Structural Cosmology and Euclid: Explicit Benchmark Conditions and Decision Rules for a Growth-Suppression Test

This document specifies an explicit phenomenological benchmark and a conditional decision protocol for a future test of growth suppression with Euclid fσ₈ measurements in Structural Cosmology (SC). An earlier source investigation could not reconstruct the baseline and amplitude conditions behind earlier numerical statements, so new comparison conditions are specified here: a scale-independent fractional reduction of 5–7 percent of a specified reference fσ₈ over 1 ≤ z ≤ 1.5. The adopted benchmark is motivated by the 5–7% suppression stated in earlier publications, but specifies new operational comparison conditions. It neither reconstructs those earlier predictions nor constitutes a newly derived SC prediction. Rejection or non-rejection applies to this benchmark under the stated conditions; it does not by itself determine the validity of the earlier claims or of SC as a whole. The paper states the reference expansion and growth equation, normalization, data-eligibility conditions, bin response, covariance requirements and a conservative 5-percent rejection rule for the composite benchmark. If the test does not reject the benchmark, the outcome is reported as “not rejected.” Failure to reject does not establish agreement, equivalence, or confirmation of the benchmark; missing requirements lead to “not executable.” Product-independent software checks on synthetic inputs are summarised as a cross-check (A) between two implementations produced in the same drafting process; they are not a third-party verification (T), which has not been made. The paper also discloses trial runs that preceded the recorded run, three injected defects that the Monte Carlo rule did not detect, and a numerical limit: in double precision the two implementations classified some inputs very close to the threshold differently, and the equality case could be examined on the production path of one of the two implementations only. The checks do not validate the implementation as a whole. Status: benchmark conditions adopted; implementation validation incomplete; the freeze of the analysis conditions before inspecting target data (F) not completed. No Euclid measurement has been analysed. The software checks use synthetic inputs. Their results are not Euclid forecasts, do not establish detectability with Euclid data, and do not constitute evidence for or against SC. Three illustrative figures and three numbered tables are included. Licences differ by file type. The paper (PDF and Markdown), its figures, the explanatory documents and records, the numerical outputs (JSON, CSV and result or log text files) and the hash lists are licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). The code files (.py) in the evidence archive are licensed under the MIT licence; the licence text is LICENSE-MIT.txt in the archive. The file-by-file assignment is LICENSE_FILE_LIST.txt and the rules are in LICENSES.md, both in the evidence archive. These licences do not extend to third-party parts. Imported libraries are not redistributed and retain their own licences; any third-party font components remain subject to their applicable licences.