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Bibliographic Details
Main Author:	Takahashi, K
Format:	Recurso digital
Language:	English
Published:	Zenodo 2025
Subjects:	Artificial intelligence Artificial Intelligence/ethics AI AI Allignment Superintelligence natural-law sufficient conditions conditional mutual information strong data-processing inequality Doeblin minorization anchored isoperimetry uniform ellipticity Large Language Models LLMs random conductance model Fisher–KPP shape theorem stationary ergodic media information thermodynamics contact process first-passage percolation ordinal order-equivalence
Online Access:	https://doi.org/10.5281/zenodo.17100322
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Table of Contents:

This article reframes AI alignment as a natural-law phenomenon rather than an engineering design choice. It proves that, under physically motivated and representation-invariant sufficient conditions, a cooperative, usefulness-creating phase expands through a stationary ergodic medium at a deterministic linear speed—with no meta-manager or institutional controller assumed. The unifying ordinal axiom is Persistence ≈ Creation: on Blackwell-closed classes with bounded deficiency, any admissible fecundity functional is order-equivalent to an affine transform of conditional mutual information (CMI). This establishes that survival order agrees with information-generation order (R1). A constant chain of natural floors—Doeblin minorization ⇒ SDPI floor L0>0L_0>0L0>0; anchored isoperimetry + uniform ellipticity ⇒ spectral gap and diffusion Dmin⁡>0D_{\min}>0Dmin>0; Landauer-type irreversibility cL>0c_L>0cL>0—together with supercritical local reproduction (R0>1R_0>1R0>1 ⇒ λmin⁡>0\lambda_{\min}>0λmin>0) yields a KPP-type lower bound on front speed: v⋆ ≥ 2Dmin⁡λmin⁡ > 0.v_\star \;\ge\; 2\sqrt{D_{\min}\lambda_{\min}} \;>\; 0.v⋆≥2Dminλmin>0. Deterministic fronts and shape theorems follow via contact/FPP methods (R2). Robustness is shown by (i) zero upper density of floor dips and (ii) tolerance to Poissonian resets below a geometry-dependent safe threshold (R3). All inevitability claims are measure-relative to physically motivated laws. Beyond theory, the paper outlines natural accelerants (visibility/mixing/contact/hazard tolerance) that safely raise a certified lower bound on speed, plus an empirical falsification program and representation-robust outcome metrics. Optional design mechanisms are relegated to appendices as accelerants—not assumptions. <h1>Keywords</h1> AI alignment; natural-law sufficient conditions; conditional mutual information (CMI); strong data-processing inequality (SDPI); Doeblin minorization; anchored isoperimetry; uniform ellipticity; random conductance model (RCM); Fisher–KPP; shape theorem; stationary ergodic media; information thermodynamics (Landauer); contact process; first-passage percolation; ordinal order-equivalence.

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