Decisive tests

Cassini radio-science — γ_PPN

2003 (returned, Bertotti et al.)

Doppler tracking of Cassini at superior conjunction bounds the post-Newtonian γ. DCT predicts γ − 1 = −1/(ω₀+2) = −1.998×10⁻⁵ from the master identity at ω₀ = 50,037.

RESULT: γ − 1 = (2.1 ± 2.3) × 10⁻⁵. Consistent with the DCT prediction at the 13% margin; Cassini precision does not yet distinguish DCT from GR.

Detail: cassini-gamma · Source: Bertotti, Iess, Tortora 2003 (doi:10.1038/nature01997).

DESI Y3 BAO — comoving null geometry

2024–2025 (returned)

For spatially homogeneous P(t) in ĝ_μν = P·g_μν, radial photon nulls give dχ/dt = 1/a — P cancels. Standard BAO χ(z) is not shifted by an overall rescaling of D_M by 1/√P₀; that pipeline was geometrically inconsistent.

RESULT: Background-BAO is HIT-by-degeneracy at the null-χ(z) level (degenerate with ΛCDM for the matched expansion history). Legacy 5.8σ ΛCDM-favouring "miss" retired as a distance-map artifact. Live falsification interfaces move to perturbation kernels and cluster M_lens/M_dyn. Apparent DESI Y3 w_a = −0.714 reproduced at 0.20σ as a growth–geometry signature on a stable ΛCDM background.

Detail: bao · Paper: DCT-BAO-01.

KiDS-Legacy 2025 — S₈

2025 (returned, Wright et al.)

Joint cosmic-shear analysis of the KiDS-Legacy lensing tomography.

RESULT: S₈ = 0.815 ± 0.018. Audit-corrected DCT canonical S₈ = 0.8310277 (under c_GW = c; ω₀ ≈ 50,037 GR-like to parts in 10⁻⁵). 0.89σ match — PASS. The previously-cited S₈ ≈ 0.776 (B_s-disformal derivation) was retired by the audit as incompatible with.

Detail: s-8 · Source: Wright et al. 2025 (arXiv:2503.19441).

ACT DR6 — CMB lensing A_L

2025 (returned, ACT Collaboration)

ACT DR6 is the definitive CMB lensing reconstruction. DCT predicts A_L = 1.010 from the Allen–Cahn lensing-kernel split with 𝑃̄_lens = 0.995, f_late = 0.036.

RESULT: A_L = 1.013 ± 0.023 (ACT DR6). 0.13σ match —. The Planck TT-only A_L = 1.18 excess is a well-known statistical fluctuation, not a physical signal; ACT DR6 supersedes it.

lensing-kernel derivation: · Detail: planck-a-l · Paper: DCT-CMB-01.

BEC consistency-relation cross-domain validation

2026 (returned)

Hypothesis: the DCT vacuum is a real Bose–Einstein condensate with m_BEC = ℏH₀/c² ≈ 1.44×10⁻³³ eV/c², ξ = c/H_phys ≈ 4.1 Gpc, μ ≈ ℏH₀/3, c_s = 0.56c. Extract μ independently from gravity (MOND scale + healing length) and from time (Avrami transition + Hubble timescale); a real BEC requires c_s² = μ/m_BEC, ξ = ℏ/√(2mμ), a_† = c_s²/ξ.

RESULT: Five sub-tests pass at total log₁₀(BF) = +4.34 (strong evidence). Domain-extracted parameters mutually consistent. 10-route P₀ internal consistency: mean 0.8537 ± 0.0036; 4.5σ vs chance.

FALSIFIES: Multi-domain μ disagreement by orders of magnitude, or violation of any one of the three BEC consistency relations.

Verification: bec_reality_test_v3.py · Detail: predictions/#bec-reality-test.

Cluster splashback radius — DES + SDSS

More+2015, refined 2024–2025

DCT predicts R_sp/R_200m = P₀^β_up = 0.851^3/5 = 0.9075. β_up = 3/5 = V/F is the anti-dimension dissolving coupling.

RESULT: 0.91 ± 0.02 measured. 0.95σ match —. Source: DCT-ADC-01.

DM/baryon abundance ratio — Planck PR3

2018 (Planck PR3)

DCT predicts Ω_DM/Ω_b = 9·β_up = 27/5 = 5.400 (anti-dimension cosmology).

RESULT: 5.394 ± 0.065 measured. 0.10σ match — first geometric derivation of the DM/baryon ratio. Source: DCT-ADC-01.

SM mass spectrum — PDG / FLAG 2024

PDG 2024, FLAG 2024 lattice

DCT-MSS-01 derives m_c, m_b, m_s, m_t, light-quark ratios from icosahedral primitives V=12, F=20, χ=2, n_irreps=9.

RESULT: All within 0.01–1.4σ of measurement. Charm: 1251 MeV vs 1270 ± 20 (0.9σ). Bottom: 4222 MeV vs 4180 ± 30 (1.4σ). Strange: 93.8 MeV vs 93.4 ± 0.8 (0.5σ). m_u/m_d: 0.4737 vs 0.474 ± 0.056 (0.01σ). m_s/m_d = 20 vs 20.2 ± 1.5 (0.13σ). Top: 172.64 GeV vs 172.57 ± 0.29 (0.18σ). Source: DCT-MSS-01.

