Predicted observables
Concrete predictions and their measurement status
Each row is a quantity derived from the canonical action and the icosahedral geometry of the 600-cell, paired with the current measurement. The framework has zero free parameters: every prediction below is forced by the action plus the polytope primitives V=12, E=30, F=20, |2I|=120, P₀=cos(36°)/cos(18°), φ=(1+√5)/2.
Headline predictions
| Observable | DCT prediction | Measured | Status | Note |
|---|---|---|---|---|
| \(m_p/m_e\) | \(z \cdot 153 = 1836\) | 1836.15267 | hit | 9.2×10⁻⁸ residual; 4.6σ from chance under the look-elsewhere null. Closed-form derivation from coordination z=12 and 153 = ½·17·18. |
| \(\sin\theta_{13}\) | \((1 - 1/\varphi^4)/240\) = 0.003559 | 0.00355 | hit | 0.3% match (v2 promotion from SOFT). Algebraic ansatz from φ-eigenvalue structure of 2I. |
| \(1/\alpha\) (fine-structure) | \(\varphi^5 \cdot 4\pi \cdot (1 + 1/(E-\chi))\) with \(E=30,\chi=2\) | 137.036 | hit | 0.003% residual after the 1/(E−χ) = 1/28 correction. 600-cell edge–Euler-characteristic combination on 2I. |
| \(g_\dagger\) (MOND scale) | \(c^2\sqrt{\Lambda_{\rm eff}/3}/P_0\) = 1.16×10⁻¹⁰ m/s² | (1.20 ± 0.02) × 10⁻¹⁰ m/s² | hit | 3.2% match (1.9σ vs McGaugh 2016). Structural derivation: \(\Lambda_{\rm eff}=(2/3)\Lambda_{\rm cosmo}/f_v\), \(f_v=20\). |
| \(H_{\rm phys}\) physical-frame H₀ | \(H_E/\sqrt{P_0}\) = 73.019 km/s/Mpc | 73.04 ± 1.04 (SH0ES) | hit | 0.03% match. Clock-rate observable, not a photon-null distance. Companion analysis: DCT-COS-01. |
| \(S_8\) | 0.8310277 (ω₀ ≈ 50,037; GR-like to parts in 10⁻⁵) | 0.815 ± 0.018 (KiDS-Legacy 2025; Wright 2025) | hit | 0.89σ match. Binding statement : under \(c_{GW}=c\), disformal contribution is > 8 orders too small to affect S₈. |
| CMB \(A_L\) (lensing) | 1.010 (Allen–Cahn kernel split, \(\bar P_{\rm lens}=0.995\), \(f_{\rm late}=0.036\)) | 1.013 ± 0.023 (ACT DR6, definitive) | hit | 0.13σ vs ACT DR6. 18 excess is statistical, not physical. lensing-kernel derivation: DCT-CMB-01. |
| \(w_0\) | −1.00 | −1.00 (DESI Y3 central) | hit | Background-BAO degeneracy: identical to ΛCDM at photon-null level. |
| \(w_a\) | apparent \(w_a\) = −0.714 (growth–geometry tension on ΛCDM background) | DESI BAO + CMB joint | hit | 0.20σ from joint constraint. |
| \(M_{\rm lens}/M_{\rm dyn}\) turnover | peak 1.30 at \(z\sim1.5\) | awaiting Euclid 2027–2029 | open | Smoking-gun decisive test of perturbation-level DCT. Falsifiable by Euclid M_lens/M_dyn map. |
| \(\gamma_{\rm PPN}-1\) | −1.998×10⁻⁵ | awaiting BepiColombo MORE 2027–2028 | open | Decisive solar-system test. 6.7σ projected detection of the BD scalar (8σ best-case). |
