The 98 meV Scalar: Neutrino Masses, the Cosmological Constant, and Koide's Relation on Fl₁,₂(ℂ³) × ℂP¹

The 98 meV Scalar: Neutrino Masses, the Cosmological Constant, and Koide's Relation on Fl₁,₂(ℂ³) × ℂP¹ | Zenodo Skip to main Communities My dashboard Log in Sign up There is a newer version of the record available. Published April 21, 2026 | Version 2.0 Preprint Open The 98 meV Scalar: Neutrino Masses, the Cosmological Constant, and Koide's Relation on Fl₁,₂(ℂ³) × ℂP¹ Authors/Creators Kirk, Harold D. Description This paper develops a sharper interpretation of the ~98 meV scale on the product Kähler–Einstein manifold M = Fl₁,₂(ℂ³) × ℂP¹. Rather than treating the neutrino mass sum and the scalar mass derived from the cosmological constant as two independent quantities that happen to agree, it identifies them as two readouts of a single propagating Weyl-invariant mode: the K-boson φ, identified with the neutrino protolepton ν* = (|ν₁⟩ + |ν₂⟩ + |ν₃⟩)/√3. A uniqueness theorem — the propagating Weyl-singlet scalar sector of M is one-dimensional — forces this identification and establishes m_φ = Σm_ν ≈ 98 meV as structural, not accidental. The mechanism is a rigid/flexible factor split. On the rigid flag factor Fl₁,₂(ℂ³), the charged-lepton protolepton ℓ* is a non-propagating bookkeeping mode, and Koide's K = 2/3 appears as an S₃-equipartition statement at the unique balance angle between the trivial and standard irreps. On the flexible ℂP¹ factor, the single Kähler modulus propagates and is the K-boson. Two geometrically independent routes converge on the same infrared scale. The first derives m_φ from the cosmological constant via a Hawkes–Cramér branching ratio, giving a scalar mass near 98 meV and a Yukawa range near 22 μm. The second derives the neutrino spectrum from the fermion power law and oscillation splittings, yielding Σm_ν ≈ 98 meV, with a structural cross-check from topological mass fractions at the ~1% level. The paper's falsifiable predictions: a normal-ordered Majorana neutrino spectrum with Σm_ν ≈ 98 meV a scalar mediator of mass m_φ ≈ 98 meV a Yukawa-range deviation from Newtonian gravity at ~22 μm a democratic coupling channel in 0νββ decay correlated signatures across cosmology, tabletop gravity, and neutrinoless double-beta decay A final section positions the K-boson relative to majorons, the Dark Dimension scenario, neutrino-coupled quintessence, and light scalar mediators: majoron-class in phenomenology, structurally distinct in mechanism. Notes Companion to the broader Fl₁,₂(ℂ³) × ℂP¹ program relating vacuum structure, fermion masses, and geometric regime formation. Files Kirk_2026_The 98 meV Scalar Neutrino Masses, the Cosmological Constant, and Koide's Relation on Fl₁,₂(ℂ³) × ℂP¹.pdf Files (466.6 kB) Name Size Download all Kirk_2026_The 98 meV Scalar Neutrino Masses, the Cosmological Constant, and Koide's Relation on Fl₁,₂(ℂ³) × ℂP¹.pdf md5:631553756d4c0a95de5e85d4abfb4558 466.6 kB Preview Download Additional details Related works Cites Preprint: 10.5281/zenodo.18662524 (DOI) Preprint: 10.5281/zenodo.19117486 (DOI) Preprint: 10.5281/zenodo.19614297 (DOI) Preprint: 10.5281/zenodo.19009401 (DOI) Preprint: 10.5281/zenodo.19008437 (DOI) Preprint: 10.5281/zenodo.18671046 (DOI) Preprint: 10.5281/zenodo.18665776 (DOI) Preprint: 10.5281/zenodo.19198650 (DOI) Preprint: 10.5281/zenodo.19198349 (DOI) Is supplemented by Preprint: 10.5281/zenodo.19198650 (DOI) Preprint: 10.5281/zenodo.19009401 (DOI) Preprint: 10.5281/zenodo.18964986 (DOI) Preprint: 10.5281/zenodo.19198349 (DOI) Dates Issued 2026-03-23 202 Views 127 Downloads Show more details All versions This version Views Total views 202 93 Downloads Total downloads 127 62 Data volume Total data volume 64.5 MB 34.5 MB More info on how stats are collected.... Versions External resources Indexed in OpenAIRE Communities Keywords and subjects Keywords product flag manifold Fl₁,₂(ℂ³) × CP¹ neutrino mass sum cosmological constant vacuum stiffness minimum exhaustion depth Hawkes vacuum formula Majorana neutrinos normal ordering fifth force short-range gravity geometric unification Details DOI DOI Badge DOI 10.5281/zenodo.19683636 Markdown [](https://doi.org/10.5281/zenodo.19683636) reStructuredText .. image:: https://zenodo.org/badge/DOI/10.5281/zenodo.19683636.svg :target: https://doi.org/10.5281/zenodo.19683636 HTML <a href="https://doi.org/10.5281/zenodo.19683636"><img src="https://zenodo.org/badge/DOI/10.5281/zenodo.19683636.svg" alt="DOI"></a> Image URL https://zenodo.org/badge/DOI/10.5281/zenodo.19683636.svg Target URL https://doi.org/10.5281/zenodo.19683636 Resource type Preprint Publisher Zenodo Rights License Creative Commons Attribution 4.0 International The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited. Read more Copyright Copyright (c) 2026 Harold Kirk Citation Export Technical metadata Created April 21, 2026 Modified April 23, 2026 Jump up About About Policies Infrastructure Principles Projects Roadmap Contact Blog Blog Support Help FAQ Developers REST API OAI-PMH Contribute GitHub Donate Funded by Powered by CERN Data Centre & InvenioRDM Status Privacy policy Cookie policy Terms of Use This site uses cookies. Find out more on how we use cookies Accept all cookies Accept only essential cookies

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