domains.

Every dissipative process — from stellar evolution to protein folding to cancer progression to transformer models — follows the same internal geometry. Two irreducible operations interact in a mandatory cyclic order, producing four phases, sixteen positions, and a generative property: each completed cycle produces higher order than the one before.

These papers develop the framework from its mathematical foundations and apply it across physics, biology, medicine, and technology. Each paper is independent and falsifiable.

Papers published

Scientific domains

384/384

Positions mapped

13 Mar 2026

Publication date

The Framework

Change is not random. It has a structure. That structure is the same at every scale.

Generative Geometry proposes that all dissipative processes — processes that consume energy and produce order — are governed by the same internal logic. Two operations, irreducible to each other, interact in a fixed cyclic order. One holds: it maintains coherence, resists separation, confines. The other crosses: it mediates exchange, enables encounter, moves across boundaries. Their interaction produces exactly four phases, each one the required input for the next. The sequence cannot be reversed.

Each cycle is a spiral, not a loop. What comes out is always more organised than what went in. This generative property — the third mechanism alongside mutation and selection, alongside force and field — is what the papers test and apply.

Operation one

Hold

Maintains coherence. Resists separation. Confines. In physics: gravity and the strong force. In biology: structural stabilisation. In teams: shared purpose.

Operation two

Cross

Enables encounter. Mediates exchange. Moves across boundaries. In physics: electromagnetism and the weak force. In biology: functional interaction. In teams: role encounter.

H × C = 4 → Φ > 0

H = hold · C = cross · Φ = generative output

All Papers · Zenodo · March 2026

Foundation

Structural reference

The First Principles of Change

A Structural Reference for the Universal Dissipative Process Sequence

Defines the complete framework: two fundamental operations, four regimes, four singularity events, sixteen positions, sixteen first principles, and one mandatory cyclic order. Does not present evidence — that is published separately. The reference paper for independent researchers who want to apply or evaluate the framework in their own domain.

13 March 2026 DOI: 10.5281/zenodo.19007201

Physics

Fundamental forces

The Code Truth

A Hypothesis on the Geometric Unification of Fundamental Forces

The four fundamental forces do not converge into one at high energies — they are organised by a geometric pattern. Two irreducible axes, each carrying two complementary forces, whose cyclic interaction produces the observable universe. The normalised gravitational and QCD beta functions differ by exactly one power of the coupling constant, confirming within-axis correspondence. The cycle integral Φ > 0 is tested against published nanocrystal recrystallisation data and confirmed. Six testable predictions follow.

13 March 2026 DOI: 10.5281/zenodo.19007157

Quantum coherence · r = −0.91

Six Directives for Quantum Coherence

From a Structural Principle the Field Has Not Considered

A trapped ytterbium ion at room temperature holds quantum coherence six million times longer than a superconducting transmon at 15 millikelvin. The field has no unifying explanation. A cross-platform analysis of ten qubit implementations shows coherence time correlates with internal structural depth (r = −0.91, R² = 83%) and does not correlate with operating temperature (r = +0.33). Each additional depth level costs approximately 77× in coherence time. Six engineering directives follow: the primary target is not the environment around the qubit but the structure within it.

13 March 2026 DOI: 10.5281/zenodo.19007461

Universal Sequence & Evidence

24 systems · 7 domains · 384/384

There Is Only One Way to Grow

The Universal Sequence of Dissipative Processes

Twenty-four dissipative processes drawn from astrophysics, chemistry, molecular biology, embryology, ecology, geophysics, and human systems follow the same sixteen-step sequence when mapped against strict relational definitions. All twenty-four systems map at 100% (384/384 positions). The sequence is logically necessary: each step requires the output of its predecessor, and no alternative order satisfies the constraints. Process universality: a single internal geometry shared by all dissipative processes, from stellar evolution to protein folding to soil formation.