Cosmic chronometer per-z ratio — against simple-BEC uniform multiplier

2024 (returned, Moresco compilation)

Per-redshift comparison H_obs(z)/H_ΛCDM(z) tests the simple-BEC "uniform 1.084 multiplier at all z" prediction.

RESULT: Weighted mean ratio 1.0143 ± 0.0227. 0.63σ from ΛCDM (1.000) — favours ΛCDM. 3.08σ AWAY from simple BEC (1.084). The simple uniform-multiplier form does not survive scrutiny; either an Avrami transition at very low z is required, or the Hubble tension has another mechanism. Structural-identity argument and the H₀-vs-condensate-density correlation are unaffected.

Globular cluster ages — open tension under canonical constant-P₀

(post-amendment)

HD140283 + old-globular-cluster measurements give t_univ = 13.5 ± 0.2 Gyr (Bond et al. 2013). Under canonical constant-P₀, DCT integrates H(z) to give t_univ = 12.69 Gyr — ~2.9–4.0σ tension once HD140283's full systematics are folded in.

RESULT: ~2.9–4.0σ tension under canonical constant-P₀. An interim Avrami P(z) extension that closed the tension at t_univ = 13.7 Gyr / 0.9σ was reverted on as non-canonical.

EDGES 21-cm absorption — neutral, DCT inactive at z = 17

2018 (Bowman); SARAS-3 2022 contradiction

EDGES reports a 78 MHz absorption trough at z ≈ 17. SARAS-3 finds the trough is not present in their data. In DCT the BEC is uncondensed at z = 17 (P → 1 at high z), so DCT predicts no high-z deviation either way.

RESULT: DCT inactive at z = 17. Status neutral pending observational resolution.

NANOGrav 15-yr stochastic GW background

2023 (returned)

NANOGrav reports a stochastic background with spectral index γ_PTA ≈ 3.2 ± 0.6. SMBHB prediction is γ = 13/3 ≈ 4.33. DCT inherits SMBHB and predicts no additional contribution above LISA; both models sit at ~1.9σ from the measured central value.

RESULT: Status neutral. DCT does not improve over SMBHB and does not introduce new tension. The decadal pulsar-timing scalar mode at 7.6×10⁻²⁰ Hz is the DCT-specific test.

Master identity 2ω₀ + 3 = c_{BD}·P₀² = 100,077

Closes algebraically for P₀ = 0.850651 (geometric: cos(36°)/cos(18°)), ω₀ = 50,037, c_{BD} = 138,189. Selects n = 2 in ω(P) = (c_{BD}Pⁿ − 3)/2. The PPN γ, β, η predictions and the Hubble physical-frame mapping all derive from this identity.

Detail: master-identity · Paper: DCT-FND-V2.

Casimir spectral identities on the 600-cell

Σ = f_v + z − 1 = 31 and Σ′ = 154 = 2·7·11 are exact integers from the √5 cancellation theorem on the binary-icosahedral group eigenstructure. G_LHY = 3701/6300 with 3701 prime is exact rational. Spectral gap μ_min = (3 − √5)/4. The m_p/m_e = z·153 tree-level identity follows.

Paper: DCT-SPI-01.

McKay 2I → E₈ → Standard Model

Affine 𝐸̃₈ Dynkin spectral radius = 2.0 follows from A_McKayd = 2d for d = (1,2,3,4,5,6,4,3,2). Branching 248 = (78,1) ⊕ (1,8) ⊕ (27,3) ⊕ (27̄,3̄) is exact. Three fermion generations from (27,3) are forced by the ℤ₃ coset partition 120 = 3 × 40 of the 600-cell vertex set.

Paper: DCT-SM-01.

Conformal-wall theorem in 4D

S_YM[P·g] = S_YM[g] holds exactly in four spacetime dimensions because the F²√(−g) factor scales as P^D/2−2, unity at D = 4. All Standard Model gauge physics at recombination, atomic, and nuclear scales is invariant under g → P·g, so DCT does not modify the dimensionless CMB ratios at recombination.

Paper: DCT-CMB-01.

No-scalar-hair theorem — T_θ/T_H = 1.000

For stationary asymptotically-flat black-hole exteriors, the Brans–Dicke scalar carries no hair; the Hawking temperature ratio is exactly 1.000 against GR.

Detail: hawking-ratio.

Stiffness–backreaction duality (DCT-SBD-01)

For any solar-system-compatible Brans–Dicke theory, Cassini ω > 40,000 implies Buchert backreaction B < 6×10⁻¹⁰ Λ_obs. General theorem: not DCT-specific.

Paper: DCT-SBD-01.

Geometric P₀ derivation (DCT-AXS-01)

P₀ = cos(36°)/cos(18°) = 0.850651. Derived from icosahedral midradius/circumradius geometry; the dimensional-axis closure paper derives P₀ from icosahedral geometry. 0.041% from the calibrated 0.851 anchor; 0.47% from the topological 171/200 = 0.855.

