Lukas Geiger

Functional Stability Theory III: Biological Stability and Nash Frustration

A conjectural framework for biological organization spanning molecular to ecosystem scales, organized around thermodynamic game theory and the Maximum Entropy Production Principle (MEPP). The paper examines whether many biological stability problems can be modeled as dissipative...

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

The abc Gap Series: Part 3 — certify the bricks Part 3 of the abc Gap Series — a connected sequence of preprints studying proposed form audits and transfer arguments in the Mochizuki/Joshi approaches to the abc conjecture (Part 1: Forensic Diagnosis, DOI 10.5281/zenodo.21899747;...

The Comparison in IUTchIII, Corollary 3.12: From Attempted Repair to Structural Diagnosis

The abc Gap Series: Part 1 — a corrected classical comparison Corrective revision of the proposed comparison at Corollary 3.12. We revisit an attempted classical repair of the comparison at Corollary 3.12 of IUTchIII. For a real analytic parameter q in (0,1), torsion-normalized J...

Construction-Conditioned Potential-Game Diagnostics for Chaperone Models

We audit explicitly constructed 2×2 chaperone and fold-switching games with the exact potential-game test of Monderer & Shapley (1996). Shared interaction contrasts produce PG games by construction; asymmetric contrasts can produce non-PG games. This modeling convention is motiva...

Prompt Archaeology: A Five-Stage Protocol for Documenting and Analysing Human-AI Research Dialogues

Prompt Archaeology proposes a five-stage protocol for retrospectively documenting, classifying, and descriptively analysing the recoverable prompt exchanges that shaped a human-AI research project, including human-to-LLM, LLM-to-sub-agent, and cross-model prompts. As large langua...

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 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...

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 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...