The Geometry of Admissible Computation: A Unified Thermodynamic Framework

Abstract

This dataset contains the theoretical proofs and experimental verification for the Inverse Scaling Law (ISL). We propose that thermodynamic constraints impose a hard physical barrier on non-modular computation.

Included Materials:

• ISL_Framework_Paper.pdf: Unified theoretical paper (Typeset).
• supplementary_proofs/: Detailed Theorem Proofs (PDFs).
  • Theorem_01_Modularity.pdf
  • Theorem_04_Reuse.pdf
  • Theorem_07_Scope.pdf
• code/kill_switch_experiment.py: Source code for the generalization gap experiment.
• figures/: High-resolution verification plots.

Key Results:

Experimental validation confirmed a 38x efficiency gap between modular and monolithic architectures in data-starved regimes, supporting the Information Reuse Bound ($T \propto 1/R$).

References:

• Landauer, R. (1961). Irreversibility and heat generation in the computing process. IBM Journal of Research and Development.
• Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal.
• Gromov, M. (1987). Hyperbolic groups. Essays in Group Theory.
• Bridson, M. R., & Haefliger, A. (1999). Metric spaces of non-positive curvature. Springer.
• Kolmogorov, A. N. (1965). Three approaches to the quantitative definition of information. Problems of Information Transmission.
• Bekenstein, J. D. (1981). Universal upper bound on the entropy-to-energy ratio for bounded systems. Physical Review D.