Empirical evidence
What the data says
DCT’s strongest existing-data results, derived from public archives. Each entry states the prediction, the data source, the verdict, and what would falsify it.
Leading result — H₀ vs condensate-density
Across 17 published H₀ measurements drawn from independent physics (CMB acoustic peaks, BAO sound horizon, Cepheid pulsation, TRGB, surface-brightness fluctuation, time-delay lensing, water-megamaser geometry, AGN reverberation), H₀ correlates monotonically with the condensate density of the measurement environment.
| Group | N | Weighted H₀ (km/s/Mpc) | Density rank | Script |
|---|---|---|---|---|
| LOW — CMB, BAO, halos, old stars | 5 | 67.63 ± 0.37 | 0.0–1.5 | script |
| MID — Cepheids, SCM, normal galaxies | 6 | 72.76 ± 1.01 | 2.0–5.0 | script |
| HIGH — AGN, lensing, megamasers | 6 | 73.06 ± 0.68 | 5.0–8.5 | script |
- Linear-in-rank slope: +0.87 ± 0.12 km/s/Mpc per rank → 7.34σ from zero.
- ΛCDM null (universal Hubble flow): χ² = 67.3 / 16 dof → p = 3 × 10⁻⁸. Rejected at >5σ.
- BEC condensate-coupling fit: χ² = 13.4 / 15 dof — clean.
- Bayes factor BEC over ΛCDM: log₁₀(BF) = +11.
ΛCDM specifies a universal Hubble flow — all methods predict the same H₀. The data reject this. The methods do not give the same H₀; they cluster monotonically by condensate density. Every alternative Hubble-tension explanation tested (early dark energy, KBC void, decaying dark matter, modified recombination) predicts a uniform H₀ shift, not a method-by-method ordering. Condensate-density coupling is the simplest framework that produces the observed pattern.
Successful predictions
Three numerical predictions DCT made from polytope topology + the canonical action that match measured values within reported uncertainty.
| Quantity | DCT prediction | Measured | Match | Mechanism |
|---|---|---|---|---|
| SH0ES Cepheid H₀ | 73.019 km/s/Mpc | 73.04 ± 1.04 | 0.02σ | H_phys = H_E / √P₀ from conformal-frame mapping; H_E = 67.4 (Planck), P₀ = 0.851 |
| CKM Jarlskog J | 3.27 × 10⁻⁵ | 3.18 × 10⁻⁵ | 3% (0.6σ) | Spinorial half-angle on \(C_3\) coset of 600-cell vertex partition |
| MOND scale a† | 1.224 × 10⁻¹⁰ m/s² | 1.20 × 10⁻¹⁰ (Milgrom) | 2.0% (0.81σ) | a† = c · H_phys / (2π · √P₀) — specific number, no fit parameter once P₀ is fixed |
Structural-identity Bayes factor
Twelve algebraic identities connecting topological invariants of the 600-cell + binary icosahedral group to measured fundamental constants. Each identity is exact on the polytope; matched to data, residuals span nine orders of magnitude.
| Quantity | Joint chance probability | Equivalent σ | After 10⁶ LEE | Bayes factor |
|---|---|---|---|---|
| 12 identities, independence assumption | 3.34 × 10⁻²⁸ | >11σ | >9σ | ~3 × 10²⁷ |
| Conservative bound (full correlation) | — | 3.9σ | — | — |
log₁₀(BF) = +27.5 in favour of the polytope-derivation hypothesis over the numerology null. Decisive by Kass–Raftery (threshold +5) by 22 orders of magnitude. The conservative bound — assuming all twelve identities are perfectly correlated through the polytope structure — is 3.9σ from the single most stringent identity alone. Identity table on the predictions page.
BEC vacuum reality test
A real Bose–Einstein condensate must satisfy specific consistency relations between its chemical potential μ, healing length ξ, sound speed c_s, and boson mass m. A theory that uses BEC vocabulary phenomenologically does not. Five cross-domain tests extract these parameters by independent routes — gravity, quantum mechanics, cosmological time — and check whether they collapse onto a single self-consistent tuple.
| Test | Predicted | Observed | log₁₀(BF) |
|---|---|---|---|
| Two μ extractions agree (gravity) | 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 natural-weak | g ∼ 0.01–0.1 | g(P) = 0.020 | +0.30 |
| Total log₁₀(BF) | +4.34 | ||
Two strongest sub-results: (i) two independent gravity-side extractions of μ — one from the MOND scale a† = c_s² / ξ, one from the BEC consistency relation ξ = ℏ / √(2mμ) — agree to a factor of 3.5 on a parameter that could have lived anywhere in 60 orders of magnitude; (ii) the BEC equilibration timescale ℏ/μ equals the Hubble time, exactly what an Avrami-transition picture predicts. Recovered parameters: μ ≈ ℏ H₀ / 3, c_s = 0.56c, healing length 4.1 Gpc, condensate depth 10¹⁰³. log₁₀(BF) ≈ +4.3 sits just below the Kass–Raftery decisive threshold of +5; this is strong circumstantial evidence the DCT vacuum is BEC, not a phenomenological projection. Direct dispersion measurement (CMB-S4 / SKA / atomic-clock cross-frame) would convert the +4.34 to >+20.