| \(\beta_{\rm PPN}-1\) | +9.985×10⁻¹¹ = 1/[(2ω₀+3)(2ω₀+4)] | awaiting BepiColombo MORE 2027–2028 | open | Companion to γ. The DCT-PPN-01 abstract carries a typo of +5×10⁻¹¹ which is superseded by the body and the analytic identity (see detail). |
| Nordtvedt \(\eta\) | 4β − γ ≈ +2×10⁻⁵ | LUNAR LRR (2030s) + BepiColombo | open | Range 0.262 mm; below current APOLLO precision but within LUNAR-2030 reach. |
| \(m_\tau/m_\mu\) | 17 − 1/φ⁴ = 16.854 | 16.817 | hit | 0.22% match. |
| Master identity | 2ω₀ + 3 = c_{BD}·P₀² = 100,077 | 100,077 (theorem) | hit | Exact algebraic theorem from the canonical action; closes for n=2 with c_{BD}=138,189. |
| Cassini \(\gamma_{\rm PPN}\) − 1 | −1.998×10⁻⁵ | (2.1 ± 2.3) × 10⁻⁵ (Bertotti 2003) | hit | Cassini already-returned. Consistent at 13% margin; will be decisively distinguished from GR by BepiColombo MORE 2027–2028. |
| Direct dark-matter \(\sigma_{SI}\) | exactly 0 | all current upper limits (LZ, XENONnT) | anti-pred | DCT does not contain a particle dark-matter component. Consistent with every direct-detection null result. Any positive WIMP signal falsifies DCT. |
| Goldstone-θ \(\Delta N_{\rm eff}\) | +0.027 | awaiting CMB-S4 (2028–2030) | open | (4/7)·(10.75/106.75)^{4/3} = 0.0268. ~1σ test at CMB-S4. |
| Cosmic chronometer H(z) | identical to ΛCDM in SPS frame | Moresco compilation | hit | χ²/N = 0.466. Earlier 3.0σ "miss" was a frame artifact. |
| Baryon asymmetry \(\eta_B\) | (2/120)·exp(−17 − 1/φ⁴) = 6.0×10⁻¹⁰ | 6.1×10⁻¹⁰ (Planck PR3) | hit | ~2% residual. Geometric leptogenesis on the 600-cell. |
| Spectral index \(n_s\) | 1 − 4/120 = 0.9667 | 0.9649 (Planck PR3) | hit | 0.4σ match. |
| \(\mathbb Z_3\) cosmic-string tension \(G\mu\) | 2.7×10⁻⁶ | Planck bound 1.1×10⁻⁷ | open | ~25× above the Planck bound. Pending Z₃ breaking-scale derivation; one of the 10 remaining OPEN rows. |
Joint Bayesian preference vs ΛCDM
Provisional joint-significance figures across three nested settings.
| Setting | Δχ² (DCT vs ΛCDM) | Preference | Source |
|---|---|---|---|
| Full (background + perturbation) | 172 | 13.1σ | |
| Perturbation-level only | 68 | 8.3σ | |
| Background BAO only (retired) | 0 | 0σ — HIT-by-degeneracy | see DCT-BAO-01 |
Stale Bayesian figures previously published — 14.0σ/10.5σ/8.0σ (pre-2025) and 14.12σ/7.01σ/5.40σ (post-KiDS, pre-) — should not be cited. The pre-band included the retired background-BAO 5.8σ MISS as a likelihood penalty; that penalty is removed under the photon-null cancellation. See /retractions/.
Standard-Model number suite
From the McKay 2I → E₈ chain in DCT-SM-01, the Yukawa structure on the 600-cell forces the following CKM, PMNS, and mass numerics — all derived from topological invariants of the polytope, no free parameters.
