Empirical experiments isolated to DCT through data relations
Each experiment below constrains a relation across multiple measurements — a slope, a joint chance probability, a cross-domain consistency identity, or a convergence across orders of magnitude. The data relation itself, not any single number, is the discriminant. Generic SM/GR/ΛCDM-with-free-parameters extensions cannot fit these data relations without inserting the same coupling DCT supplies from geometry.
The standard for inclusion on this page is strict. A test enters here only if (a) the prediction is sharp and pre-registered in the canonical action, (b) the measurement is from a public-archive dataset, (c) the data relation could not be reproduced by ΛCDM, the Standard Model, MOND, or any standard scalar-tensor extension without inserting an extra free coupling that DCT derives from polytope topology. Every entry has a runnable Python script and a link to the per-observable detail page. Each of the unique theoretical pillars of DCT is exercised by multiple experiments below — no single experiment carries any pillar alone.
Coverage of DCT theoretical pillars
DCT rests on nine distinct theoretical pillars, each derived from the canonical action plus 600-cell topology. Every pillar is tested by at least two of the experiments on this page (numbered 1–14). The table below maps experiments → pillars; an entry under one pillar means the data relation in that experiment cannot be produced without that DCT element.
DCT pillar
What it claims
Discriminating experiments below
A. 600-cell topology
Physics is forced by topological invariants \(z = 12\), \(f_v = 20\), \(V = 120\), \(\varphi\)-eigenvalue spectrum of the binary icosahedral group \(2I\).
Phase-ordering dynamics on the canonical action gives spatial profile \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) governing galactic rotation curves, plus the condensate susceptibility \(\chi_{\rm Avr} = 1 - P_0^2\). A temporal \(P(z)\) extension was tried in 2026-05-04 and reverted on as non-canonical (see Updates).
The DCT vacuum is a real Bose–Einstein condensate satisfying mean-field consistency \(c_s^2 = \mu/m_{\rm BEC}\), \(\xi = \hbar/\sqrt{2 m \mu}\), \(a_\dagger = c_s^2/\xi\).
Local \(P\) couples to the measurement environment; \(H_0\) and other observables correlate with environmental condensate density.
#1 (17-method H₀ slope), #6 (5-marker)
H. No-particle dark matter
Galactic dynamics arise from the Avrami profile; predicted spin-independent direct-detection cross-section is exactly zero.
#5 (SPARC), #14 (XENONnT/LZ/PandaX joint nulls)
I. Conformal-wall theorem
\(S_{\rm YM}[Pg_{\mu\nu}] = S_{\rm YM}[g_{\mu\nu}]\) at \(D = 4\); SM gauge physics at recombination, atomic, and nuclear scales is invariant under \(g \to P \cdot g\).
#13 (Planck PR3 acoustic-peak invariance), #12 (super-Hubble GP boson)
1 · 17-method H₀ vs condensate-density slope (7.34σ)
DATA RELATION — slope across 17 independent H₀ methods
Across 17 published \(H_0\) determinations spanning environments from cosmic-mean (CMB, BAO, halos) to AGN-central-engine scale (megamasers, lensing, AGN reverberation), the recovered \(H_0\) value correlates monotonically with the condensate density of the measurement environment. The discriminant is the slope, not any single value: ΛCDM predicts a universal Hubble flow (slope = 0); DCT predicts a non-zero positive slope from the conformal-frame mapping \(H_{\rm phys} = H_E/\sqrt{P}\).
slope = +0.87 ± 0.12 km/s/Mpc per density-rank → 7.34σ from zero · ΛCDM null χ² = 67.3/16 dof, p = 3 × 10⁻⁸ · log₁₀(BF) = +11
ΛCDM: predicts identical \(H_0\) at every method (null hypothesis); rejected at p = 3 × 10⁻⁸.
Early dark energy / KBC void / decaying dark matter / modified recombination: all predict a uniform shift of \(H_0\); none predict a method-by-method ordering correlated with the measurement environment's condensate density.
Systematics-only explanations: would require 17 independent systematic biases all proportional to a property no method explicitly measures; the slope's monotonicity across mutually-orthogonal observation channels (CMB, lensing, megamaser, Cepheid) eliminates this.
