Pre-registered Predictions

The TSTU framework predicts two distinct but correlated signatures: (1) a structure growth rate slightly suppressed relative to ΛCDM — fσ₈(0.5) ≃ 2 % below the Planck ΛCDM expectation (Paper IX), and (2) an enhanced gravitational coupling μ ≃ 1.018 specifically inside cosmic voids where the chameleon mechanism is unscreened (Paper VI). Void-stacked E_G testing (Hamaus-style) at z ≃ 0.5–1.0 provides a quantitative target for DR2/DR3.

fσ₈(z=0.5) TSTU

≃ 0.468 (Paper IX) · 0.465 (Paper XI)

fσ₈(z=0.5) ΛCDM

≃ 0.480 (Paper IX §3.3)

μ(voids) TSTU

1.018 (canon)

E_G deficit

1.1 % (canon)

δE bound (Paper VI)

≲ 2 × 10⁻⁶

Falsification (pre-registered decision table, Paper IX): the fiducial model is falsified if Euclid measures μ(voids) < 1.005 at > 2σ, or if void E_G equals global E_G in the lowest-density quintile at > 2σ. If μ(voids) > 1.010 at > 2σ the model is not falsified but recalibrated (β, H₀, w₀ — Paper X); above 1.030 at > 3σ the measurement exceeds the prediction and forces an extension of the formalism; Paper IX tabulates that stronger-coupling branch at μ ≃ 1.036 and ≃ 3.4 % deficit. Full support: fσ₈(0.5) ∈ [0.455, 0.482]; above 0.485, TSTU under-predicts growth and β must be raised. Associated null prediction: |Δ_BAO| < 0.2 % over z ∈ [0.2, 1.5].

Paper XIV §3.4 distinguishes three mechanisms that drive the invariant to its threshold Y_c. One of them, stochastic fluctuation of the background field, requires no neighbour: it therefore puts a floor on the event rate that the two-body encounter cannot cross. The temporal rarefaction must then plateau in the deepest voids instead of continuing to grow. The registered quantity is not “a plateau exists”, which would be untestable, but a ratio of ratios: the growth of the RSD/lensing decoupling between two depth bins. Systematics cancel twice — once inside each ratio, once between the bins.

𝒜 = ℛ(−0.95)/ℛ(−0.85), channel α alone

3.79

𝒜 with a 1% β channel

2.78

𝒜 with a 10% β channel

2.09

𝒜 ΛCDM and MOND

1.000 exactly

Selection threshold

δ_min ≤ −0.60

Falsification: a measurement consistent with 𝒜 = 1 at 3σ refutes the decoupling itself, and with it the event-projected reading of Paper XIV. A clean power law down to the deepest bins, with no plateau at survey sensitivity, refutes the β channel of §3.4 and forces its removal from the classification. Any value between 1 and 3.79 measures that channel's share: the classification stops being a taxonomy and becomes a quantity. The exponent is not free — it is the tracer bias, measured by the very survey that tests the prediction.

Paper XIII's analytical enclosure (1.070 ≤ G_eff ≤ 1.623) predicts a +0.25 dex stellar-mass excess at z ≈ 9 compared to ΛCDM expectations. The Labbé+2023 data (6 candidates) qualitatively corroborate; upcoming NIRSpec spectroscopic confirmation will validate or refute the photometrically-inferred masses.

ΔlogM★ TSTU

+0.25 dex (Bondi +0.18, halo +0.07)

t_coll (z=9) TSTU

500 Myr

t_coll (z=9) ΛCDM

552 Myr (+10%)

G_eff,max

1.350

Falsification: if NIRSpec confirmation reveals that the Labbé candidates are photometric artifacts (masses overestimated by > 0.3 dex), the framework's most emblematic prediction falls.

Paper XV (May 2026) refines the H₀ prediction: a non-circular ΛCDM-pure refit of Pantheon+SH0ES with full STAT+SYS covariance yields H₀ = 73.42 ± 1.01 km/s/Mpc (χ²/dof = 0.897), in 0.29σ agreement with SH0ES. The Paper II value (76.2) is identified as a statistical circularity artifact under the joint TSTU prior (Paper XV §3.5). The new TSTU prediction is H₀(z=0.5) ≃ 71.5 km/s/Mpc via linear-growth reframing (Paper XV §3.6), in 1.90σ marginal tension with ΛCDM-pure.

H₀(z=0.5) TSTU (Paper XV)

≃ 71.5 km/s/Mpc

H₀ ΛCDM-pure refit

73.42 ± 1.01

H₀ SH0ES 2022

73.04 ± 1.04

H₀ Planck 2018

67.4 ± 0.5

χ²/dof Paper XV refit

0.897

Falsification protocol (Paper XV §3.6): if TDCOSMO 2027–2030 returns H₀(z=0.5) ∈ [71.0, 72.0] km/s/Mpc, the TSTU linear-growth mechanism is confirmed. If TDCOSMO returns H₀(z=0.5) ≳ 75 or ≃ 73.4 km/s/Mpc at > 2σ, Paper XV Model A is falsified and structural revision is required.