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Paper CLXXXVIII: The Frozen e₇ Lattice as the Origin of the Cosmological Constant: Two Zero-Free-Parameter Derivations of ρΛ, the Metric Signature, and w = −1

Authors: Jagadeesan, Bharathi Dasan;

Paper CLXXXVIII: The Frozen e₇ Lattice as the Origin of the Cosmological Constant: Two Zero-Free-Parameter Derivations of ρΛ, the Metric Signature, and w = −1

Abstract

We derive the cosmological constant ρΛ from first principles via two independent, zero-free- parameter routes grounded in the One-Octonion Brane-Bulk framework. The starting point is that the matter–antimatter asymmetry δM/M = 6.10×10 ¹ (Paper CLX) produces exactly one ⁻ ⁰ unpaired e₇ lattice node per baryon. Each e₇ node is frozen — left-handed, color-singlet, unable to annihilate — because [e₄,e₅,e₆] = −2e₇ algebraically forbids a partner. These frozen nodes constitute a spatially isotropic, Lorentzian lattice whose causal geometry derives the metric signature (−,+,+,+) and whose isotropy forces w = −1, both without free parameters. Route A (top-down, Papers XLII + G₂ mode selection): The Fano zero-point vacuum energy is ρΛ(XLII) = ħH₀²/(ℓ_P²c). Of the 14 G₂ generators, only e₇ is frozen; the other 13 cancel through H /H pairing. This gives ρΛ = ħH₀²/(14ℓ_P²c) = 4.589×10 ¹ J/m³, which is 87.4% of the ⁺ ⁻ ⁻ ⁰ observed value. Route B (bottom-up, e₇ node counting): Each frozen node carries vacuum energy Eγ = 19.51 GeV (Paper CLXXIX, G₂-curved transit). The node density is n_b = δM/M × n_γ = 0.2505 m ³. ⁻ The spatial Lorentzian fraction 3/4 and sump frozen fraction f_sump = exp(−t/T_sump) = 0.827 give ρΛ = (3/4) × n_b × f_sump × Eγ = 4.859×10 ¹ J/m³, which is 92.5% of the observed value. ⁻ ⁰ The two routes agree with each other to 5.6% and with observation to 7.5–12.6%. The residual gap is within the theoretical uncertainty of the framework parameters. Both routes bracket the observed ρΛ = 5.251×10 ¹ J/m³ from below with zero free parameters. ⁻ ⁰ Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.

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Keywords

One-Octonion Brane-Bulk Framework, G2, auxetic brane, Klein quartic, Fano plane, octonion

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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