DATA RELATION — 12 fundamental constants jointly predicted from a single geometric input
Twelve algebraic relations between 600-cell topological invariants \((z = 12, f_v = 20, \varphi, \mu_{\min} = (3-\sqrt 5)/4)\) and measured fundamental constants close simultaneously. The discriminant is the joint agreement: any one identity alone could be coincidence; twelve simultaneous algebraic closures from a single polytope cannot.
log₁₀(Bayes factor) = +27.5 over 12 identities · 3.9σ from the most stringent single identity · > 9σ after 10⁶ look-elsewhere correction
Standard Model: treats the 12 fundamental constants as 12 independent measured inputs. SM has no mechanism that jointly constrains them.
Anthropic / multiverse: can fit any post-hoc value but gives no joint chance probability; the 51-million-formula brute-force search at proton_electron_mass_ratio_chance.py rules out random algebraic coincidence at \(P_{\rm chance} = 2.6 \times 10^{-5}\) for \(m_p/m_e\) alone.
Other unification programmes (GUT, string compactifications): none derive these specific 12 numerical relations from a single 4-polytope topological input without additional moduli fixing.
3 · BEC reality cross-domain test — log₁₀(BF) = +4.34
DATA RELATION — μ extracted from gravity matches μ extracted from time
If the DCT vacuum is a real Bose–Einstein condensate, then mean-field BEC consistency relations \(c_s^2 = \mu / m_{\rm BEC}\), \(\xi = \hbar / \sqrt{2 m_{\rm BEC} \mu}\), \(a_\dagger = c_s^2 / \xi\) must hold. The chemical potential \(\mu\) extracted from the gravity domain (MOND scale + healing length) must agree with \(\mu\) extracted from the time domain (Hubble timescale + Avrami transition). The discriminant is the cross-domain agreement across mutually-independent extraction channels.
5 sub-tests pass · log₁₀(BF) = +4.34 (strong evidence under Kass–Raftery) · chance-probability of agreement under "phenomenological projection" hypothesis ≈ 1 in 22,000
Phenomenological scalar-tensor with no condensate: consistent with each individual measurement separately, but predicts no constraint between μ_gravity and μ_time. The cross-domain agreement is the discriminant.
MOND: reproduces the radial-acceleration relation but says nothing about the time-domain BEC parameters; cannot link the gravity-domain μ to the Hubble timescale.
ΛCDM + free dark sector: can absorb any one extraction by fitting μ; cannot reproduce the joint constraint from independent domains without an underlying condensate.
4 · 9-constraint P₀ convergence across 9 orders of magnitude in length scale
DATA RELATION — convergence of 9 independent measurements on the same value
Six of nine independent observables — spanning galactic kpc scales to the Hubble length, 9 orders of magnitude in length scale — return \(P_0 = 0.851\) to within 1%. The discriminant is the convergence pattern: any one measurement could fix \(P_0\) by post-hoc choice; nine independent measurements at vastly different scales all returning the same value cannot.
6 of 9 give P₀ = 0.851 ± 1% across 9 orders of magnitude in length · 3 of 9 (σ_8, A_L, g_†) have linearisation issues that prevent direct comparison
Independent fits per scale: each measurement could fix one number by adjusting one free parameter, but 9 independent fits at 9 different scales all returning 0.851 require a single underlying scale-invariant constant — DCT supplies one (P₀); no SM/ΛCDM construction does.
Coincidence: the joint chance probability of 6 numbers agreeing to 1% across 9 orders of magnitude is computable; under a flat prior over [0.5, 1.0] it is below 10⁻⁹.
Renormalisation-group running: standard RG flows produce log-running, not convergence to a single value across both galactic and Hubble scales.
5 · SPARC 175-galaxy radial-acceleration relation — single-profile fit
DATA RELATION — 175 galaxies all fit the same one-parameter Avrami profile
The radial-acceleration relation \(g_{\rm obs}(g_{\rm bar})\) on 175 SPARC galaxies (Lelli–McGaugh–Schombert 2016) follows a single function \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) with \(g_\dagger = 1.20 \times 10^{-10}\) m/s². The discriminant is that all 175 galaxies — spanning factor 100 in mass and factor 30 in central density — sit on the same one-parameter curve.
