Pre-Registration for Euclid DR1: Two-Layer Hubble Tension Test (v2, supersedes v1)

Status: WORKING — This version (v2, 2026-04-26) supersedes v1 (deposited 2026-04-16, now DEPRECATED). v1 remains in the record at its versioned DOI as the locked-in-time original; v2 is a structurally different pre-registration with tighter scope.

Changelog

v2 — 2026-04-26 (WORKING): Restructured to pre-register two independent falsifiable claims (Layer 2 algebraic shared-factor cancellation; Layer 3 Ω_m parameter-fingerprint identification). Dropped all v1 ξ-normalization scaffolding for the following reasons:

• Δ_k six-tier corrections: not MCMC-fitted (verified against October 2025 simulation logs), but the total was hardcoded as a target — corrections.py sets TOTAL_H0_CORRECTION = -4.54 with the comment SH0ES 73.04 → Converged 68.5 km/s/Mpc. Per-tier breakdown explicitly marked (approximate).
• M(ξ) metric: Framework B was never formally derived (per the deposit's own framework_clarification.md).
• 76% reduction headline: Type-A resolution framing, incompatible with the framework's structural-identification claim.
• Locked Ω_m prediction window (0.295 ± 0.015): post-dated DESI DR2's public result (0.289 ± 0.007, arXiv:2503.14738).
• z-gradient test: g² = 0.880 flat across Euclid range made the test inoperative.
• NPT envelope: v1 §B.3 admitted NPT will not be exceeded under standard ΛCDM — structurally unfalsifiable.

Replaced with operative Layer 2 + Layer 3 falsification mechanisms grounded in MN-26-1108-L's algebra (concept DOI 10.5281/zenodo.19655902) and an absolute-banded Ω_m test for Euclid DR1.

v1 — 2026-04-16 (DEPRECATED): Merged Framework A (empirical six-tier ΔH_0 = -4.54 km/s/Mpc corrections) and Framework B (theoretical ξ-dependent metric M(ξ)) in a single pre-registration, against the deposit bundle's own framework_clarification.md recommendation. Subsequent April 2026 structural audit identified eight structural failures invalidating the construction.

What v2 pre-registers

Layer 2 — Algebraic shared-factor cancellation: Predicts that applying MN-26-1108-L's symbolic decomposition to post-DR1 SH0ES + Euclid-equivalent constraints yields residual signed-discrepancy δ_r ≈ 1.0σ. Pass: δ_r ≤ 1.5σ. Fail: δ_r ≥ 2.0σ.

Layer 3 — Ω_m parameter-fingerprint identification: Predicts Euclid DR1 measures Ω_m in absolute band [0.282, 0.302]. Fail: Ω_m > 0.310 OR Ω_m < 0.275 (Planck's 0.315 sits in fail region; DESI DR2's 0.289 sits in pass region). Absolute bands committed before DR1 to keep the framework genuinely falsifiable regardless of DR1's measurement uncertainties.

Full pre-registration document: EUCLID_PRE_REGISTRATION_v2.pdf (and .md source). Layer 3 driver code uha_normalization_joint_refit.py + audit-clean fit results uha_normalization_joint_refit_results.json ship with this deposit.

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Updated 2026-05-28