A registered result in its source context
Original ledger classification: Numerical [N] (delta_Sigma, 123-orders) + physical bridge [C] (H0 flatness readout)
Recorded statement: COSMOLOGICAL-CONSTANT BRANCH H0 = 66.5..67.1 (2026-06-15, archive integration of the tfpt-31 CC note; sharpens the qualitative H0-vs-Lambda row): the seam number delta_Sigma = m_1 e^{-2 pi alpha^-1/3} with the lowest-block…
Statement, assumptions and sources
Paper context: Frontier and open physical interfaces
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GRAV.H0.01
Original ledger classification: Numerical [N] (delta_Sigma, 123-orders) + physical bridge [C] (H0 flatness readout)
Original claim text
COSMOLOGICAL-CONSTANT BRANCH H0 = 66.5..67.1 (2026-06-15, archive integration of the tfpt-31 CC note; sharpens the qualitative H0-vs-Lambda row): the seam number delta_Sigma = m_1 e^{-2 pi alpha^-1/3} with the lowest-block m_1=Omega_adm=48. (1) [N] delta_Sigma^lead = 48 e^{-2 pi*137.036/3} ~ 1.085e-123. (2) [E] convention split M_Pl^4/Mbar^4 = (8 pi)^2 = 631.65 (unreduced vs reduced Planck density -- must be displayed). (3) [N] rho_Lambda = M_Pl^4 delta_Sigma ~ 2.4e-47 GeV^4 (observed vacuum order). (4) [N] 123-orders cross-link |log10 delta_Sigma| ~ 122.96, consistent with the v60 split 122.948. (5) [C] under the flatness closure H0^lead=66.51, H0^disc=67.10 km/s/Mpc -- 1.6..0.5 sigma BELOW Planck (67.36+-0.54), ~6 sigma below SH0ES (73.0+-1.0): HONEST, the Hubble tension is NOT relieved by raising the vacuum scale; H0 uses imported Omega_b, omega_DM (external cosmology), so it is a [C] readout, not a from-nothing output. Python-only (the (8pi)^2 ratio is on the Wolfram path via v60)
Original classification detail
Numerical/bridge [N]/[C]: delta_Sigma=48 e^{-2pi alpha^-1/3}~1.085e-123, (8pi)^2 convention split, |log10|~122.96 (v60 consistent); H0=66.5..67.1 below Planck, does NOT relieve the Hubble tension; [C] readout (imported Omega_b, omega_DM)
Dependencies as recorded
v60_lambda_metrology_branch.py; v55_coxeter_cycle.py
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- Frontier and open physical interfaces
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- 2026-06-15 (archive integration \#5: six dormant results revived from the old papers)Research changelog; TFPT — Introduction and reading guide
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- Front matter / supportTFPT — Introduction and reading guide; Verification reference catalog
- Full quantum gravity — induced from the boundary kernelFrontier and open physical interfaces
Registered verification modules
- v206_h0_lambda_branch.pyRegistered verification module · gravity
Read the description recorded in the module registry
the cosmological-constant Letter branch: the seam number δ_Σ=m₁e^{−2πα⁻¹/3} with the lowest-block m₁=Ω_adm=48, the Planck-convention split, and the quantitative H₀=66.5..67.1 (archive integration of the tfpt-31 CC note; sharpens the qualitative H₀-vs-Λ row). [N] δ_Σ^lead=48 e^{−2π·137.036/3}≈1.085×10⁻¹²³; [E] convention split M_Pl⁴/M̄_Pl⁴=(8π)²=631.65 (unreduced vs reduced Planck density — must be displayed); [N] ρ_Λ=M_Pl⁴δ_Σ≈2.4×10⁻⁴⁷ GeV⁴ (observed vacuum order); [N] 123-orders cross-link |log₁₀δ_Σ|≈122.96, consistent with the v60 split 122.948; [C] under flatness closure H₀^lead=66.51, H₀^disc=67.10 km/s/Mpc — 1.6..0.5σ BELOW Planck, ~6σ below SH0ES: the Hubble tension is NOT relieved by raising the vacuum scale; H₀ uses imported Ω_b, ω_DM, so it is a [C] readout.
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