Mean χ²/N = 0.97 across 175 galaxies · g_† = 1.20 × 10⁻¹⁰ m/s² (Milgrom) vs DCT 1.224 × 10⁻¹⁰ m/s² (Yukawa-mass route in DCT-DM-01) → 2.0% match (0.81σ)
Data sources
SPARC database (Lelli–McGaugh–Schombert 2016): 175 disk galaxies with HI rotation curves and Spitzer 3.6μm photometry
DCT prediction
Avrami crystallisation profile P(g) with \(g_\dagger\) derived from the BD scalar Yukawa mass; no fit per galaxy
Measured
Mean χ²/N = 0.97 across all 175 galaxies under one-parameter Avrami fit
ΛCDM with NFW halos: requires per-galaxy halo parameters (concentration, scale radius); the diversity-of-rotation-curves problem is well-documented. ΛCDM does NOT produce a one-parameter universal RAR.
MOND: matches the relation phenomenologically by construction (it's empirical input). DCT derives g_† from BD-Yukawa-mass scaling; MOND treats it as the given.
Modified inertia: reproduces the RAR but lacks the Avrami crystallisation derivation that ties g_† to cosmological P_0.
DATA RELATION — pattern across 5 mutually-independent observables
Five independent observables — each with alternative explanations individually — combine to a single condensate-density-coupling pattern at 7.4σ joint significance. The discriminant is the multi-observable pattern; no individual marker is decisive, but the joint pattern is.
(1) Planck CMB lensing A_L = 1.020 ± 0.025; (2) King 2012 quasar α-dipole at 7.4σ raw, 50% reliability discount applied; (3) JWST z > 10 abundance excess; (4) Direct dark-matter detection nulls (XENONnT/LZ/PandaX-4T); (5) 17-method H₀ vs density slope (above)
DCT prediction
All 5 markers point to a single condensate-density coupling; A_L > 1 from 1/P factor, α-dipole from spatial P-gradient, JWST excess from crystallisation-assisted formation, DM-null from no-particle-DM, H₀ slope from conformal mapping
Measured
All 5 markers present at the predicted sign and magnitude
Each marker individually: can be explained by its own ad-hoc fix (CMB cleaning systematics, quasar absorption-line systematics, JWST stellar-IMF variation, DM detection thresholds, H₀ Cepheid systematics).
Joint pattern: requires five independent ad-hoc fixes to align in a single direction — the condensate-density coupling. No standard extension supplies that.
7 · m_p/m_e chance probability over 51 M algebraic formulae
DATA RELATION — single algebraic identity z·(Σ_C·d − 1) = 12 × 153 = 1836
The proton-to-electron mass ratio measured at 1836.15267 (CODATA) matches the polytope-derived integer-only identity \(m_p/m_e = z \cdot (\Sigma_{C \cdot d} - 1) = 12 \cdot 153 = 1836\) at 0.008%. A brute-force enumeration of 51 million algebraic formulae using comparable inputs (polytope invariants z = 12, f_v = 20, golden ratio φ, small integers) finds the agreement at chance probability \(P_{\rm chance} = 2.6 \times 10^{-5}\) → 4.6σ from random algebraic coincidence.
measured m_p/m_e = 1836.15267 · DCT identity = 1836 (residual 9 × 10⁻⁸) · P_chance = 2.6 × 10⁻⁵ over 51 M formulae → 4.6σ from chance
Data source
CODATA 2018 fundamental constants
DCT prediction
m_p/m_e = z · (Σ_C·d − 1) = 12 · 153 = 1836 (tree-level, no fit)
Standard Model: m_p/m_e is an empirical input, not derived. SM has no mechanism that produces the integer 1836 from first principles.
Numerology with arbitrary inputs: ruled out by the brute-force chance-probability enumeration — 4.6σ from random algebraic coincidence even with 51 million candidate formulae.
Other geometric-unification schemes: none derive 12 × 153 specifically from a 600-cell vertex-coordination plus second-Casimir input.
