Projected Galaxy-Axis Structure Across Cosmic Time

Projected Galaxy-Axis Structure Across Cosmic Time is an exploratory observational and computational study of whether projected galaxy major-axis orientations exhibit reproducible structure when galaxies are ordered by redshift-derived cosmic age. The study documents the full evidentiary trajectory of an initially striking pattern rather than presenting the favorable exploratory result in isolation. An original 28-point sequence, approximately transcribed from a pre-existing plot, showed strong lag-1 axial coherence and a broad quadratic or reversal structure under a custom permutation and leave-one-out cross-validation analysis. The sequence yielded C1 = 0.705964 with a one-sided Monte Carlo p = 0.000300, together with a quadratic-versus-linear predictive gain of 0.118303 with p = 0.002700. However, both the data sequence and the primary statistics were examined or developed after the motivating pattern had already been observed. These values are therefore treated explicitly as exploratory rather than as prespecified discovery significance. A same-sample rerun reproduced the original numerical results exactly, establishing computational reproducibility of the implemented analysis but providing no independent empirical confirmation. The fixed statistics were subsequently applied to two public-data follow-up samples. An SDSS DR17 selected-28 sample retained nominal lag-1 coherence, with C1 = 0.225730 and p = 0.031697, but failed the quadratic component, with G_curve = -0.062229 and p = 0.472453. The archived joint criterion therefore failed. A later post hoc audit of the complete archived 614-object usable SDSS parent sample found no positive chronological coherence, with C1 = -0.026184 and p = 0.831. The audit also showed that the selected-28 result was sensitive to representative-object choice. A second replication attempt using HST ACS-GC/COSMOS data was designed to cover the earlier cosmic-time interval missing from the SDSS sample. Twenty-eight targets spanning cosmic ages of approximately 4.2 to 13.2 Gyr were populated from a quality-controlled candidate pool, but neither primary statistic reproduced. The ACS-GC/COSMOS sample yielded C1 = -0.180386 with p = 0.865513 and G_curve = -0.019420 with p = 0.222378. The manuscript also subjects the full record to an archive-level methodological audit. It documents limitations including graph-transcribed exploratory inputs, post hoc statistic construction, deterministic database-query caps, SDSS position-angle precision limitations, ACS-GC acquisition truncation, unpropagated photometric-redshift uncertainty, sky-footprint effects, morphology dependence, intrinsic alignments, coordinate-basis issues, and other potential survey systematics. These limitations are not treated as explanations that rescue the original signal. Instead, they define the boundary of what the existing evidence can support. The central conclusion is deliberately narrow. The archived record does not establish a survey-independent, time-dependent projected galaxy-axis pattern, and the complete exploratory signature should currently be regarded as not replicated. The scientific contribution is therefore twofold. First, the study provides a transparent record of how an unusual exploratory pattern behaved under progressively harder reproducibility, replication, and sensitivity tests, including negative results. Second, it converts the weaknesses exposed by those tests into a prospective confirmation framework for a substantially stronger experiment. That framework emphasizes population-scale sampling, validated shape estimators, explicit uncertainty propagation, native axial statistics, sky and systematics modeling, sealed spatial holdouts, predefined decision rules, injection and recovery sensitivity analysis, and an independently held-out survey. This Fourth Edition is released as Public Version 1.0 together with a theory-neutral reproducibility supplement containing machine-readable analysis tables, archived permutation null distributions, jackknife outputs, SDSS parent-sample audit products, ACS-GC acquisition-audit material, a reproduction script requiring no live database queries, and SHA-256 integrity information. Status: Preprint; not peer reviewed. Research status of the reported signature: Not replicated.