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-lensing
convergence equation on the post-merger cluster Abell 2744 (z = 0.308).

The master equation predicts κ_QTT = κ_N − [c²/(16π G Σ_crit)] · ∇²⊥ O_occ
+ (Planck-suppressed creation term) + Σ_RD/Σ_crit, with the line-of-sight
invariant O_occ = ∫ ln(ρ_b/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 no
fitted multiplier. The shock-induced creation term is Planck-suppressed
(|κ_C| ~ 10⁻⁶⁵) and negligible at A2744's Mach M ≈ 1.4. Phase 1 tests
the residual-shape prediction R_obs = κ_obs − Σ_b/Σ_crit ≡ R_QTT against
three independent A2744 lensing reconstructions (CATS, Sharon, Diego).

Results:
- The Pearson correlation r(R_obs, R_QTT) 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 H_0
  branch, A_theory(Δt) = (1/8π)(ΔT/T_0)², equivalent to
  A = 2.087×10⁻⁴ · (Δt/Gyr)², at the headline post-pericentre bracket
  Δt = 0.4 Gyr returns A_pred(0.4) = 3.339×10⁻⁵, matching the empirical
  log-Hessian median (A_emp = 3.32×10⁻⁵) to 0.54%.

Disclosed corpus-internal ambiguity: the Candidate H reference time
T_ref admits two A1-compatible interpretations, T_ref = T_0 (H_0 branch,
used here, matches A_emp at 0.54%) and T_ref = T_0/(1+z) (H_z branch,
over-predicts at A2744 by ~71%). A third reference T_sound = R_cluster/c
is flagged for completeness. Discrimination at A2744 is not decisive
given the Δt literature uncertainty (~25% propagating to ~50% in A_H);
the H_0/H_z/T_sound trichotomy is locked as falsifier F-PH1-4 for the
Phase 3 high-redshift extension (El Gordo at z = 0.87, MACS J0025 at
z = 0.586), where the (1+z)² branch separation rises to 250% and 152%
respectively.

Verdict: SHAPE_LOCKED_AMPLITUDE_HEADLINE_CONFIRMED (H_0 branch, A2744
z = 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 scaling
falsifier, Phase 1.5), F-PH1-4 (H_0/H_z/T_sound trichotomy, Phase 3).
The original RD v2.3 falsifier set continues to apply unchanged.

H1 path Failure notice and data: https://zenodo.org/records/20095339

Scientific-record package for the first formal H1 out-of-sample QTT cluster-lensing test on MACS J0025.4-1222 and El Gordo / ACT-CL J0102-4https://zenodo.org/records/20095339915. The H1 branch with present-ledger Candidate H amplitude and L_LOS fallback source fails the two-cluster comparison. A forensic audit confirms that the failure is not a verdict-changing implementation bug. The package includes protocol locks and small audit/manifests only; raw data, FITS maps, Chandra products, RELICS products, and generated science maps are intentionally excluded.