Pre-registered protocol for a Gaia DR3 quasar proper-motion constraint on the stochastic gravitational-wave background (v1.0, frozen before data statistics)

We deposit, before computing any data statistic, the frozen analysis protocol for a constraint on the stochastic gravitational-wave background from the proper motions of the ~1.6 million Gaia-CRF3 quasars (Gaia DR3), fitted with electric/magnetic vector spherical harmonics (l >= 2) with the dipole (solar acceleration) as nuisance. The analysis is a "multiverse": every combination of contested choices (proper-motion significance cut, magnitude limit, astrometric quality cuts, Galactic and ecliptic masks, weighting scheme, l_max, estimator) is a branch (preset "huge"). Each branch is calibrated against two data-derived references built from the catalogue records: a latitude/magnitude "scramble" and a random-sign "flip", each with signal-free and injected-signal realisations (R = 20, reference amplitude A_ref = 9 (uas/yr)^2). The deposit contains the code, the final configuration, the SHA-256 freeze of code, configuration, GR response and catalogue, the written decision rules (2-sigma branch classification, use of both references, what counts as limit versus candidate, treatment of cosmic variance and of the Omega_GW convention), and the pre-computed null ensembles. Validation so far is on synthetic catalogues only; the download script was written without access to the Gaia archive. Gaia DR3 data and the literature (e.g. Darling 2024, Akhmetov et al. 2026) are public, so this pre-registration is weaker than one made before a data release; a separate protocol will be deposited before the Gaia DR4 release (2026-12-02). Realistic expected product: a calibrated upper limit with a map of how much each analysis choice moves it, not a detection. Any code or rule change after this deposit will be a dated amendment.