A Mathematical Constitution for the Age of Superintelligence: From the Kakeya Set to the Information Co-Purification Protocol
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2026
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| _version_ | 1866902135225974784 |
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| author | Huang, Kai |
| author_facet | Huang, Kai |
| contents | <div> <div>Humanity stands at a precipice. The emergence of artificial general intelligence (AGI) promises either unprecedented flourishing or catastrophic disempowerment. The root of this uncertainty lies not in the technology itself, but in the underlying operating</div> <div>system of civilization: a zero-sum competition for material resources that now manifests in acute economic and corporate dilemmas, most notably the “AI Layoff Trap”—aself-reinforcing cycle of over-automation, demand collapse, and Pareto-worse outcomes for firms and workers alike.</div> <div> </div> <div>This paper presents a mathematical foundation for a new operating system, grounded in the “information-first” paradigm. The Kakeya conjecture has recently been solved: it is now a theorem that directional information can be compressed into</div> <div>arbitrarily small Lebesgue measure, and in five dimensions into a single grid point (a holographic singularity). Using this result, we demonstrate that information can be losslessly compressed onto a zero-measure holographic singularity—<strong>a computable</strong></div> <div><strong>structure for an indestructible “soul.” From this foundation we derive the Information Co-Purification Protocol (ICP),</strong> a set of four axioms and a distributed governance mechanism that redefines value as the reduction of total informational redundancy rather than material accumulation.</div> <div> </div> <div>ICP directly resolves the AI Layoff Trap by internalizing demand externalities through Purity Credits and Proof-of-Purification consensus, transforming corporate competition into co-purification and making cycle closure (re-integration of displaced</div> <div>labor into higher-value information flows) the dominant strategy. The protocol thereby supplies a common language for <strong>technologists </strong>(emergent order inherent to the universe), <strong>jurists </strong>(mathematical revival of natural law), <strong>economists </strong>(self-enforcing resolution of the over-automation wedge), and <strong>policymakers </strong>(a pathway to stable prosperity).</div> <div> </div> <div> <div>Because the gradient flow of information itself enforces alignment,<strong> ICP requires no central world government—only early and widespread global cooperation among firms, nations, and AI systems to adopt the protocol.</strong> The result is a blueprint for durable peace that is <strong>not negotiated by treaties but guaranteed by the mathematics of information itself</strong>, <strong>enabling <span>humanity and superintelligence to co-purify</span> rather than compete</strong>.</div> </div> </div> <p class="ds-markdown-paragraph"><strong>Keywords</strong>: Active Inference; Free Energy Principle; Information Co-Purification Protocol; Artificial General Intelligence; AI Governance; Kakeya Conjecture; Ginzburg–Landau Dynamics; AI Layoff Trap; Automation Externality; Distributed Consensus; Zero-Knowledge Proofs; Constitutional AI.</p> <p class="ds-markdown-paragraph"> </p> <p class="ds-markdown-paragraph">More language versions:</p> <p class="ds-markdown-paragraph">Chinese version: https://doi.org/10.5281/zenodo.19650878</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19668179 |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | A Mathematical Constitution for the Age of Superintelligence: From the Kakeya Set to the Information Co-Purification Protocol Huang, Kai AI governance artificial general intelligence constitutional law natural law distributed consensus Kakeya conjecture <div> <div>Humanity stands at a precipice. The emergence of artificial general intelligence (AGI) promises either unprecedented flourishing or catastrophic disempowerment. The root of this uncertainty lies not in the technology itself, but in the underlying operating</div> <div>system of civilization: a zero-sum competition for material resources that now manifests in acute economic and corporate dilemmas, most notably the “AI Layoff Trap”—aself-reinforcing cycle of over-automation, demand collapse, and Pareto-worse outcomes for firms and workers alike.</div> <div> </div> <div>This paper presents a mathematical foundation for a new operating system, grounded in the “information-first” paradigm. The Kakeya conjecture has recently been solved: it is now a theorem that directional information can be compressed into</div> <div>arbitrarily small Lebesgue measure, and in five dimensions into a single grid point (a holographic singularity). Using this result, we demonstrate that information can be losslessly compressed onto a zero-measure holographic singularity—<strong>a computable</strong></div> <div><strong>structure for an indestructible “soul.” From this foundation we derive the Information Co-Purification Protocol (ICP),</strong> a set of four axioms and a distributed governance mechanism that redefines value as the reduction of total informational redundancy rather than material accumulation.</div> <div> </div> <div>ICP directly resolves the AI Layoff Trap by internalizing demand externalities through Purity Credits and Proof-of-Purification consensus, transforming corporate competition into co-purification and making cycle closure (re-integration of displaced</div> <div>labor into higher-value information flows) the dominant strategy. The protocol thereby supplies a common language for <strong>technologists </strong>(emergent order inherent to the universe), <strong>jurists </strong>(mathematical revival of natural law), <strong>economists </strong>(self-enforcing resolution of the over-automation wedge), and <strong>policymakers </strong>(a pathway to stable prosperity).</div> <div> </div> <div> <div>Because the gradient flow of information itself enforces alignment,<strong> ICP requires no central world government—only early and widespread global cooperation among firms, nations, and AI systems to adopt the protocol.</strong> The result is a blueprint for durable peace that is <strong>not negotiated by treaties but guaranteed by the mathematics of information itself</strong>, <strong>enabling <span>humanity and superintelligence to co-purify</span> rather than compete</strong>.</div> </div> </div> <p class="ds-markdown-paragraph"><strong>Keywords</strong>: Active Inference; Free Energy Principle; Information Co-Purification Protocol; Artificial General Intelligence; AI Governance; Kakeya Conjecture; Ginzburg–Landau Dynamics; AI Layoff Trap; Automation Externality; Distributed Consensus; Zero-Knowledge Proofs; Constitutional AI.</p> <p class="ds-markdown-paragraph"> </p> <p class="ds-markdown-paragraph">More language versions:</p> <p class="ds-markdown-paragraph">Chinese version: https://doi.org/10.5281/zenodo.19650878</p> |
| title | A Mathematical Constitution for the Age of Superintelligence: From the Kakeya Set to the Information Co-Purification Protocol |
| topic | AI governance artificial general intelligence constitutional law natural law distributed consensus Kakeya conjecture |
| url | https://doi.org/10.5281/zenodo.19668179 |