Volume 34: Cross-Stratum Control-Mixup Falsifier and Invariance Certification

Defines a minimal, test-only cross-stratum control-label mixup that falsifies V33 residual-invariance while V34 remains certified and stable. Provides thresholds, audits, and a fully reproducible ledger. Core results Failure threshold: r* = 0.003. Seed sweep at r = 0.005 and B = 10 000: V33 FAIL across seeds with p = 1.0×10⁻⁴ (p_floor). Effect sizes (seed 7): Δ 0.011 → 0.098; d 0.009 → 0.070; ‖{r̄_e}‖₂ 1.69×10⁻³ → 1.60×10⁻². Negative controls at r = 0.005 (seed 23): no-mix PASS p≈0.775; train-only same-env PASS p≈0.787; test-only same-env PASS p≈0.777; reversed-direction FAIL p≈8.0×10⁻⁴. V34 certificate stability: G3 symmetry PASS (sym_max_abs ≤ 1e−9, mid_deriv_abs ≤ 1e−9, asym_proj_energy_rel ≤ 1e−6). G5 ROM mass stable (δ_m ≤ 1e−3, m̂_anchor ≈ 2.16667×10⁻²). G6 path monotone PASS (drift_sup = 0). detJ_min = 1.331 ≥ 1e−3. Φ/Φ₀ = 1.0005 with Φ₀ = 4.320789337050. Canonical constructs V33 residual-invariance test: T = |E[r|odd] − E[r|even]|. Permutation p with fixed test group sizes. Cross-stratum parity-targeted mixup: test-only; targets are low-|u| within env; donors are strictly cross-env; even envs receive high-tail donors; odd envs receive low-tail donors; rate r ∈ [0.001, 0.005]. Env-block sanity p_env: exact enumeration over C(6,3) = 20 balanced labelings. V34 certificate: anchors on G3, G5, G6, detJ_min, and Φ/Φ₀ with fixed thresholds. Findings A 0.5% test-only cross-stratum swap is sufficient to induce a reliable V33 FAIL while V34 remains PASS. The threshold r* = 0.003 is stable across seeds. Anchors are invariant under the induced shift; no drift in Φ; no loss of Jacobian margin. Continuity Extends V33’s Φ discipline to a representation-robust certificate. Reuses V26 determinant guard logic and V27 symmetry discipline inside the V34 anchor set. Reproducibility and provenance Notebook-native protocol. Training untouched by falsifier. Test-only swaps with RNG seed s_mix = 1337. Artifacts: summary_sweep.json, rate_sweep.json, neg_controls.json, v34_novelty.json, v34_gates.json, env.json, manifest.json, PDF article, and notebook PDF. Environment: Python 3.12.x. All files listed in manifest with SHA-256. Results re-computable offline.