Lukas Geiger

The Embodied Relational Constructivist Self-Framework (ERCS): An Integrative Conceptual Framework for Developmental Psychology

This theoretical review introduces the Embodied Relational Constructivist Self-Framework (ERCS), an integrative developmental framework linking constructivist, self-psychological, attachment-theoretical and embodied-cognition traditions. The paper is the first article in a planne...

The Curvature Relaxation Model: A Four-Paper Program for Geometric Cosmology Without the Dark Sector

A four-paper series presenting the Curvature Relaxation Model (CRM), a geometric framework that derives dark-matter phenomenology from scalar-curvature dynamics without postulating new particles. CORE-PAPERS Paper I: Game-Theoretic Foundation — Establishes the CRM through thermod...

The Bridge Certificate: A Line-Level Audit Instrument for Inter-Theoretic Transfer Arguments, with Four Applications to the abc Literature (DRAFT)

Part 3 of the abc Gap Series — a connected sequence of papers that locate, formalize, verify, and repair the central gap in the Mochizuki/Joshi approaches to the abc conjecture (Part 1: Forensic Diagnosis, DOI 10.5281/zenodo.21899747; tool supplement: DOI 10.5281/zenodo.21924253)...

The Bridge Certificate: A Line-Level Audit Instrument for Inter-Theoretic Transfer Arguments, with Four Applications to the abc Literature (DRAFT)

Part 3 of the abc Gap Series — a connected sequence of papers that locate, formalize, verify, and repair the central gap in the Mochizuki/Joshi approaches to the abc conjecture (Part 1: Forensic Diagnosis, DOI 10.5281/zenodo.21899747; tool supplement: DOI 10.5281/zenodo.21924253)...

A Conditional Height-Dominance Architecture for Beal's Conjecture: A Zookeeper-Style Reduction with a Power-Residue Sieve Companion (DRAFT)

This paper formulates a conditional reduction architecture for Beal's conjecture alongside an effective power-residue sieve companion. Positioned within the Height-Dominance and Zookeeper reduction series, the manuscript approaches Beal's conjecture ($A^x + B^y = C^z$ with $\gcd(...

A Conditional Height-Dominance Architecture for Beal's Conjecture: A Zookeeper-Style Reduction with a Power-Residue Sieve Companion (DRAFT)

This paper formulates a conditional reduction architecture for Beal's conjecture alongside an effective power-residue sieve companion. Positioned within the Height-Dominance and Zookeeper reduction series, the manuscript approaches Beal's conjecture ($A^x + B^y = C^z$ with $\gcd(...

Functional Stability Theory III: Biological Stability and Nash Frustration

DRAFT version. This preprint is part of an active research programme and remains subject to revision, correction, and journal review. A conjectural framework for biological organization spanning molecular to ecosystem scales, organized around thermodynamic game theory and the Max...

The abc Landscape: Obstructions, Failed Routes, and HCT Diagnostics (DRAFT)

This paper systematizes a sequence of Frey-curve approaches to the abc conjecture and shows why they stop short — deliberately negative, but structural. The routes examined arose from theta products, Tate uniformisation, Tamagawa budgets, period lattices, modular degrees, level l...

Functional Stability Theory II: Chemical Stability and Autocatalytic Selection

A game-theoretic framework for prebiotic chemistry, interpreting autocatalytic networks, hypercycles, and chirality selection as Nash-equilibrium-like structures of thermodynamic games. Building on Dynamic Kinetic Stability (DKS) and the England inequality, we propose that the Ma...

QG-CRM: Ultraviolet Completion of the Curvature Relaxation Model via Quantum Quadratic Gravity

```html Paper VI of the Curvature Relaxation Model (CRM) series. DRAFT We present QG-CRM, the ultraviolet-completed Curvature Relaxation Model. The γR² term in the CRM Lagrangian admits a natural UV completion via asymptotically free quantum quadratic gravity (QQG), following Liu...