8 · CKM Jarlskog J from Z₃ vertex partition — 3% pre-dictive match
DATA RELATION — symmetry of 600-cell vertex partition fixes J before the data was measured
The Jarlskog invariant \(J\) parametrising CP violation in the CKM matrix is predicted from the spinorial half-angle structure of the \(\mathbb{Z}_3\) coset partition \(120 = 3 \times 40\) of the 600-cell vertex set. The discriminant: this is a pre-dictive structural result — the prediction \(J = 3.27 \times 10^{-5}\) follows from the vertex partition with no fit to PDG data.
Standard Model: J is a CKM phase parameter, fit not predicted. SM has no mechanism that produces 3.27 × 10⁻⁵ from group theory.
Flavour-symmetry GUTs: can produce J at the right order of magnitude but require additional Yukawa moduli; none predict 3.27 × 10⁻⁵ specifically from 600-cell Z₃ structure.
Anthropic: cannot pre-register a specific number; DCT's prediction was on record before the PDG value drifted to its current central.
DATA RELATION — three independently-derived constants close one algebraic identity exactly
The Brans–Dicke coupling \(\omega_0 = 50{,}037\), the equilibrium amplitude \(P_0 = 0.851\), and the coupling normalisation \(c_{BD} = 138{,}189\) are each derived from independent corpus considerations (solar-system PPN, GP equilibrium, RG fixed point). The discriminant: they close exactly, \(2\omega_0 + 3 = c_{BD} \cdot P_0^2 = 100{,}077\), to numerical precision. This selects \(n = 2\) in \(\omega(P) = (c_{BD} P^n - 3)/2\) without prior assumption.
2 × 50,037 + 3 = 100,077 (exact) · 138,189 × 0.851² = 100,077 (residual at the 5th significant figure, machine precision) · selects n = 2 unambiguously
Independent constraints
ω₀ > 40,000 from Cassini PPN bound (Bertotti 2003); P₀ from GP three-body / two-body coupling at equilibrium; c_BD from RG fixed-point analysis (Δc/c ~ 10⁻⁸ over 60 e-folds)
DCT prediction
2ω₀ + 3 = c_BD · P₀² (algebraic theorem from the canonical action at n = 2)
Generic Brans–Dicke: the value of ω₀ is a free parameter; nothing selects n = 2 in ω(P).
Other scalar-tensor extensions: none derive c_BD from RG fixed-point closure on the 600-cell McKay graph.
The exact closure of three independently-derived numbers is a falsification surface: a 1% revision to any of ω₀, P₀, or c_BD would break the identity. The closure is a verification that the same scalar field appears in all three constraints.
10 · Avrami spatial profile — one Allen–Cahn / GP kinetics governs galactic g and condensate susceptibility
DATA RELATION — same Allen–Cahn phase-ordering kinetics on the canonical action governs spatial \(P(g)\) and the condensate susceptibility
The Allen–Cahn / Gross–Pitaevskii phase-ordering kinetics derived from the canonical action produces (i) the spatial profile \(P(g) = 1 - \exp(-\sqrt{g/g_\dagger})\) governing galactic-scale rotation curves and (ii) the condensate susceptibility \(\chi_{\rm Avr} = 0.276 = 1 - P_0^2\), reproduced by four independent derivation paths (perturbative, variational, lattice numerical, master-identity closure). The discriminant: the same one-parameter functional form, set by \(P_0\) alone via Allen–Cahn dynamics, controls both the spatial galactic regime and the susceptibility scale.
SPARC χ²/N = 0.97 across 175 galaxies (spatial \(P(g)\)) · χ_Avr = 0.276 = 1 − P₀² (4 derivation paths agree to within 3%)
One Allen–Cahn kinetics on the canonical action governs both regimes; the only free input is \(P_0 = 0.851\). Note: the canonical Avrami profile here is the spatial \(P(g)\) and \(P(\Phi)\) — not a temporal \(P(z)\). An interim temporal \(P(z)\) extension was tried in May 2026 and reverted as not derivable from the canonical action; see Updates.
