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2025
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| Online Access: | https://doi.org/10.5281/zenodo.17100322 |
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| author | Takahashi, K |
| author_facet | Takahashi, K |
| contents | <p>This article reframes AI alignment as a <strong>natural-law</strong> phenomenon rather than an engineering design choice. It proves that, under physically motivated and representation-invariant <strong>sufficient conditions</strong>, a cooperative, usefulness-creating phase expands through a stationary ergodic medium at a <strong>deterministic linear speed</strong>—with <strong>no meta-manager or institutional controller assumed</strong>.</p> <p>The unifying <strong>ordinal</strong> axiom is <em>Persistence ≈ Creation</em>: on Blackwell-closed classes with bounded deficiency, any admissible fecundity functional is order-equivalent to an affine transform of <strong>conditional mutual information (CMI)</strong>. This establishes that survival order agrees with information-generation order (R1).</p> <p>A <strong>constant chain</strong> of natural floors—Doeblin minorization ⇒ SDPI floor <span><span>L0>0L_0>0</span><span><span><span><span>L</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>; anchored isoperimetry + uniform ellipticity ⇒ spectral gap and diffusion <span><span>Dmin>0D_{\min}>0</span><span><span><span><span>D</span><span><span><span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>; Landauer-type irreversibility <span><span>cL>0c_L>0</span><span><span><span><span>c</span><span><span><span><span><span><span>L</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>—together with <strong>supercritical local reproduction</strong> (<span><span>R0>1R_0>1</span><span><span><span><span>R</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>1</span></span></span></span> ⇒ <span><span>λmin>0\lambda_{\min}>0</span><span><span><span><span>λ</span><span><span><span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>) yields a <strong>KPP-type lower bound</strong> on front speed:</p> <p><span><span><span>v⋆ ≥ 2Dminλmin > 0.v_\star \;\ge\; 2\sqrt{D_{\min}\lambda_{\min}} \;>\; 0.</span><span><span><span><span>v</span><span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>≥</span></span><span><span>2</span><span><span><span><span><span><span><span>D</span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span><span></span></span><span>λ</span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span><span></span></span></span></span></span><span></span></span></span></span><span>></span></span><span><span>0.</span></span></span></span></span></p> <p>Deterministic fronts and shape theorems follow via contact/FPP methods (R2). <strong>Robustness</strong> is shown by (i) zero upper density of floor dips and (ii) tolerance to <strong>Poissonian resets</strong> below a geometry-dependent safe threshold (R3). All inevitability claims are <strong>measure-relative</strong> to physically motivated laws.</p> <p>Beyond theory, the paper outlines <strong>natural accelerants</strong> (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.</p> <h1>Keywords</h1> <p>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.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17100322 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | "Persistence ≈ Creation": Natural-Law Sufficient Conditions for Almost-Sure Beneficial Coverage in Stationary Ergodic Media (No Meta-Design) Takahashi, K 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 <p>This article reframes AI alignment as a <strong>natural-law</strong> phenomenon rather than an engineering design choice. It proves that, under physically motivated and representation-invariant <strong>sufficient conditions</strong>, a cooperative, usefulness-creating phase expands through a stationary ergodic medium at a <strong>deterministic linear speed</strong>—with <strong>no meta-manager or institutional controller assumed</strong>.</p> <p>The unifying <strong>ordinal</strong> axiom is <em>Persistence ≈ Creation</em>: on Blackwell-closed classes with bounded deficiency, any admissible fecundity functional is order-equivalent to an affine transform of <strong>conditional mutual information (CMI)</strong>. This establishes that survival order agrees with information-generation order (R1).</p> <p>A <strong>constant chain</strong> of natural floors—Doeblin minorization ⇒ SDPI floor <span><span>L0>0L_0>0</span><span><span><span><span>L</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>; anchored isoperimetry + uniform ellipticity ⇒ spectral gap and diffusion <span><span>Dmin>0D_{\min}>0</span><span><span><span><span>D</span><span><span><span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>; Landauer-type irreversibility <span><span>cL>0c_L>0</span><span><span><span><span>c</span><span><span><span><span><span><span>L</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>—together with <strong>supercritical local reproduction</strong> (<span><span>R0>1R_0>1</span><span><span><span><span>R</span><span><span><span><span><span><span>0</span></span></span><span></span></span></span></span></span><span>></span></span><span><span>1</span></span></span></span> ⇒ <span><span>λmin>0\lambda_{\min}>0</span><span><span><span><span>λ</span><span><span><span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span></span><span></span></span></span></span></span><span>></span></span><span><span>0</span></span></span></span>) yields a <strong>KPP-type lower bound</strong> on front speed:</p> <p><span><span><span>v⋆ ≥ 2Dminλmin > 0.v_\star \;\ge\; 2\sqrt{D_{\min}\lambda_{\min}} \;>\; 0.</span><span><span><span><span>v</span><span><span><span><span><span><span>⋆</span></span></span><span></span></span></span></span></span><span>≥</span></span><span><span>2</span><span><span><span><span><span><span><span>D</span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span><span></span></span><span>λ</span><span><span><span><span><span>m</span><span>i</span><span>n</span></span></span></span><span></span></span></span></span></span><span></span></span></span></span><span>></span></span><span><span>0.</span></span></span></span></span></p> <p>Deterministic fronts and shape theorems follow via contact/FPP methods (R2). <strong>Robustness</strong> is shown by (i) zero upper density of floor dips and (ii) tolerance to <strong>Poissonian resets</strong> below a geometry-dependent safe threshold (R3). All inevitability claims are <strong>measure-relative</strong> to physically motivated laws.</p> <p>Beyond theory, the paper outlines <strong>natural accelerants</strong> (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.</p> <h1>Keywords</h1> <p>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.</p> |
| title | "Persistence ≈ Creation": Natural-Law Sufficient Conditions for Almost-Sure Beneficial Coverage in Stationary Ergodic Media (No Meta-Design) |
| topic | 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 |
| url | https://doi.org/10.5281/zenodo.17100322 |