Compression Physics Nulls vs Metallics: Synthetic Controls and Transform Test for Frontier Normalized Efficiency Geometry

This record contains the article “Compression Physics: Nulls vs Metallics — Synthetic Controls and Transform Tests for Frontier-Normalized Efficiency Geometry” and an accompanying reproducibility kit (ZIP). This paper is a validation companion to Compression Physics via Metallic Odds Maps and is designed as a pipeline QA + false-positive calibration study for metallic-odds claims. Using the same slice representation (Y,X,Cmax⁡)(Y,X,C_{\max})(Y,X,Cmax) and frontier-normalized efficiency GEC0=Y/(XCmax⁡)∈[0,1]\mathrm{GEC}_0 = Y/(X C_{\max}) \in [0,1]GEC0=Y/(XCmax)∈[0,1], the work maps GEC0\mathrm{GEC}_0GEC0 into odds-space coordinates and runs the full compression pairing / merge procedure that generates transition pairs (tn,tn+1)(t_n, t_{n+1})(tn,tn+1). It then fits the metallic reciprocal map tn+1=k+β/tnt_{n+1} = k + \beta/t_ntn+1=k+β/tn and compares it against the standard constant and proportional nulls using AIC separation and permutation significance, matching the decision logic used in the metallic-odds proof harness. The central goal is not to search for φ\varphiφ in synthetic data, but to quantify how often the complete harness produces (i) reciprocal preference and (ii) a strict φ\varphiφ-targeted event under controls where no metallic dynamics are injected. To do this, the paper constructs synthetic control slices by sampling row-level efficiency-like values from simple families (beta, uniform, near-frontier mixture, a chemostat-like proxy, and an AR(1) correlated control), defining Cmax⁡C_{\max}Cmax within each slice, and normalizing to GEC0\mathrm{GEC}_0GEC0. The entire pipeline is then re-run under three transforms (odds, odds\sqrt{\mathrm{odds}}odds, and logit) and across multiple sample sizes, producing a structured validation grid of synthetic experiments. Key outcomes reported include: Reciprocal preference is common under odds-based coordinates (and especially under odds\sqrt{\mathrm{odds}}odds), consistent with reciprocal structure emerging naturally from frontier-normalized aggregation geometry rather than being an artifact of a single dataset. Strict φ\varphiφ-targeted events are rare on synthetic controls when defined conservatively as: reciprocal preference (ΔAIC>6\Delta\mathrm{AIC}>6ΔAIC>6 with permutation p