Pre-registered cosmological predictions of a golden-ratio phase-space hypothesis (locked 19 October 2026)

This record time-stamps quantitative cosmological predictions before the data that can test them: DESI analyses including observations after 9 April 2024, Euclid growth measurements, and next-generation CMB limits on early dark energy.

Hypothesis. Let x = 1/φ ≈ 0.618034, the fixed point of x = 1/(1 + x). Each dark-sector parameter that differs from ΛCDM is set by a ladder term α_d x^d, with α_d = 1 for linear or volumetric modes (d = 1, 3) and ½ for transverse or plasma modes (d = 2, 4). For 1 + w₀, w_a and f_EDE the ladder term is the departure itself; for growth it is the value of γ.

Predictions:

• P1: w₀ = −φ/2 = −0.80902
• P2: w_a = −1/φ = −0.61803 (equivalently w_a = 1 + 2w₀)
• P3: w = −1 (dark-energy density maximum) at z = 1/√5 = 0.44721
• P4: w(0.3) = −0.9516 and w(0.5) = −1.0150
• P5: growth index γ = 1/φ = 0.618
• P6: early-dark-energy fraction f_EDE = x⁴/2 = 0.07295
• P7 (derived): S₈ ≈ 0.81

H₀ is explicitly not predicted.

PREDICTIONS.md lists the falsification criteria fixed in advance, the data status at lock time, an overlap caveat (future DESI analyses contain the DR2 data used to choose P1–P4) and honest caveats: current data measure x ≈ 0.55–0.69, consistent with 1/φ but unable to single it out; P6 is under pressure from CMB limits.

The SHA-256 hash of PREDICTIONS.md is 70b9cfb23fc1e0d119ebd81aed270933960fa52256f89f505f799bb3a81767f2 (also in PREDICTIONS.sha256).

borse_analysis_v2.zip contains the analysis code and outputs:

• fits to DESI DR2 BAO + Planck distance priors + Pantheon+/Union3/DESY5/DES-Dovekie supernovae;
• the prediction's position in DESI's official DR2 posteriors and robustness checks across CMB choices;
• the free-x fit and control constants;
• Bayes factors;
• pivot and fixed-redshift tests;
• robustness tests: DESI's binned w(z), BAO without CMB (r_d free), and the predicted early dark energy included;
• momentum-exchange and energy-exchange mechanism tests;
• the look-elsewhere test;
• growth-index fits to SDSS and DESI DR1 fσ₈;
• a CAMB cross-check;
• exact symbolic proofs;
• an automated check that every number in the paper matches the outputs;
• a verification ledger.