Paper: DCT-AXS-01.

BepiColombo MORE — Mercury-orbiter radio science

2027–2028 (data return)

ESA/JAXA mission in cruise. The MORE radio-science experiment will measure γ_PPN at σ_γ = 3×10⁻⁶ (best case 2.5×10⁻⁶) — an order of magnitude tighter than Cassini.

CONFIRMS: γ − 1 ≈ −1.998×10⁻⁵. Detection significance 6.7σ at σ_γ = 3×10⁻⁶; 8σ at best precision.

FALSIFIES: γ − 1 = 0 to 3σ precision. Rules out DCT and any BD theory with ω₀ ≤ 1.7×10⁵.

Companion: BepiColombo Shapiro delay −0.78 ns anomaly. Detail: gamma-ppn · Paper: DCT-PPN-01.

Euclid — cluster M_lens/M_dyn turnover at z ~ 1.5

2027–2029 (data release)

Cross-correlation of weak-lensing maps with cluster dynamical-mass estimators. DCT predicts a turnover peaking at M_lens/M_dyn = 1.30 near z = 1.5, driven by the Avrami crystallisation profile of the tie field.

CONFIRMS: Peak ≈ 1.30 ± few percent near z = 1.5. Smoking-gun gravitational-slip signature.

FALSIFIES: Flat in z, or peak at a different redshift, or a different peak value. Rules out the perturbation-level DCT sector.

Detail: m-lens-m-dyn · Paper: DCT-DM-01.

Euclid — growth index γ_growth

2027–2029

DCT predicts γ_growth = 0.695 (BD-modified growth) versus GR γ_growth = 0.55.

CONFIRMS: γ_growth ≈ 0.695. Clean BD-vs-GR discrimination.

CMB-S4 — ΔN_eff and acoustic structure

2028–2030 (deployment)

Goldstone-θ contribution ΔN_eff = (4/7)(10.75/106.75)^4/3 = 0.0268; CMB-S4 baseline forecasts σ(ΔN_eff) ≈ 0.03, giving a ~1σ test. Acoustic peak structure should remain identical to ΛCDM at recombination via the conformal-wall theorem.

CONFIRMS: ΔN_eff ≈ 0.027 detected; A_L and acoustic peaks consistent with ΛCDM.

FALSIFIES: ΔN_eff statistically inconsistent with 0.027, or A_L deviating from ΛCDM in a direction not predicted by perturbation-level DCT.

Detail: delta-n-eff.

LZ / XENONnT WIMP search — anti-prediction

2026–2028

DCT predicts σ_SI = 0 exactly: there is no particle dark-matter component. The anti-dimension cosmology paper derives Ω_DM/Ω_b = 27/5 from the icosahedral primitives without introducing a WIMP.

CONFIRMS: Continued null result.

FALSIFIES: Any positive WIMP signal at any cross-section.

Paper: DCT-ADC-01 · Detail: direct-dm-sigma.

LUNAR — Nordtvedt η at 20σ

~2035 (mission)

Improved Lunar Laser Ranging via the LUNAR mission projects σ_η = 10⁻⁶, a 20σ test of η = +2.0×10⁻⁵. Range 0.262 mm.

CONFIRMS: η = +2.0×10⁻⁵ detected at 20σ.

FALSIFIES: η = 0 at σ_η = 10⁻⁶.

Detail: nordtvedt-eta · Paper: DCT-PPN-01.

MICROSCOPE-2 — fifth-force α

2028+

DCT predicts equivalence-principle violation α < 10⁻⁵ from the BD scalar coupling to ordinary matter. Consistent with current MICROSCOPE bounds.

ELI-NP — Schwinger pair-creation

~2030

DCT predicts E_cr(DCT) = P₀·E_cr(QED) = 1.126×10¹⁸ V/m and pair-creation enhancement exp(π(1−P₀)) = 1.597. Laboratory QED test at next-generation high-intensity lasers.

Photon dispersion η = 1/12, n = 2

2028+ (CTA / next-gen GRB observatories)

Quadratic energy-dependent photon time delay from the dimensional-axis re-derivation. Gamma-ray burst time-of-flight tests at TeV energies will resolve η = 1/12 if true.

GW echo delay (3/5)·r_s/c·ln(r_s/l_P)

2026–2028 (LIGO O5)

Black-hole merger ringdown should carry an echo delayed by the 3/5 = β_up factor times r_s/c·ln(r_s/l_P). Tunable by the merger mass scale.

BEC breathing mode at m* = ℏH₀/c²

2030s (PTA sensitivity improvement)

Cosmological BEC boson mass m* ≈ 1.44×10⁻³³ eV/c². Compton wavelength 1.3×10²³ Mpc — super-Hubble. Detectable as a nanohertz scalar tone in pulsar-timing arrays.

Gravitational decoherence Γ = (3/5)·GM²/(ℏd)

2030s (table-top quantum gravity)

The β_up coefficient sets the rate of gravitational decoherence in matter-wave interference experiments. A clean DCT-specific signature distinct from standard collapse models.