Self-Reference, M¨obius Iteration, and the 13th Axis: The SL(2,Z) Structure of Recursive Observation in the R12 Rendering Algebra
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2026
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| _version_ | 1866901432502845440 |
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| author | Lim, Han-Jun |
| author_facet | Lim, Han-Jun |
| contents | <p>Abstract</p> <p>The rendering algebra R12 ∼= M12(C) of Array Cosmology uses 12 axes, yet the ratio 13/12 appears universally in physical formulae—the proton mass (144 × 13/2), the baryon knot constant (Kknot = (13/12)Znoise/144), and the proton-toelectron mass ratio (µ = 1836 + (13/12)(π − 3)). We show that this “13th axis” is the mathematical signature of recursive self-observation, governed by the M¨obius transformation f(x) = x/(1 − x) whose matrix M =1 0−1 1 ∈ SL(2,Z). Thirteen<br>A-layer results are proved.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19153044 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Self-Reference, M¨obius Iteration, and the 13th Axis: The SL(2,Z) Structure of Recursive Observation in the R12 Rendering Algebra Lim, Han-Jun <p>Abstract</p> <p>The rendering algebra R12 ∼= M12(C) of Array Cosmology uses 12 axes, yet the ratio 13/12 appears universally in physical formulae—the proton mass (144 × 13/2), the baryon knot constant (Kknot = (13/12)Znoise/144), and the proton-toelectron mass ratio (µ = 1836 + (13/12)(π − 3)). We show that this “13th axis” is the mathematical signature of recursive self-observation, governed by the M¨obius transformation f(x) = x/(1 − x) whose matrix M =1 0−1 1 ∈ SL(2,Z). Thirteen<br>A-layer results are proved.</p> |
| title | Self-Reference, M¨obius Iteration, and the 13th Axis: The SL(2,Z) Structure of Recursive Observation in the R12 Rendering Algebra |
| url | https://doi.org/10.5281/zenodo.19153044 |