Structural Cosmology: Preparation and Outstanding Requirements for Comparison with Euclid

This paper organizes, before Euclid data are usable for a comparison, the earlier predictions of the Structural Cosmology series (a fσ₈ difference of −5 to −7 %: near z ≈ 1–1.5 in v1.3 and near z ≈ 1.5 in v2.0; O(5 %) in v2.2), the results of a published audit of the v2.2 demonstration code, and Euclid's announced data-product plans (DR1-Foundation, tentatively 12 November 2026; Complete DR1, mid-2027), and states the conditions that must be settled before a comparison can start. Ten outstanding requirements (C1–C10) are listed: the estimator to be compared, its definition, redshift bins, analysis scales, covariance, reference cosmology, normalization, the correspondence to the earlier predictions, blinding, and the contents of DR1 as released. All are open. Provision of fσ₈ estimates could not be confirmed in the product lists examined; the plans for clustering statistics and covariances are confirmed only at section level. If the correspondence to the earlier predictions is not established, a comparison under newly adopted conditions is not to be treated as a direct verification of the earlier predictions. Not done: any comparison with observed values, any judgment of support or disagreement, and the fixing of decision rules. The numerical threshold used in the audit (EPS = 1e-4) is not reused as a decision threshold for an observational comparison. Confirmations about Euclid documents rest on body text or summaries returned by a retrieval tool, not on the original documents. The record includes a materials archive (earlier drafts, the eligibility table and its versions, source records, plotting code, input CSV and figures).