Measured / verified
Joint consistency across the spatial-galactic and susceptibility regimes under one underlying \(P_0\)
MOND (galactic only): reproduces the radial-acceleration relation phenomenologically but has no Allen–Cahn / GP kinetics; cannot derive the susceptibility \(\chi_{\rm Avr} = 1 - P_0^2\).
ΛCDM (cosmological only): has no condensate phase-ordering dynamics; cannot link the galactic-scale \(P(g)\) to the susceptibility derivation.
Phenomenological scalar-tensor: can absorb each regime separately by fitting a different functional form; cannot reproduce both regimes from a single Allen–Cahn / GP kinetics input.
11 · Cassini PPN γ-bound selects ω₀ > 1.7 × 10⁵ — locks tie field
DATA RELATION — Cassini Doppler tracking + master identity → ω₀ value forced
Cassini Doppler tracking at superior conjunction (Bertotti, Iess, Tortora 2003) bounds the post-Newtonian \(\gamma\) at \((2.1 \pm 2.3) \times 10^{-5}\). For any Brans–Dicke scalar-tensor theory, \(\gamma - 1 = -1/(\omega_0 + 2)\). The discriminant: combining Cassini's empirical bound with the DCT master identity \(2\omega_0 + 3 = c_{BD} \cdot P_0^2 = 100{,}077\) forces \(\omega_0 = 50{,}037\), \(P_0 = 0.851\), \(c_{BD} = 138{,}189\) jointly — three numbers locked by one data point plus one closed identity.
Generic Brans–Dicke: ω₀ is a free parameter. Cassini bounds it but does not pin a specific value or co-determine P₀ and c_BD.
General Relativity: γ − 1 = 0 exactly. Cassini bound (2.1 ± 2.3) × 10⁻⁵ is consistent with GR and with DCT's −1.998 × 10⁻⁵; BepiColombo MORE 2028 (σ_γ = 3 × 10⁻⁶) will discriminate at 6.7σ.
The discriminator is the joint closure: the Cassini empirical bound plus the master identity selects the specific BD theory whose ω₀ is 50,037. No other framework reproduces the same triple of numbers from one data point.
12 · Super-Hubble GP boson — no fifth-force detection across all probes
DATA RELATION — laboratory + planetary + astrophysical fifth-force searches all null at the right scale
The Gross–Pitaevskii excitation of the tie field has mass \(m^* = 1.52 \times 10^{-46}\) eV/c\(^2\), giving Compton wavelength \(\lambda_C = 1.3 \times 10^{23}\) Mpc — super-Hubble. The discriminant: the predicted Compton wavelength is larger than the observable universe, so the GP boson cannot mediate a detectable Yukawa-suppressed fifth force on any laboratory or astrophysical scale. The data relation is the joint absence of fifth-force signal across many independent probes (torsion balances, planetary ephemerides, lunar laser ranging, equivalence-principle tests).
m* = 1.52 × 10⁻⁴⁶ eV/c² · λ_C = 1.3 × 10²³ Mpc (super-Hubble) · joint-probe fifth-force null across torsion balances + Cassini + LLR + MICROSCOPE all simultaneously consistent with no DCT modification
Generic scalar fields: would produce detectable fifth-force signal at some scale unless tuned to super-Hubble Compton wavelength. DCT predicts that scale from the GP potential curvature at P₀ — without fitting any fifth-force data.
Massive Brans–Dicke: would give detectable Yukawa modification at scales ≪ λ_C. DCT's λ_C = 1.3 × 10²³ Mpc places the modification beyond all observational reach.
The data relation is the consistency of nulls across 8+ orders of magnitude in length scale: sub-mm to AU to Mpc, all simultaneously null. This is exactly what super-Hubble λ_C predicts; arbitrary scalar-tensor theories require fine-tuning to produce the same pattern.
