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Document 4 of the TFPT 5.0 setHonest frontier
TFPT 5.02026-06-08473 KBSHA-256 ecd115a5…5516
Paper 4Honest frontier

Frontier Items

η_B, m_p/m_e, Koide, dark matter and quantum gravity — honest status

The honest frontier: which physics has a genuine TFPT handle and which does not. For each of η_B, m_p/m_e, the Koide relation, dark matter and full quantum gravity, this note states the genuine structural handle, the precision it currently lands at, and — crucially — what is not a clean compiler power and is deliberately not forced onto the ladder. This document is the status authority for the frontier items.

Inputs
  • ›The closed branch of Documents 1–3 (compiler, SM packet, scale grammar).
Contribution
  • ›η_B = 6.1×10⁻¹⁰ as a downstream readout from the closed Ω_b h² (not a fundamental compiler power).
  • ›The Koide relation computed exactly: Q = 0.664, 0.33% below the democratic target 2/3 = |ℤ₂|/N_fam.
  • ›The axion dark-matter candidate fixed (θ_i = 170° closed), with f_a = M_scal/128 a conjecture; full QG R + R² heat-kernel grounded, ambient measure open.
Not claimed here
  • ›η_B as a fundamental compiler power, the absolute axion relic abundance, an exact Koide 2/3, and m_p/m_e as a compiler number are all explicitly not claimed.
  • ›Hard rule: Koide, η_B, the axion relic scale and m_p/m_e are not compiler powers unless their missing QFT/cosmology transfer is supplied.
Falsification surface
  • ›Fails if a frontier item is silently asserted as a forced compiler power; m_p/m_e is explicitly left open [A] and only fails if mis-asserted.
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Highlights
η_B6.1×10⁻¹⁰Downstream readout from Ω_b h² [P]
Koide Q0.6640.33% below 2/3 = |ℤ₂|/N_fam [P]
m_a≈ 23.8 µeVAxion candidate; f_a = M_scal/128 [P]
m_p/m_eopen [A]Cross-sector ratio, not a compiler power

Key formulas

  • η_B (downstream)
    ηB=6.1×10−10\eta_B = 6.1\times 10^{-10}
    From closed Ω_b h² = 0.0222; not a compiler power. [P]
  • Koide
    Q=0.664→Q⋆=23=∣Z2∣NfamQ = 0.664 \to Q_\star = \tfrac{2}{3} = \tfrac{|\mathbb{Z}_2|}{N_{\mathrm{fam}}}
    Near-miss, 0.33% below 2/3; not exact at source. [P]
  • Axion DM
    fa=Mscal/128,ma≈23.8 μeVf_a = M_{\mathrm{scal}}/128, \quad m_a \approx 23.8\,\mu\text{eV}
    Candidate fixed, θ_i = 170° closed; f_a conjectural. [P/A]
  • QG gap-decoupling
    Δeff=Δ−2∥V∥=1.648>0\Delta_{\mathrm{eff}} = \Delta - 2\|V\| = 1.648 > 0
    R + R² grounded (G2); ambient measure (G6) open. [F/A]

Baryon asymmetry η_B — downstream readout

From the closed baryon fraction Ω_b = (4π − 1)β_rad, the asymmetry follows as a cosmological readout. As a fundamental compiler power it is not closed — the leptogenesis Boltzmann solve is not carried out.

Ωb=(4π−1)βrad=0.04894,Ωbh2=0.0222\Omega_b = (4\pi - 1)\beta_{\mathrm{rad}} = 0.04894, \qquad \Omega_b h^2 = 0.0222
ηB=6.09×10−10(observed 6.1×10−10)\eta_B = 6.09\times 10^{-10} \quad (\text{observed } 6.1\times 10^{-10})

The Koide relation — near 2/3, computed exactly

The source-level Koide quotient from the lepton φ₀-ladder is 0.664, 0.33% below the democratic compiler target 2/3 = |ℤ₂|/N_fam. A source→pole transfer conjecture brings it onto 2/3, but is not a derivation.

QTFPT=∑ℓm^ℓ(∑ℓm^ℓ)2=0.66446…,Q⋆=∣Z2∣Nfam=23Q_{\mathrm{TFPT}} = \frac{\sum_\ell \hat m_\ell}{(\sum_\ell \sqrt{\hat m_\ell})^2} = 0.66446\ldots, \qquad Q_\star = \frac{|\mathbb{Z}_2|}{N_{\mathrm{fam}}} = \frac{2}{3}
λ2=(23)6=Q⋆ ∣R+(A3)∣\lambda_2 = \left(\tfrac{2}{3}\right)^6 = Q_\star^{\,|R^+(A_3)|}

Dark matter — candidate fixed, scale pending

The candidate is the determinant-line axion of the strong-CP sector; WIMPs are ruled out (no spare E₈ singlet). The misalignment angle is closed; the decay constant is a conjecture.

θi=π(1−φseam(α⋆))=170.4∘\theta_i = \pi(1 - \varphi_{\mathrm{seam}}(\alpha_\star)) = 170.4^\circ
fa=Mscal2dim⁡S+∣μ4∣=Mscal128≈2.39×1011 GeV,ma≈23.8 μeVf_a = \frac{M_{\mathrm{scal}}}{2\dim S^+ |\mu_4|} = \frac{M_{\mathrm{scal}}}{128} \approx 2.39\times 10^{11}\,\text{GeV}, \quad m_a \approx 23.8\,\mu\text{eV}

Full quantum gravity — induced from the seam

c₃ = 1/(8π) is the gravitational seam constant; the spectral action gives R + R² structurally (G2), and the closed admissible sector is gap-decoupled from the un-built ambient (G5, Decoupling Theorem). The ambient measure (G6) is holographically reduced to a finite seam-boundary measure — the strict-TOE completion target, no longer a bulk problem.

2∥Vmetric∥=0.785<Δ=6log⁡32=2.433,Δeff=1.648>02\|V_{\mathrm{metric}}\| = 0.785 < \Delta = 6\log\tfrac{3}{2} = 2.433, \qquad \Delta_{\mathrm{eff}} = 1.648 > 0
Mscal2/MˉPl2=c37,Mscal=3.06×1013 GeVM_{\mathrm{scal}}^2/\bar M_{\mathrm{Pl}}^2 = c_3^7, \qquad M_{\mathrm{scal}} = 3.06\times 10^{13}\,\text{GeV}

Key formulas at a glance

  • η_B (downstream)
    ηB=6.1×10−10\eta_B = 6.1\times 10^{-10}

    From closed Ω_b h² = 0.0222; not a compiler power. [P]

  • Koide
    Q=0.664→Q⋆=23=∣Z2∣NfamQ = 0.664 \to Q_\star = \tfrac{2}{3} = \tfrac{|\mathbb{Z}_2|}{N_{\mathrm{fam}}}

    Near-miss, 0.33% below 2/3; not exact at source. [P]

  • Axion DM
    fa=Mscal/128,ma≈23.8 μeVf_a = M_{\mathrm{scal}}/128, \quad m_a \approx 23.8\,\mu\text{eV}

    Candidate fixed, θ_i = 170° closed; f_a conjectural. [P/A]

  • QG gap-decoupling
    Δeff=Δ−2∥V∥=1.648>0\Delta_{\mathrm{eff}} = \Delta - 2\|V\| = 1.648 > 0

    R + R² grounded (G2); ambient measure (G6) open. [F/A]