33-facet pass / neutral / fail
Independent pass over 33 named facet tests. Background BAO is PASS under the May 2026 null-geometry revision (homogeneous \(P(t)\) cancels in \(\chi_{\rm null}\); legacy \(\Delta\chi^2\) artefact retracted). Interim Avrami \(P(z)\) profiles remain non-canonical (see Updates). Tally: audit_fails.py. Each facet row in the full registry states a null baseline (\(\Lambda\)CDM, Einstein GR, Standard Model, or a spelled combination) and the DCT contrast versus that baseline: /empirical/facets/ (facet_registry.json).
| Result | Count | Examples |
|---|---|---|
| PASS | 19 | Prior 18 plus background BAO / \(\chi(z)\) under homogeneous conformal \(P\) (detail). |
| NEUTRAL | 13 | W boson, α, Higgs, sound horizon r_s, J₂, BBN Y_p, EHT shadow (below precision), electron a_e (below precision), cosmic dipole (qualitative), Ω_DM h² (order-of-magnitude only), Li/H (shared SM tension). |
| FAIL | 1 | KiDS-Legacy 2025 \(S_8 = 0.815 \pm 0.018\) vs DCT canonical \(0.776\) under constant-\(P_0\) growth (\(\sim\!2\sigma\)). |
Negatives
Predictions where the simple form does not survive current data, or where the test went against DCT.
- Cosmic chronometer per-z H(z) ratio — H_obs/H_LCDM = 1.014 ± 0.023 across 31 measurements. 0.63σ from ΛCDM (1.000), 3.08σ against simple BEC (1.084). Either BEC's H(z) shape is more complex than a uniform √P₀ multiplicative (Avrami transition at very low z), or cosmic chronometers carry a systematic relative to SH0ES Cepheids. Documented; resolution open.
- PTB Yb⁺/Sr clock 31σ diurnal — magnitude DCT-consistent (5.6 × 10⁻¹⁸) but degenerate with HVAC at the 21-day baseline; sidereal/solar amplitude ratio 1.04. Cannot disambiguate without a 60+ day continuous campaign.
- King 2012 quasar α-dipole reproduction — 7.4σ at 1.05 × 10⁻⁵, pole RA = 17.7h Dec = −62.8°, matching King to 3% / 5°. But the King 2012 result itself is contested by ESPRESSO 2020 and Murphy 2022 nulls; reliability discounted to 50%.
- Background BAO (homogeneous \(P\)) — legacy \(\Delta\chi^2 \approx 33.6\) from a mistaken uniform \(D_M\) rescaling is retracted (null \(\chi(z)\) unchanged). Methodology: /observables/bao/, DCT-BAO-01. Live tests: perturbation kernels, cluster \(M_{\rm lens}/M_{\rm dyn}\).
Pre-registered T-harness
Reproducible checks under /files/code/empirical/: each folder has recipe.md, run.py, and result.md / result.json after a run. These complement the headline scripts on /code/; numbers are wired to the same public datasets cited in /observables/.
Discriminant contract. A headline empirical result is not counted here if it could be dismissed as “ΛCDM / Einstein GR / the Standard Model would have looked the same anyway.” Each pre-registered harness names a null baseline (what the baseline theory predicts for that observable or statistic) and a DCT target. The recipe states which hypothesis the public data actually stress: for example ΛCDM’s single universal H₀ vs a deterministic frame ratio; GR’s \(\gamma=1\) vs a locked Brans–Dicke \(\gamma\); the SM’s unconstrained Yukawa/CKM numerology vs polytope-fixed integers; a canonical WIMP cross section vs a hard \(\sigma_{\rm SI}=0\); or a naive uniform \(H/H_{\Lambda{\rm CDM}}=1/\sqrt{P_0}\) caricature vs per-\(z\) chronometer data. NEUTRAL in the table means “current data do not separate DCT from the stated null at this precision,” not “no discrimination was attempted.”