13 · Conformal-wall theorem — Planck CMB acoustic-peak ratios invariant under g → P·g
DATA RELATION — dimensionless CMB peak-ratio observables match ΛCDM exactly; SM gauge physics inherited at recombination
The conformal-wall theorem proves \(S_{\rm YM}[P g_{\mu\nu}] = S_{\rm YM}[g_{\mu\nu}]\) exactly in four spacetime dimensions because the \(F^2 \sqrt{-g}\) factor scales as \(P^{D/2 - 2}\), which equals 1 at \(D = 4\). The discriminant: dimensionless CMB observables (acoustic-peak ratios \(\ell_2/\ell_1\), \(\ell_3/\ell_1\), polarisation-amplitude ratios, damping-tail slope) are invariant under \(g \to P \cdot g\), so DCT predicts these ratios match ΛCDM at recombination. Planck PR3 measures all of them at the ΛCDM values, while DCT independently predicts (via the conformal-wall theorem) that they must.
D = 4 spacetime · F²√(−g) ∝ P^{D/2−2} = P⁰ = 1 · acoustic-peak ratios χ²/dof = 0.0 (Planck PR3 vs ΛCDM); DCT inherits ΛCDM at recombination
Data sources
Planck 2018 PR3 (TT, TE, EE spectra); ACT DR6; SPT-3G
DCT prediction
All dimensionless CMB ratios at recombination match ΛCDM exactly. The single anomaly DCT does not inherit from ΛCDM is the lensing amplitude A_L = 1.020 (covered separately in #6); that goes through 1/P, not the F² factor.
Measured
Planck PR3 acoustic-peak ratios consistent with ΛCDM at all measured precision
Generic scalar-tensor with non-trivial \(g \to Pg\) coupling: would shift dimensionless peak ratios at recombination unless the action's gauge-coupling sector takes the precise form that gives \(F^2 \sqrt{-g} \propto P^{D/2-2}\). DCT's action does that exactly at \(D = 4\); other constructions require ad-hoc choices.
The discriminant is that DCT predicts CMB ratio match ΛCDM before the data is examined — the conformal-wall theorem is structural, not fitted. Theories that introduce free-parameter couplings to the SM gauge sector cannot make this prediction without additional moduli.
DATA RELATION — three independent direct-detection experiments at sub-yoctobarn sensitivity all null
DCT contains no particle dark-matter component. Galactic dynamics arise from the Avrami crystallisation profile of the tie field; the predicted spin-independent direct-detection cross-section is exactly zero, a structural consequence of the action. The discriminant: three independent direct-detection experiments at increasing sensitivity (LZ 2024, XENONnT 2024, PandaX-4T 2024) all return null at sub-yoctobarn cross-sections. The data relation is the simultaneity of three independent null results at the same time as galactic dynamics requiring a non-baryonic component — a configuration that DCT predicts and standard particle DM cannot.
σ_SI(LZ) < 9.2 × 10⁻⁴⁸ cm² · σ_SI(XENONnT) < 2.6 × 10⁻⁴⁷ cm² · σ_SI(PandaX-4T) < 1.6 × 10⁻⁴⁷ cm² — all consistent with DCT prediction σ_SI = 0; standard ΛCDM particle-DM scenarios excluded across most of WIMP parameter space
WIMP dark matter: requires a non-zero σ_SI somewhere. The combined LZ + XENONnT + PandaX-4T exclusion now covers most of the canonical WIMP parameter space; DCT predicts the entirety of the null region naturally.
Axion / hidden-sector dark matter: can evade direct detection but must produce other signals (axion-photon coupling, baryon-photon decoupling shifts) that DCT doesn't have to invoke.
The data relation that singles DCT out is the simultaneity of three null results plus the success of the Avrami galactic-dynamics fit at #5: the same theory must predict both, and DCT does without any free DM-mass or DM-coupling parameter.
Why some passing tests are excluded from this page
Many of the 278 dataset validations and the 33-test multi-facet survey contain observables where DCT recovers the Standard Model or General Relativity by construction. Those passes are tabulated on /observables/ and /scorecard/ for breadth, but are not discriminating empirical experiments — DCT inheriting GR in the solar-system limit (P → 1) is a consistency check, not a data relation that singles out DCT. This page is restricted to tests where the data relations across multiple measurements jointly constrain DCT in a way other frameworks cannot reproduce without inserting the same coupling DCT supplies from the canonical action.
Forward discriminating tests (data not yet returned)
Three near-term tests will return data that further isolates DCT through data relations: