Paper CXXXIV: The Generalised Uncertainty Principle as G2 Non-Associativity Expansion: Planck Floor, Hurwitz Ceiling, and the Uniqueness Theorem of Octonions
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| Format: | Recurso digital |
| Langue: | anglais |
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2026
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| _version_ | 1866901494410772480 |
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| author | Jagadeesan, Bharathi Dasan |
| author_facet | Jagadeesan, Bharathi Dasan |
| contents | <p>We show that the Generalised Uncertainty Principle (GUP) tower — the infinite series of Heisenberg corrections at the Planck scale — is identical to the Baker– Campbell–Hausdorff (BCH) expansion of the octonionic associator [ei, ej, ek] = (eiej)ek −ei(ejek) in the algebra G2 = Aut(O). The leading BCH term recov- ers the Heisenberg uncertainty principle exactly. Higher-order GUP corrections correspond to successive octonionic associator corrections. The BCH series diverges at the Planck scale — establishing the sub-Planck prohibition (Paper CX) as a the- orem, not an axiom. The V 2 + D2 length-dependence of Prediction P188 (Paper CXII) is the Borel resummation of this GUP tower in the G2 representation. We then prove the Uniqueness Theorem: the Planck floor h = ℓP mP c (minimum brane phase-space area) and the Hurwitz ceiling (sedenions beyond O have zero divisors) intersect exactly and uniquely at G2. The universe could not have been otherwise.</p><p><em>Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: <a href="https://doi.org/10.5281/zenodo.19120873">10.5281/zenodo.19120873</a>. Community: <strong>one-octonion-brane-bulk</strong>. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.</em></p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_20300159 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Paper CXXXIV: The Generalised Uncertainty Principle as G2 Non-Associativity Expansion: Planck Floor, Hurwitz Ceiling, and the Uniqueness Theorem of Octonions Jagadeesan, Bharathi Dasan One-Octonion Brane-Bulk Framework G2 octonion Klein quartic Fano plane auxetic brane <p>We show that the Generalised Uncertainty Principle (GUP) tower — the infinite series of Heisenberg corrections at the Planck scale — is identical to the Baker– Campbell–Hausdorff (BCH) expansion of the octonionic associator [ei, ej, ek] = (eiej)ek −ei(ejek) in the algebra G2 = Aut(O). The leading BCH term recov- ers the Heisenberg uncertainty principle exactly. Higher-order GUP corrections correspond to successive octonionic associator corrections. The BCH series diverges at the Planck scale — establishing the sub-Planck prohibition (Paper CX) as a the- orem, not an axiom. The V 2 + D2 length-dependence of Prediction P188 (Paper CXII) is the Borel resummation of this GUP tower in the G2 representation. We then prove the Uniqueness Theorem: the Planck floor h = ℓP mP c (minimum brane phase-space area) and the Hurwitz ceiling (sedenions beyond O have zero divisors) intersect exactly and uniquely at G2. The universe could not have been otherwise.</p><p><em>Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: <a href="https://doi.org/10.5281/zenodo.19120873">10.5281/zenodo.19120873</a>. Community: <strong>one-octonion-brane-bulk</strong>. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.</em></p> |
| title | Paper CXXXIV: The Generalised Uncertainty Principle as G2 Non-Associativity Expansion: Planck Floor, Hurwitz Ceiling, and the Uniqueness Theorem of Octonions |
| topic | One-Octonion Brane-Bulk Framework G2 octonion Klein quartic Fano plane auxetic brane |
| url | https://doi.org/10.5281/zenodo.20300159 |