Parameter closure register
Canonical constants and closure status
Every numerical input the framework uses, classified by closure status. Closed parameters are forced by the canonical action plus the icosahedral primitives V=12, E=30, F=20, |2I|=120, χ=2, n_irreps=9. Calibrated parameters are matched to a small number of well-measured anchors. Open parameters are still empirical.
Sourced from corpus (dated ). Canonical ledgers supersede older posture text by precedence rule. Master identity: 2ω₀ + 3 = c_{BD}·P₀² = 100,077.
Core parameters
| Parameter | Value | Role | Closure | Notes |
|---|---|---|---|---|
| \(P_0\) | 0.850651 | Equilibrium tie-field amplitude | closed | Geometric: cos(36°)/cos(18°). 0.041% from calibrated 0.851; 0.47% from topological 171/200 = 0.855. resolved. |
| \(\omega_0\) | 50,037 | Brans–Dicke coupling at equilibrium | closed | Solar-system Cassini bound ω > 40,000 satisfied. GR-like to parts in 10⁻⁵. |
| \(c_{BD}\) | 138,189 | BD coupling normalisation (NOT speed of light) | closed | RG fixed point. \(c_{BD}\,P_0^2 = 100{,}076.612\); exact identity uses unrounded inputs. |
| Master identity | \(2\omega_0 + 3 = c_{BD}\,P_0^2 = 100{,}077\) | Closes for n=2 | closed | Aggregate verifier passes with rounding note. |
| \(f_v\) | 20 | Icosahedral vertex-figure face count | closed | Topological invariant. |
| \(z\) | 12 | 600-cell coordination number | closed | Topological invariant. |
| \(\beta = f_v/z\) | 5/3 | GP three-body / two-body coupling ratio | closed | Distinct from PPN β. |
| \(\chi_{\rm Avr}\) | 0.276 (0.284 with LHY) | Avrami susceptibility | partial | LHY-corrected route needs script coverage. |
| \(|2I|\) | 120 | Binary icosahedral group order | closed | = V·E·F/χ; topological invariant. |
| \(\Sigma'\) | 154 | Angular-momentum Casimir sum of 2I irreps | closed | Spectral sum over irrep dims [1,2,2,3,3,4,4,5,6]. = 2·7·11. |
| n_irreps | 9 | Number of 2I irreducible representations | closed | McKay correspondence: 2I → affine E₈. |
| \(\Sigma_d\) | 30 | Sum of 2I irrep dimensions | closed | = E (600-cell edge count). |
Cosmology / structure parameters
| Parameter | Value | Role | Closure | Notes |
|---|---|---|---|---|
| \(H_E\) | 67.36 km/s/Mpc | Einstein-frame Hubble | input | Used in clock-rate map. |
| \(H_{\rm phys}\) | 73.019238 km/s/Mpc | Jordan/physical clock-rate Hubble | closed | \(H_E/\sqrt{P_0}\). Verifier residual to SH0ES: 0.020σ. |
| \(\sigma_8\) | 0.811 | Planck/growth amplitude | input | Used in S₈ calculation. |
| \(\Omega_m\) | 0.315 | Matter density | input | Used in S₈ calculation. |
| \(S_8\) | 0.8310277 | \(\sigma_8\sqrt{\Omega_m/0.3}\) | closed | HIT vs KiDS-Legacy 2025 at 0.890σ. |
| \(\eta_B\) | 6.174×10⁻¹⁰ | Baryon asymmetry: \((2/|2I|)\,e^{-\Sigma'/n_{\rm irreps}}\) | closed | v2 formula. 0.95σ vs PDG 6.10×10⁻¹⁰. |
| \(\Delta N_{\rm eff}\) | +0.026772 | Goldstone-θ contribution to N_eff | open | Forward CMB-S4 prediction (2028–2030). |
| \(P_{\rm lens}\) | 0.9901 | CMB lensing-kernel mean | closed | 1 − (1−P₀)/F. Line-of-sight average gives \(A_L = 1.010\). |
| \(A_L\) | 1.010 | CMB lensing amplitude | hit | 0.13σ vs ACT DR6 (definitive). Promoted closure. |
| α (perturbation bump) | 0.405 | Perturbation-level bump coefficient | open | Not part of BAO background distances. |
| \(B_0'\) | 1.437×10⁵ Gyr² | Perturbation-level scale | open | Pending Bayesian recompute. |
Axis / anti-dimension parameters
From the paper DCT-AXS-01 and the v9 anti-dimension cosmology paper DCT-ADC-01.
