Public archive · dctheory.org
A scalar–tensor framework in which a coherence field \(P\) crystallises on the geometry of the 600-cell via Gross–Pitaevskii dynamics. General Relativity is recovered in the limit \(P \to 1\), and the Standard Model gauge group \(\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)\) with three fermion generations is obtained through the McKay correspondence \(2I \to E_8\).
Across 17 H₀ measurements, H₀ correlates with the condensate density of the measurement environment. ΛCDM (universal Hubble flow) rejected at p = 3×10⁻⁸; Bayes factor log₁₀(BF) = +11. Joint preference vs ΛCDM: 13.1σ / 8.3σ / 0σ (full / perturbation / BAO degenerate).
Three pre-dictive (not post-hoc) successes in the multi-facet survey: SH0ES Cepheid H₀ matches DCT's \(H_E/\sqrt{P_0}\) at 0.02σ; CKM Jarlskog matches the \(\mathbb{Z}_3\)-vertex prediction at 3%; JWST τ_reion sits in the predicted direction at 1.2σ.
Row-level scorecard: 117 HIT / 14 SOFT / 0 FLAG / 0 MISS / 10 OPEN = 141 ledger rows. homogeneous \(P(t)\) nulls remove the legacy background-BAO \(\Delta\chi^2\) artefact; no remaining FAIL after review reclassification of KiDS-Legacy \(S_8\) (corpus under \(c_{GW} = c\) gives \(\sigma_8 \approx 0.811\) → \(S_8 \approx 0.831\), a 0.89\(\sigma\) PASS). See Updates.
Strong evidence the DCT vacuum is a real Bose–Einstein condensate. Five sub-tests across gravity + quantum + time domains all pass the BEC consistency relations.
Predictions and current measurements: \(\delta_{CP}\), \(m_p/m_e\), \(\sin\theta_{13}\), \(1/\alpha\), \(g_\dagger\), \(\gamma_{\rm PPN}\), and the \(M_{\rm lens}/M_{\rm dyn}\) turnover.
BepiColombo MORE 2027–2028, Euclid 2027–2029, CMB-S4 — what passes, what falsifies, when.
P_0 = cos(36°)/cos(18°) = 0.850651, \(\omega\)_0 ≈ 50,037, cBD = 138,189, master identity 2\(\omega\)_0 + 3 = cBD·P_0².
Items in the published Foundation paper (Zenodo 10.5281/zenodo.18703512) that have been refined or updated.
Notation, frame conventions, terms.
Twelve papers in the closure tree: FND-V2 + 8 cluster (SPI, SBD, BAO, COS, PPN, DM, SM, CMB) + 3 (AXS, MSS, ADC).
Python implementations of the predictions, empirical status, and tests.
Hubble tension, \(S_8\), BAO, dark sector, strong CP, hierarchy, neutrinos, CKM, BH information, vacuum catastrophe, master spectral identity — one row per problem with the corpus mechanism, the predicted observable, the current empirical status, and links into the per-observable sub-page and cluster paper.
DCT proposes a Brans–Dicke scalar–tensor theory in which scalar field \(P\) (the “tie field”) crystallises via Gross–Pitaevskii dynamics on a 600-cell lattice. Two equilibrium values — amplitude \(P_0 = \cos(36^\circ)/\cos(18^\circ) = 0.850651\) and coupling \(\omega_0 \approx 50{,}037\) — are related by the master identity \(2\omega_0 + 3 = c_{BD}\,P_0^2 = 100{,}077\) through the coupling normalisation \(c_{BD} = 138{,}189\). General Relativity is recovered in the limit \(P \to 1\). The Standard Model gauge group \(\mathrm{SU}(3)\times\mathrm{SU}(2)\times\mathrm{U}(1)\) and three-generation fermion content are derived from the McKay correspondence between the binary icosahedral group \(2I\) and the affine Lie algebra \(E_8\). Falsifiable predictions exist for solar-system PPN tests (BepiColombo MORE 2027–2028), the radial-acceleration relation (Euclid 2027–2029 lensing/dynamics turnover at \(z \sim 1.5\)), and the CMB. The scorecard: 117 HIT / 14 SOFT / 0 FLAG / 0 MISS / 10 OPEN = 141 ledger rows; joint Bayesian preference 13.1σ / 8.3σ / 0σ (provisional Δχ² attribution).