13 March 2026 DOI: 10.5281/zenodo.19007180

Fractal resolution · 30% → 97.5%

Fractal Depth Resolves the Conservation Degeneracy

How going one level deeper eliminates the mapping residual

The universal sequence paper reported 88.8% mapping fidelity across 20 systems, with the 11.2% mismatch concentrated at positions 14–15 in the conservation regime. This update tests whether going one fractal level deeper — mapping positions 14 and 15 at 64-position resolution — resolves the degeneracy. Ten systems mapped at the deeper resolution produce 80 sub-positions. Fidelity at positions 14 and 15 rises from 30% to 97.5%. The framework predicts its own resolution limit and the method to overcome it.

13 March 2026 DOI: 10.5281/zenodo.19007279

Biology & Evolution

Genetic code · Evolution

The Third Mechanism

Evidence from the Genetic Code for a Generative Property of Dissipative Cycling

Evolutionary theory invokes two mechanisms: mutation produces variation; selection shapes it. This paper proposes a third: a generative property intrinsic to dissipative cycling, in which each passage through a cycle produces higher informational order than the one before. Chemical evidence from the genetic code shows codon structure is organised by exactly two operations in a mandatory cyclic order — invariant across all 37 known genetic code variants in 4 billion years of evolution. Three independent lines of published evidence are unified: spontaneous gene duplication, Constructive Neutral Evolution, and the Lenski Long-Term Evolution Experiment.

13 March 2026 DOI: 10.5281/zenodo.19007207 Code on GitHub →

Intervention & Medicine

Intervention framework · 8 strategies

The Geometry of Intervention

Eight strategies for influencing any four-phase process, derived from first principles

Derives a complete framework for intervening in any process that proceeds through four sequential phases. Eight strategies (four to resist a crossing, four to enable it), a formula for the effectiveness of each — Crossing(k) = P&sub0; × r^k — a proof that no strategy is geometrically privileged over any other, and structural conditions that determine which strategies are available at each point. Going one fractal level deeper and covering all four sub-phases within any single phase produces approximately 96% blockade regardless of which phase is chosen.

13 March 2026 DOI: 10.5281/zenodo.19007218

Oncology · 36 intervention points

A Structural Argument for Multi-Angle Cancer Intervention

What the mathematics of sequential thresholds predicts about combination therapy

If cancer is a dissipative system running a sixteen-step cycle, every step contains a threshold that must be crossed for the tumour to advance. The mathematics of sequential gates shows that attacking a threshold at all four of its sub-steps blocks 99% of crossings, while attacking a single sub-step blocks only 70%. Four moderate drugs beat one miracle drug. Thirty-six intervention points are identified across nine actionable positions in the tumour lifecycle, with the molecular target and existing drug named at each. 89% are approved or in clinical trials.

13 March 2026 DOI: 10.5281/zenodo.19007259

Extinction therapy · Cancer ecology

The Four Ecological Perturbations

A structural prediction for extinction therapy derived from the geometry of intervention

Gatenby et al. (2020) demonstrated cancer extinction through a two-step strategy. They identified four categories of second-strike perturbation: habitat disruption, demographic perturbation, predator introduction, and foraging restriction. This paper proposes these four categories are the four operations of Generative Geometry. Three testable predictions follow: all four categories are equally effective; covering all four simultaneously should produce ~96% blockade regardless of timing; and the escalation sequence (widen before deepen, deepen before force) should outperform all alternative orderings. Testable in the existing Gillespie simulation framework.

13 March 2026 DOI: 10.5281/zenodo.19007347

Technology

AI · Transformer models

Why Generative AI Generates

A structural explanation for emergence in transformer models

Why does stacking layers produce qualitatively new capabilities? Why do emergent abilities appear at sharp thresholds rather than gradually? Each transformer layer applies four sequential operations to the output of the previous layer; each layer's processing changes the representation on which the next layer operates. The model generates because the recursive structure prevents it from merely retrieving. Three testable predictions follow: layer ablation should show non-linear degradation with middle layers contributing most; information distance per layer should be strictly positive and super-additive; deep narrow models should generate more than shallow wide models at matched parameter count.

13 March 2026 DOI: 10.5281/zenodo.19007402

Raimo van der Klein, 2026. All papers published open access under CC BY 4.0.
The framework is developed further in Riding Change: How Change Moves, and How to Move With It.
Hardcover · IngramSpark · Q2 2026 · ISBN 978-90-836865-0-9