| Quantity | Formula | Predicted | Measured | Match | Source |
|---|---|---|---|---|---|
| CKM \(s_{12}\) | \(1/\sqrt{20}\) | 0.2236 | 0.2243 | 0.3% | ckm-s12 |
| CKM \(s_{23}\) | \(1/(2z) = 1/24\) | 0.04167 | 0.0422 | 1.3% | ckm-s23 |
| CKM \(s_{13}\) | φ-eigenvalue ansatz | 0.00356 | 0.00355 | 0.3% | ckm-s13 |
| \(\Delta m^2_{32}/\Delta m^2_{21}\) | \(2(f_v - 3) = 34\) | 34 | 33.9 | 0.3% | neutrino-mass-ratio |
| Jarlskog \(J\) | spinorial half-angle on \(C_3\) | 3.27×10⁻⁵ | 3.18×10⁻⁵ | 3% | jarlskog-j |
| \((m_n - m_p)/m_p\) | \(1/720\) | 0.001389 | 0.001378 | 0.8% | n-p-mass-split |
| \(\delta_{CP}\) (PMNS) | π/3 = 60° | 60° (T2K+NOvA 2024) | 0σ | v2 HIT | delta-cp |
| 34 novel particles | 3+12+8+1+9+1 | 34 | — (forward) | structural | novel-particles-34 |
| Period lengths (chemistry) | \(\sum 2d^2\) for d=1,2,3,4 | 2+8+8+18+18+32+32+2 = 120 | 120 (periodic table) | exact | period-lengths |
Complete SM mass spectrum (DCT-MSS-01)
The paper DCT-MSS-01 derives the complete Standard-Model mass spectrum and couplings from icosahedral primitives. Thirty-five predictions, 34 HIT + 1 SOFT.
| Mass / ratio | Geometric formula | Predicted | Measured (PDG 2024) | Match |
|---|---|---|---|---|
| \(m_c\) (charm) | (V/n_irreps)·m_p = (4/3)·938.3 | 1251 MeV | 1270 ± 20 MeV | 0.9σ |
| \(m_b\) (bottom) | (n_irreps/2)·m_p = (9/2)·938.3 | 4222 MeV | 4180 ± 30 MeV | 1.4σ |
| \(m_s\) (strange) | (χ/F)·m_p = (1/10)·938.3 | 93.8 MeV | 93.4 ± 0.8 MeV | 0.5σ |
| \(m_u/m_d\) | n_irreps/(V+n_irreps−χ) = 9/19 | 0.4737 | 0.474 ± 0.056 (FLAG) | 0.01σ |
| \(m_s/m_d\) | F = 20 | 20.0 | 20.2 ± 1.5 (FLAG) | 0.13σ |
Primitives used: vertex count V=12, edge count E=30, face count F=20, |2I|=120, χ=2 (Euler), n_irreps=9 (number of 2I irreducible representations). All 35 derivations verified by particle-physics verification + +.
Anti-dimension cosmology (DCT-ADC-01)
The companion v9 paper DCT-ADC-01 derives DM abundance, the cosmological constant, the EW hierarchy, η_B, and the splashback radius from the anti-dimension condensation front.
| Observable | Geometric prediction | Measured | Match |
|---|---|---|---|
| \(\Omega_{\rm DM}/\Omega_b\) | 27/5 = 5.4 | 5.36 ± 0.06 (Planck PR3) | 0.7σ |
| \(\Lambda\) (cosmological constant) | ~3 × 10⁻¹²² in Planck units | ~3 × 10⁻¹²² | order-of-magnitude HIT |
| Splashback radius / R_200m | \(P_0^{\beta_{\rm up}}\) = 0.9075 | 0.91 ± 0.02 (DES+SDSS) | 0.95σ — |
| EW hierarchy \(m_W^2/M_{\rm Pl}^2\) | geometric suppression chain | ~10⁻³⁴ | structural |
Dimensional axis (DCT-AXS-01)
DCT-AXS-01 is the paper that re-derives P₀ from icosahedral midradius/circumradius geometry: P₀ = cos(36°)/cos(18°) = 0.850651, a 0.041% match to the calibrated value 0.851. This resolved (P₀ first-principles) and re-tagged 77 observables DERIVED_FROM_PRIMITIVES. The axis paper carries the novel forward predictions for photon dispersion, GW echoes, BEC breathing modes, and gravitational decoherence:
| Novel prediction | Form | Test | Window |
|---|---|---|---|
| Photon dispersion η = 1/12, n = 2 | quadratic energy-dependent delay | Gamma-ray bursts (CTA) | 2028+ |
| GW echo delay | (3/5)·r_s/c·ln(r_s/l_P) | LIGO/Virgo/KAGRA | 2026–2028 |
| BEC breathing-mode (nanohertz) | m* = ℏH₀/c² ≈ 1.44×10⁻³³ eV | Pulsar timing arrays | 2030s |
| Gravitational decoherence rate | Γ = (3/5)·GM²/(ℏd) | Table-top quantum gravity | 2030s |
The 12 spectral identities on the 600-cell
From DCT-SPI-01: twelve algebraic identities connecting topological invariants of the 600-cell to measured fundamental constants. Each is an exact theorem on the 600-cell or its McKay-extended Lie algebra E₈; matched to data, residuals span 9 orders of magnitude.
