Euclid DR1: A Pre-Registered Contender Showdown

ESA expects DR1-Foundation in November 2026, with exact dates to be communicated.A pre-registration card locking five Mode Identity Theory predictions against four named contenders (ΛCDM, w₀wₐCDM, EDE, MOND) ahead of Euclid Data Release 1, each with a stated falsification threshold. Λ epoch-independence Observable: dark-energy density versus redshift (spectroscopic BAO plus weak lensing). Prediction: Λ_obs = 3/R² is the topological first positive eigenvalue, so Ω_DE(z) is flat across all DR1 redshift bins. Λ is constant in cosmic time, not a fitted parameter. a0(z) evolution Observable: the acceleration scale at z ≈ 1 to 1.5 via galaxy-galaxy weak lensing and the stellar-mass-halo-mass relation. Prediction: a0(z) = a0(0) · H(z)/H0, so the acceleration scale grows with redshift (about 2.4× local at z = 1.5, about 20.5× at z = 10). w_eff(z) trajectory Observable: the dark-energy equation of state from spectroscopic BAO plus photometric weak lensing. Prediction: w_eff(z) > −1 at all z in the fiducial-matter split (proven analytically); any apparent CPL phantom crossing is a template-projection artifact, not a physical crossing. Stellar mass function at z ≳ 10 Observable: abundance of ~10^10 solar-mass galaxies at z > 10 in wide-area photometry. Prediction: JWST-class massive galaxies persist in Euclid statistics, reachable with standard star-formation efficiency (ε_SF ≲ 1) given a0(z = 10) ≈ 20.5× local. (1+z)^1 coefficient in H²(z) Observable: a linear-in-(1+z) term in the expansion rate extracted from high-precision BAO. Prediction: this coefficient is negative with magnitude |β| < 0.012 tied to the phase parameter s0, and the term is absent from every standard FLRW component (radiation, matter, curvature, Λ). version 2 edits: 2026-06-21 and 2026-07-12: Row I's prediction cells were reworded from "the topological ground eigenvalue" and "a topological eigenvalue" to "topologically fixed". 2026-07-07: Row II's threshold was rewritten. It read "kinematic follow-up finds a₀ consistent with a₀(0) at ≥ 2σ" and now reads "kinematic follow-up rules out the predicted a₀(z) evolution at ≥ 2σ, with a₀(z=1.5) consistent with the constant a₀(0)". 2026-09-21: Row I was given a scoring rule that fixes how matter is treated in the reconstruction. 2026-09-23: Row IV was given its scoring rule. It is scored against the full-efficiency ceiling of Boylan-Kolchin (2023), on the first qualifying Euclid measurement. 2026-09-24: the card's ground rules, including the rule that an edit voids a row, were replaced by a short scoring section that opens with the deposit rule. 2026-09-24: Row IV's power rule was made exact: - a fail can come from either statistic once one is powered; - a pass needs both statistics powered; - a count's power is judged at the count a population at half the ceiling would give. Dated notes were added on 2026-06-26; 2026-07-18 (a clarification, a note on Row II, and the schedule update); 2026-09-01; 2026-09-02; and 2026-09-03. The surrounding prose was also edited.