Shape-Locked Validation of the QTT Substrate-Curvature Cluster-Lensing Equation on Abell 2744 Across Three Independent Reconstructions

We test the parameter-free Quantum Traction Theory (QTT) cluster-lensingconvergence equation on the post-merger cluster Abell 2744 (z = 0. 308). The master equation predicts κQTT = κN − c²/ (16π G Σcrit) · ∇²⊥ Oₒcc+ (Planck-suppressed creation term) + ΣRD/Σcrit, with the line-of-sightinvariant Oₒcc = ∫ ln (ρb/ρ_*) dz. The prefactor 1/ (16π) = (1/4) · (1/4π) is forced by QTT axioms A4 (real two-component dial trace) and A7 (modular bundle 2π closure / Newton–Poisson normalisation), with nofitted multiplier. The shock-induced creation term is Planck-suppressed (|κC| ~ 10⁻⁶⁵) and negligible at A2744's Mach M ≈ 1. 4. Phase 1 teststhe residual-shape prediction Rₒbs = κₒbs − Σb/Σcrit ≡ RQTT againstthree independent A2744 lensing reconstructions (CATS, Sharon, Diego). Results: - The Pearson correlation r (Rₒbs, RQTT) across all three reconstructions and three causal-blur brackets passes Test C (r > 0. 5) at 9/9 tuples with r = 0. 53–0. 71. The strongest match (r = 0. 71) is for Diego, the only reconstruction without a light-traces-mass assumption. - Source-form robust: log-Hessian, completed-visible-address, and capacity-Hessian forms all give the same forced-coefficient slope A = (2. 65–3. 49) × 10⁻⁵, agreeing to 11% in median. - The RD v2. 3 §9 gauge-safe linearisation audit returns SAFE at all 4 lock positions × 3 beam scales. - The QTT corpus-internal Candidate H amplitude prediction on the H₀ branch, Aₜheory (Δt) = (1/8π) (ΔT/T₀) ², equivalent to A = 2. 087×10⁻⁴ · (Δt/Gyr) ², at the headline post-pericentre bracket Δt = 0. 4 Gyr returns Aₚred (0. 4) = 3. 339×10⁻⁵, matching the empirical log-Hessian median (Aₑmp = 3. 32×10⁻⁵) to 0. 54%. Disclosed corpus-internal ambiguity: the Candidate H reference timeTᵣef admits two A1-compatible interpretations, Tᵣef = T₀ (H₀ branch, used here, matches Aₑmp at 0. 54%) and Tᵣef = T₀/ (1+z) (Hᵦ branch, over-predicts at A2744 by ~71%). A third reference Tₛound = Rcluster/cis flagged for completeness. Discrimination at A2744 is not decisivegiven the Δt literature uncertainty (~25% propagating to ~50% in AH) ;the H₀/Hᵦ/Tₛound trichotomy is locked as falsifier F-PH1-4 for thePhase 3 high-redshift extension (El Gordo at z = 0. 87, MACS J0025 atz = 0. 586), where the (1+z) ² branch separation rises to 250% and 152%respectively. Verdict: SHAPELOCKEDAMPLITUDEHEADLINECONFIRMED (H₀ branch, A2744z = 0. 308 only). The deposit tarball contains the full reproducibility infrastructure: - 44-commit pre-registration audit trail (PREREGISTRATION. md) - Pipeline source code (~28 Python modules; ~20-minute end-to-end wall-time on commodity hardware) - SHA256 manifest of all data inputs (HFF v4 lensing, ASTRODEEP cluster catalogues, Chandra Source Catalog 2. 1 SIA broadband products) with canonical archive URLs- 19 JSON ledgers of audit and verification outputs- Paper LaTeX source (v1. 0–v1. 3) + figures (5 PNGs at 300 dpi) - Zenodo deposit checklist with locked deterministic SHA256s Pre-registered Phase 1 falsifiers: F-PH1-1 (residual-shape match), F-PH1-2 (substrate-counting normalisation), F-PH1-3 (Δt² scalingfalsifier, Phase 1. 5), F-PH1-4 (H₀/Hᵦ/Tₛound trichotomy, Phase 3). The original RD v2. 3 falsifier set continues to apply unchanged.