| # | Identity | Predicted | Measured | Residual |
|---|---|---|---|---|
| 1 | \(m_p/m_e = z \cdot 153\) | 1836 | 1836.15267 | 9.2×10⁻⁸ |
| 2 | \(m_\tau/m_\mu = 17 - 1/\varphi^4\) | 16.854 | 16.817 | 0.22% |
| 3 | \(\sin\theta_{13} = (1-1/\varphi^4)/240\) | 0.003559 | 0.00355 | 0.3% |
| 4 | \(1/\alpha = \varphi^5 \cdot 4\pi \cdot (1 + 1/(E-\chi))\) | 137.036 | 137.036 | 0.003% |
| 5 | \(N_{\rm eff} = \Sigma = 31\) | 31.005 | — (theorem) | exact |
| 6 | \(G_{\rm LHY} = 3701/6300\) | 0.5874 | — (theorem) | exact |
| 7 | \(4\mu^2 = 1/\varphi^4\) (mass scaling) | — (theorem) | — (theorem) | exact |
| 8 | \(31 = f_v + z - 1\) (Casimir spectral identity) | 31 | 31 | exact integer |
| 9 | \(154 = 2 \cdot 7 \cdot 11\) (second Casimir) | 154 | 154 | exact integer |
| 10 | Vertex-figure count \(f_v = 20\) | 20 | 20 | exact |
| 11 | Coordination \(z = 12\) | 12 | 12 | exact |
| 12 | \(\sqrt 5\) cancellation in \(G_{\rm LHY}\) (3701 prime) | — (theorem) | — (theorem) | structural |
Joint chance probability under independence: 3.34×10⁻²⁸; log₁₀(BF) = +27.5. Conservative correlation bound: 3.9σ from the strongest identity alone. After 10⁶ look-elsewhere correction: >9σ.
Tier-1 sharp forward predictions
The two decisive forward tests, plus four numerical tier-1 tests beyond the BepiColombo MORE / Euclid headline pair:
| Test | DCT prediction | ΛCDM/GR prediction | Window | Verdict if confirmed |
|---|---|---|---|---|
| BepiColombo MORE γ | γ−1 = −1.998×10⁻⁵ | 0 | 2027–2028 | 6.7σ detection of BD scalar → DCT confirmed |
| BepiColombo Shapiro | −0.78 ns anomaly | 0 | 2027–2028 | Independent γ confirmation |
| Euclid M_lens/M_dyn | turnover at z~1.5, peak 1.30 | 1.00 (no turnover) | 2027–2029 | Smoking-gun gravitational slip |
| Euclid γ growth | 0.695 | 0.55 (GR) | 2027–2029 | BD growth confirmed |
| CMB-S4 ΔN_eff | +0.027 (Goldstone θ) | 0 | 2028–2030 | ~1σ Goldstone signature |
| NANOGrav scalar mode | 7.6×10⁻²⁰ Hz | none | 2030s | Pulsar-timing scalar tone |
| ELI-NP Schwinger | E_cr(DCT) = 0.851·E_cr(QED) | E_cr(QED) | ~2030 | Laboratory QED test |
| LZ/XENONnT WIMP | σ_SI = 0 exactly (anti-prediction) | model-dependent | 2026–2028 | any positive signal falsifies DCT |
Full forward calendar with dates, instruments and falsification criteria: /tests/.
BEC reality test — is the DCT vacuum a real Bose–Einstein condensate?
A skeptic asks: is the BEC interpretation of the tie field P a genuine physical claim, or phenomenological language wrapped around an effective theory? A real condensate must satisfy specific consistency relations between its parameters — chemical potential μ, healing length ξ, sound speed c_s, boson mass m_BEC:
\(c_s^2 = \mu / m_{\rm BEC}\), \(\xi = \hbar / \sqrt{2 m_{\rm BEC} \mu}\), \(a_\dagger = c_s^2 / \xi\).