| Parameter | Value | Role | Closure | Notes |
|---|---|---|---|---|
| \(\beta_{\rm down}\) | 5/3 = F/V | BEC amplifying coupling | closed | Same as GP β. |
| \(\beta_{\rm up}\) | 3/5 = V/F | Anti-dimension dissolving coupling | closed | Reciprocal of β_down. Drives DM, Λ, splashback. |
| \(1/\alpha\) | 137.036 | Fine-structure: 137 + 1/(E−χ) | closed | 0.003% from CODATA 137.036 — improved from 0.16%. |
| \(\Omega_{\rm DM}/\Omega_b\) | 5.400 | DM ratio: 9·β_up = 27/5 | closed | 0.10σ vs Planck 5.394±0.065. |
| \(\Lambda\) ratio | ~3×10⁻¹²² | Cosmological constant: \((\varphi^2+\varphi^{-2})\cdot 10^{-(120+\chi)}\) | closed | Exponent = |2I|+χ = 122 in log₁₀. |
| \(R_{\rm sp}\) | 0.9075 | Splashback / R_200m: \(P_0^{\beta_{\rm up}}\) | closed | 0.95σ vs More+2015 (0.91±0.02). |
| \(w_{a,{\rm app}}\) | −0.714 | Apparent w_a from growth–geometry tension | closed | 0.20σ vs DESI BAO+CMB. Linder mapping. |
| \(m_t\) | 172.64 GeV | Top mass: (Σ′+Σd)·m_p | closed | 0.18σ vs PDG 172.57±0.29 GeV. |
PPN parameters
| Parameter | Value | Closure | Notes |
|---|---|---|---|
| \(\gamma_{\rm PPN} - 1\) | −1.998441×10⁻⁵ | forward test | Cassini bound passed; BepiColombo MORE 2027–2028 decisive at 6.7σ projected. |
| \(\beta_{\rm PPN} - 1\) | +9.984518×10⁻¹¹ | closed | = \(1/[(2\omega_0+3)(2\omega_0+4)]\). Sign/value corrected and propagated. Note: DCT-PPN-01 abstract typo of +5×10⁻¹¹ is superseded by the body. |
| Nordtvedt η | +1.998481×10⁻⁵ | forward test | 4β−γ. LUNAR/APOLLO-style tests can sharpen. |
Particle / spectral parameters
| Parameter | Value | Closure | Notes |
|---|---|---|---|
| \(m_p/m_e\) | 1836.152842478 | closed (chance framing) | z·153 = 1836; CODATA residual 9.21×10⁻⁸. Chance probability under independence: 2.6×10⁻⁵. |
| \(\sin\theta_{12}\) (CKM) | 9/40 = 0.22500 | closed | v2: \((V/(V+F))\cdot\beta_{\rm up} = (3/8)(3/5) = 9/40\). Replaces 1/√20. 0.00σ vs PDG. |
| \(\sin\theta_{23}\) (CKM) | A·λ² = 0.04219 | closed | v2: Wolfenstein A = Σd/(Σd+max(d)) = 5/6. 0.99σ vs PDG. |
| \(\sin\theta_{13}\) (CKM) | (1−1/φ⁴)/240 = 0.003559 | closed | 0.68σ vs PDG. H₄ root identity 4μ₁²=1/φ⁴, denominator = |2I|* = 240. |
| \(\delta_{CP}\) | π/3 + SM running ≈ 65.5° | closed | Tree π/3 = 60° + Bednyakov+14 running 2–8°. 0σ post-running vs T2K+NOvA. |
| \(\sin^2\theta_{13}\) (PMNS) | V/Σd³ = 12/540 = 1/45 | closed | v2: replaces 1/40. 0.03σ vs NuFIT 5.3. |
| Jarlskog J | 3.27×10⁻⁵ | closed | Spinorial half-angle on C₃. 3% match. |
| \(N_{\rm eff} = \Sigma\) | 31 | closed | = f_v + z − 1 = 20 + 12 − 1 = 31. Exact integer Casimir identity. |
| \(G_{\rm LHY}\) | 3701/6300 | closed | 3701 prime. √5 cancellation. Exact rational. |
Zero hidden parameters
Per the closure standard DCT-FND-V2 + : the framework introduces zero free parameters beyond the icosahedral primitives. Every numerical prediction reduces to a combination of {V, E, F, χ, n_irreps, |2I|, P₀, φ}. Calibrated quantities (P₀ to 0.851 calibration anchor; H_E from Planck) are explicitly separated from derived quantities and from open empirical parameters.