| ID | Question | Null baseline (what would fake it) | Verdict (latest run) | Files |
|---|---|---|---|---|
T_H0_ENVELOPE | Two-method \(H_{\rm SH0ES}/H_{\rm Planck}\) vs \(1/\sqrt{P_0}\) | \(\Lambda\)CDM: one true H₀; tension = fluctuation or systematic, not a deterministic density-dependent ratio. | PASS (two-method ratio) | run.py · recipe.md · result.md |
T_CC_NEUTRAL | Cosmic-chronometer \(H/H_{\Lambda{\rm CDM}}\) mean vs 1 vs naive \(1.084\) | \(\Lambda\)CDM: \(\langle r\rangle\to 1\). Naive caricature: uniform \(1/\sqrt{P_0}\) at all \(z\) (not corpus-canonical; included as sharp falsifier). | NEUTRAL vs \(\Lambda\)CDM; negative vs naive uniform BEC | run.py · recipe.md · result.md · twin dct_eddington_ratio_per_z.py |
T_PPN_GAMMA | Cassini \(\gamma-1\) vs DCT \(-9.992\times10^{-6}\) | Einstein GR: \(\gamma-1=0\) exactly. Brans–Dicke only reproduces GR in the \(\omega\to\infty\) limit unless \(\omega\) is fixed. | NEUTRAL (await BepiColombo) | run.py · recipe.md · result.md |
T_DM_NULL | Direct-detection \(\sigma_{\rm SI}=0\) vs xenon limits | \(\Lambda\)CDM particle DM: non-zero spin-independent cross section in canonical WIMP band (benchmark models). | NEUTRAL (extending agreement) | run.py · recipe.md · result.md |
T_PARTICLE_STRUCTURE | Seven structural SM rows from SPI / Foundation | Standard Model: Yukawa, CKM, and mass ratios are fitted parameters with no structural prediction from first principles at this precision. | Mixed (fractional-level PASS; PDG-\(\sigma\) strict harder) | run.py · recipe.md · result.md |
Public-data inventory
Public-archive data, used directly in the analyses on this page. Detailed scale tabulation lives on the empirical-status page. Total: ~22 million samples across 13 archives, including 20.4M LIGO strain samples (GWOSC GWTC-1+2.1+3), 1.3M PTB Yb⁺/Sr clock samples (PTB-OAR), 305 Euclid Q1 strong-lens systems, 293 King 2012 absorbers, 175 SPARC galaxies (Lelli–McGaugh–Schombert 2016), 76 NANOGrav 15-yr pulsars, 31 cosmic-chronometer H(z) measurements, 17 H₀ method values, 97 NIST atomic observables, 12 CODATA / PDG structural identities, 7-bin DESI Y1 BAO, KiDS-Legacy 2025 S₈, Lange 2021 LPI bound.
The broader internal "278/278 PASS" / 3.3M-data-points framing of the same programme is not used as a headline figure here because (a) its underlying samples include synthetic-mock subsets (~14 of 15 LIGO events, 10K of 11.7K SNe, 100K-pixel synthetic CMB) and (b) the master-Bayes-factor aggregate log₁₀(BF) = +69.5 is sensitive to alternative-theory specification. The cleanest defensible single statistics on this page are the 17-method H₀ correlation slope (7.34σ), the structural-identity Bayes factor (+27.5), the BEC reality test (+4.34), and the per-test 33-facet 20/13/0 after the BAO geometry revision.
What would falsify all of the above
- BepiColombo MORE 2028 measures γ − 1 = 0 ± 3 × 10⁻⁶. Falsifies the conformal-frame mapping; falsifies the BD coupling at ω₀ ≤ 1.7 × 10⁵. Forecast detection significance at the DCT prediction γ − 1 = −1.998 × 10⁻⁵: 6.7σ (8σ best-case).
- Euclid DR1 (Oct 2026) finds the cluster M_lens / M_dyn ratio flat in z, or peaks at a different z, or a different value than 1.30 ± few percent at z ≈ 1.5.
- Independent reproduction of the 17-method H₀ analysis with pre-registered condensate-density quantification gives slope < 5σ.
- Direct-detection finds a particle dark-matter signal (any positive WIMP / axion / dark-photon detection at >5σ).
- Refinement of CODATA moves any of the 12 structural-identity matches outside its current residual band by >3σ without a corresponding refinement of the polytope derivation.
Source documents (DCT cluster paper bodies): 17-method H₀ correlation, structural-identity Bayes factor v2, BEC reality test, multi-facet empirical tests, cosmic-chronometer findings, master combined, plus the public-data archives cited inline.