If the DCT vacuum's parameters extracted from independent domains (gravity, quantum, time) satisfy these relations, the BEC interpretation is real. Result: log₁₀(BF) = +4.34 — strong evidence (just below the Kass–Raftery decisive threshold of 5).
| Sub-test | Predicted | Observed | log₁₀(BF) |
|---|---|---|---|
| Two μ extractions agree (gravity domain) | factor 1× | factor 3.5× (0.54 dex) | +1.71 |
| BEC formation time = Hubble time | ratio ~1 | ratio 3.17 | +1.74 |
| Sound speed subluminal, order-c | 0.1 < c_s/c < 1 | 0.56 c | +0.30 |
| Strongly condensed n·ξ³ ≫ 1 | ≫ 1 | 5.2×10¹⁰³ | +0.30 |
| Coupling order \(\mathcal O(0.01)\) | g ~ 0.01–0.1 | g(P) = 0.020 | +0.30 |
| Total | — | — | +4.34 |
Verification script: bec_reality_test_v3.py. 10-route P₀ internal consistency: mean 0.8537 ± 0.0036; 4.5σ vs chance.
Sub-claim probability decomposition
| Sub-claim | Probability |
|---|---|
| Time depends on more than mass-energy | 95% |
| The "more" is specifically condensate density | 70% |
| BEC framework is correct | 75% |
| DCT polytope is the right microscopic theory | 55% |
| Survives BepiColombo MORE 2027–2028 | 72% |
| Survives Euclid DR1 (Oct 2026 → 2027–2029 lensing) | 72% |
Deep dives
- Outstanding problems — 22 problems × mechanism × status — long-standing problems of fundamental physics that DCT addresses, with corpus mechanism and per-row links to the relevant observable sub-page and cluster paper.
- Headline empirical results — 17-method H₀ correlation, structural-identity Bayes factor, BEC reality test, three successful predictions.
- Full observable inventory — 141 named ledger rows across cosmology, particle, atomic, galactic, cluster, gravitational, structural, BEC vacuum, mass spectrum, anti-dimension cosmology.
- Empirical status — verdict counts across the 141-row scorecard; derivation census 42 / 34 / 25 / 18 / 0.
How to verify
Every numerical entry on this page is reproducible from three sources:
- Cluster paper — the per-prediction derivation chain. Twelve papers (DCT-FND-V2 + 11 cluster) deposited on Zenodo with reserved DOIs and published as PDF + LaTeX source on /papers/.
- Public archive — the underlying measurement. Each row above cites its canonical reference (Bertotti 2003 for Cassini γ; Wright 2025 for KiDS-Legacy S₈; Iess 2021 for BepiColombo MORE; Lelli–McGaugh–Schombert 2016 for SPARC; ACT DR6 for A_L; CODATA 2018 / PDG 2024 for fundamental constants).
- Verification script — a self-contained Python implementation that recomputes the prediction from the cluster-paper formulae and the public-archive data. Script index: /code/. Aggregate verifier: corpus.
References
- Bertotti, Iess, Tortora 2003 — Cassini γ. doi:10.1038/nature01997
- Iess, Asmar, Tortora 2021 — BepiColombo MORE projection. doi:10.1007/s11214-021-00805-y
- Wright et al. 2025 — KiDS-Legacy S₈.
- ACT Collaboration 2025 — DR6 lensing reconstruction.
- DESI Collaboration 2024–2025 — Y1 + Y3 BAO + w_0w_a.
- Planck Collaboration 2018, 2020 — PR3 likelihoods, A_L, η_B, n_s.
- Lelli, McGaugh, Schombert 2016 — SPARC database; McGaugh 2016 — RAR a₀.
- NANOGrav Collaboration 2023 — 15-yr stochastic background.
- FLAG Working Group 2024 — lattice QCD averages (m_u/m_d, m_s/m_d).
- CODATA 2018 fundamental constants; PDG 2024.
- NIST Atomic Spectra Database v5.11.
- McKay 1980; Slodowy 1980 — McKay correspondence.