The Entanglement Theorem: Universal Concept Coupling as a Geometric Consequence of High-Dimensional Encoding
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2026
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| _version_ | 1866901924353146880 |
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| author | McEntire, Jeremy |
| author_facet | McEntire, Jeremy |
| contents | Proves that universal entanglement is a mathematical theorem, not an empirical observation. When k concepts are encoded in d>>k dimensions, concentration of measure ensures every direction carries all concepts with EI->c>1 as d/k->infinity. Three lemmas (concentration on sphere, JL preservation, PCA disentanglement) establish the proof. Four corollaries: superlinear amplification, concept-type independence, the specialist bound (compositional architecture as geometric necessity), and the alignment implication (surgical concept editing is geometrically limited). Positions against Mueller et al. (2025), Erogullari et al. (2025), and Liu et al. (2026). |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18880971 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Entanglement Theorem: Universal Concept Coupling as a Geometric Consequence of High-Dimensional Encoding McEntire, Jeremy entanglement theorem concentration of measure Johnson-Lindenstrauss specialist bound compositional architecture AI alignment concept editing PCA high-dimensional geometry Proves that universal entanglement is a mathematical theorem, not an empirical observation. When k concepts are encoded in d>>k dimensions, concentration of measure ensures every direction carries all concepts with EI->c>1 as d/k->infinity. Three lemmas (concentration on sphere, JL preservation, PCA disentanglement) establish the proof. Four corollaries: superlinear amplification, concept-type independence, the specialist bound (compositional architecture as geometric necessity), and the alignment implication (surgical concept editing is geometrically limited). Positions against Mueller et al. (2025), Erogullari et al. (2025), and Liu et al. (2026). |
| title | The Entanglement Theorem: Universal Concept Coupling as a Geometric Consequence of High-Dimensional Encoding |
| topic | entanglement theorem concentration of measure Johnson-Lindenstrauss specialist bound compositional architecture AI alignment concept editing PCA high-dimensional geometry |
| url | https://doi.org/10.5281/zenodo.18880971 |