Papers
Twelve papers compose the closure tree: the revised Foundation paper DCT-FND-V2, the eight original cluster papers (SPI / SBD / BAO / COS / PPN / DM / SM / CMB), and the three v8/papers (AXS / MSS / ADC). Plus the published Foundation paper v1 and the February 2026 archive.
For a problem-by-problem matrix of which paper owns which derivation and the current empirical status of each, see /outstanding-problems/.
Each paper carries a reserved Zenodo DOI. Status: drafts, awaiting simultaneous deposit. Cross-references between cluster papers resolve via the reserved DOIs.
Revised version of the February 2026 Foundation paper. Mathematical framework unchanged; revisions reconcile the v1 tension framing with post-2025 data, replace the conformal-frame Hubble-tension framing with the perturbation-level programme, and update cosmological-data references through KiDS-Legacy 2025, DESI DR2/Y3, ACT DR6, and Planck PR3.
Twelve algebraic identities connecting topological invariants of the 600-cell + binary icosahedral group + McKay correspondence to E₈ against measured fundamental constants. Joint chance probability under independence: 3.34×10⁻²⁸; log₁₀(BF) = +27.5.
For any solar-system-compatible Brans–Dicke theory with present-epoch coupling ω₀ > 40,000 (Cassini bound), cosmological backreaction in the scalar sector is bounded above by 6×10⁻¹⁰ Λ_obs. General BD theorem; not DCT-specific.
Null propagation: homogeneous P(t) cancels from radial photon χ(z); the legacy Δχ² pipeline was a mistaken D_M map. Background-BAO is HIT-by-degeneracy with ΛCDM at the photon-null level. Perturbation-level programme on ΛCDM background remains the live scored framework.
Joint Bayesian preference of DCT vs ΛCDM under post-2025 cosmology data: 13.1σ / 8.3σ / 0σ across the three nested-test settings (full / perturbation / BAO degenerate). Provisional via Δχ² attribution; full MCMC marginalisation pending. Companion DCT-BAO-01 carries the homogeneous-BAO null geometry.
Non-adjustable PPN predictions: γ−1 = −1.998×10⁻⁵, β−1 = +9.985×10⁻¹¹ = 1/[(2ω₀+3)(2ω₀+4)], Nordtvedt η = +2×10⁻⁵. Cassini consistent at 13% margin. BepiColombo MORE 2027–2028 projects 6.7σ (8σ best-case) decisive binary test of DCT.
Spatial Avrami P(g) from Allen–Cahn on the 600-cell; RAR with g_† derived as c²√(Λ_eff/3)/P₀ at 1.9σ vs Milgrom; SPARC real-data χ²/dof ≈ 2.4 comparable to MOND. Smoking gun: cluster M_lens/M_dyn peak ≈ 1.30 at z ~ 1.5 (Euclid-era). σ_SI = 0 exactly.
Standard Model gauge group SU(3) × SU(2) × U(1) and three-generation fermion content derived from the McKay correspondence. m_p/m_e at 9.2×10⁻⁸; CKM s_12 at 0.3%; Δm² ratio at 0.3%; Jarlskog J at 3%; δ_CP = π/3. ℤ₃ cosmic-string tension at ~25× Planck bound: open structural question.
4D conformal-wall theorem S_YM[P·g] = S_YM[g] makes 8 of 9 Planck PR3 features structurally invariant between DCT and ΛCDM. The single feature where DCT differs is A_L: DCT predicts 1.010 from the Allen–Cahn lensing-kernel split; ACT DR6 measures 1.013 ± 0.023 (0.13σ HIT). lensing-kernel derivation complete.
Three additional papers added in the v8 (axis re-derivation) and v9 (mass spectrum + anti-dimension cosmology) closure passes. Reserved DOIs pending — see corpus draft directly.
Re-derives P₀ = cos(36°)/cos(18°) = 0.850651 from icosahedral midradius/circumradius geometry, resolving (P₀ first-principles, 0.041% from calibrated 0.851). Introduces the anti-dimension dual coupling β_up = 3/5 = V/F. 1/α improved to 0.003% via the 1/(E−χ) correction. Novel forward predictions: photon dispersion η = 1/12, GW echoes (3/5)·r_s/c·ln(r_s/l_P), BEC breathing-mode boson m* = ℏH₀/c², gravitational decoherence Γ = (3/5)·GM²/(ℏd).
Thirty-five predictions, 34 HIT + 1 SOFT. m_c = (V/n_irreps)·m_p (0.9σ), m_b = (n_irreps/2)·m_p (1.4σ), m_s = (χ/F)·m_p (0.5σ), m_t = (Σ′+Σ_d)·m_p (0.18σ); light-quark ratios m_u/m_d = 9/19 (0.01σ), m_s/m_d = F = 20 (0.13σ). All from icosahedral primitives V=12, F=20, χ=2, n_irreps=9. First geometric derivation of the SM Yukawa structure.
Ω_DM/Ω_b = 9·β_up = 27/5 (0.10σ vs Planck PR3); Λ ~ (φ²+φ⁻²)·10⁻⁽¹²⁰⁺χ⁾ ≈ 3×10⁻¹²² (order-of-magnitude); splashback R_sp/R_200m = P₀^{β_up} = 0.9075 (0.95σ); apparent w_a = −0.714 from growth–geometry tension (0.20σ); η_B = (2/|2I|)·exp(−Σ′/n_irreps); EW hierarchy m_W²/M_Pl² ~ 10⁻³⁴. The β_up = 3/5 dual sector drives all these closures.
The published Foundation paper (19 February 2026). 14 pages, Sections I–XIV; 32 positive predictions, 12 anti-predictions; the canonical action and the McKay derivation of the Standard Model gauge structure. Superseded but still resolvable by DCT-FND-V2 once that draft deposits.
Twenty-five numbered Foundation papers (DCT_00 – DCT_29) plus six Evidence compilations (DCT_E01 – DCT_E06). The canonical action lives in DCT_00; the polished cluster papers above carry the current numerical values where they differ.
Browse the Foundation archive →
Each cluster paper carries its own reserved Zenodo DOI (or pending deposit for the v8/papers). Cite the paper that contains the result you are using; cite DCT-FND-V2 for the framework as a whole and DCT-FND-V1 for the published February 2026 deposit.
Plain prose:
N. G. Parrott (2026). Dimensional Coherence Theory: Unifying Quantum Mechanics, General Relativity, and the Standard Model. Zenodo. https://doi.org/10.5281/zenodo.18703512.
BibTeX, RIS, and per-paper citations: /cite/