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<0.05p<0.05p<0.05) plus ∣k−φ∣<0.1|k-\varphi|<0.1∣k−φ∣<0.1. In the reported grid, strict events occur at a low rate and concentrate in specific family/transform cells rather than appearing as a universal pipeline artifact. An affine reciprocal competitor un+1=a+bun+c/unu_{n+1}=a + b u_n + c/u_nun+1=a+bun+c/un is tested as a flexibility check. Under odds-based transforms, the fitted linear term typically collapses toward b≈0b\approx 0b≈0, indicating the added degree of freedom is largely unused and the affine model degenerates back to the metallic form; under logit, the affine model tends to exploit a substantial linear component, consistent with chart mismatch between additive log-odds and ratio-based aggregation. As a positive control, the Tanouchi et al. E. coli 27∘C27^\circ\mathrm{C}27∘C slice reproduces a strongly constrained kkk near 1.631.631.63 with decisive separation from null behavior at large sample size, while aggressive downsampling erases detectability—highlighting the sample-size dependence of metallic detection. The accompanying reproducibility kit includes: the synthetic-control generator and scripts needed to reproduce the validation grid (families, transforms, sample sizes, and seeds), the proof harness used for this companion study (including transform variants, permutation tests, and reporting of reciprocal preference and strict φ\varphiφ events), summary tables / figures derived from the grid runs, and configuration notes describing precondition guardrails (single-frontier checks, soft clamp policy, sub-ceiling coverage, and diversity requirements). Upstream empirical datasets referenced as positive controls remain under their original licenses and terms. The kit focuses on derived artifacts and scripts sufficient to reproduce the synthetic grid, refit metallic and null models, recompute AIC gaps and permutation ppp-values, and regenerate the figures/tables reported in the paper. See README.md inside the ZIP for exact commands and expected outputs. Relationship to prior work: this paper supplements the metallic-odds manuscript by providing a structured QA and false-positive calibration layer over the same modeling pipeline, and it builds on the broader Compression Physics / GEC (CSK) framework introduced in the prior reports.