Solution to the Acosta Problem: The Tau Lepton Mass from the Partial Splitting of x³ − x − 1 in F₆₁
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2026
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| author | ACOSTA PADILLA, ALFREDO LUIS |
| author_facet | ACOSTA PADILLA, ALFREDO LUIS |
| contents | <p>The companion paper "The Acosta Correspondence Law" (Zenodo, March 2026) posed the Acosta Problem: derive the tau lepton mass ratio m_tau/m_e = 3477 from the polynomial x³ − x − 1 = 0 and the geometry of the 23-channel vacuum V23, with zero free parameters. This paper solves it.</p> <p>The prime 61 is uniquely determined by three conditions forced by x³ − x − 1 and V23: (C1) the polynomial has exactly one root r in F₆₁, and that root satisfies r = p − N_G = 61 − 4 = 57; (C2) that root factors as r = 57 = 3 × 19 = degree × N_EM; (C3) 61 is the prime of index 23² − 511 = 18 in the prime sequence. Conditions (C1) and (C2) together fix p = 61 algebraically — uniqueness is exact, not numerical. The tau mass follows as the product of the polynomial's root in its partial splitting prime by that prime:</p> <p>m_tau / m_e = r(61) × 61 = 57 × 61 = 3477 (error 0.007%, PDG: 1776.86 MeV)</p> <p>The lepton series is now closed with zero free parameters: electron = 1, muon = 9 × Prime(9) = 9 × 23 = 207, tau = r(61) × 61 = 3477. There is no fourth charged lepton because A5 has no irreducible representation of dimension d > 5.</p> |
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| id | zenodo_https___doi_org_10_5281_zenodo_19024755 |
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| publishDate | 2026 |
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| spellingShingle | Solution to the Acosta Problem: The Tau Lepton Mass from the Partial Splitting of x³ − x − 1 in F₆₁ ACOSTA PADILLA, ALFREDO LUIS tau lepton mass derivation lepton mass hierarchy solution x³ minus x minus 1 splitting prime partial splitting prime algebraic number theory structured vacuum theory TVS23 zero free parameters particle physics cubic polynomial discriminant minus 23 Z[rho] ring prime decomposition Acosta Correspondence Law lepton series closed knot topology lepton masses A5 representation theory leptons dodecahedral vacuum geometry Mathematical Physics High Energy Physics – Theory, Number Theory (math.NT), Algebraic Number Theory Mathematical Physics, Theoretical Physics <p>The companion paper "The Acosta Correspondence Law" (Zenodo, March 2026) posed the Acosta Problem: derive the tau lepton mass ratio m_tau/m_e = 3477 from the polynomial x³ − x − 1 = 0 and the geometry of the 23-channel vacuum V23, with zero free parameters. This paper solves it.</p> <p>The prime 61 is uniquely determined by three conditions forced by x³ − x − 1 and V23: (C1) the polynomial has exactly one root r in F₆₁, and that root satisfies r = p − N_G = 61 − 4 = 57; (C2) that root factors as r = 57 = 3 × 19 = degree × N_EM; (C3) 61 is the prime of index 23² − 511 = 18 in the prime sequence. Conditions (C1) and (C2) together fix p = 61 algebraically — uniqueness is exact, not numerical. The tau mass follows as the product of the polynomial's root in its partial splitting prime by that prime:</p> <p>m_tau / m_e = r(61) × 61 = 57 × 61 = 3477 (error 0.007%, PDG: 1776.86 MeV)</p> <p>The lepton series is now closed with zero free parameters: electron = 1, muon = 9 × Prime(9) = 9 × 23 = 207, tau = r(61) × 61 = 3477. There is no fourth charged lepton because A5 has no irreducible representation of dimension d > 5.</p> |
| title | Solution to the Acosta Problem: The Tau Lepton Mass from the Partial Splitting of x³ − x − 1 in F₆₁ |
| topic | tau lepton mass derivation lepton mass hierarchy solution x³ minus x minus 1 splitting prime partial splitting prime algebraic number theory structured vacuum theory TVS23 zero free parameters particle physics cubic polynomial discriminant minus 23 Z[rho] ring prime decomposition Acosta Correspondence Law lepton series closed knot topology lepton masses A5 representation theory leptons dodecahedral vacuum geometry Mathematical Physics High Energy Physics – Theory, Number Theory (math.NT), Algebraic Number Theory Mathematical Physics, Theoretical Physics |
| url | https://doi.org/10.5281/zenodo.19024755 |