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Preprint . 2026
License: CC BY
Data sources: Datacite
ZENODO
Preprint . 2026
License: CC BY
Data sources: Datacite
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Shape-Locked Validation of the QTT Substrate-Curvature Cluster-Lensing Equation on Abell 2744 Across Three Independent Reconstructions

Authors: Attar, Ali;

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

Abstract

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 κ_QTT = κ_N − [c²/(16π G Σ_crit)] · ∇²⊥ O_occ+ (Planck-suppressed creation term) + Σ_RD/Σ_crit, with the line-of-sightinvariant 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 nofitted multiplier. The shock-induced creation term is Planck-suppressed(|κ_C| ~ 10⁻⁶⁵) and negligible at A2744's Mach M ≈ 1.4. Phase 1 teststhe residual-shape prediction R_obs = κ_obs − Σ_b/Σ_crit ≡ R_QTT againstthree 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 timeT_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/cis flagged for completeness. Discrimination at A2744 is not decisivegiven 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 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: SHAPE_LOCKED_AMPLITUDE_HEADLINE_CONFIRMED (H_0 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 (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.

Keywords

post-merger cluster, parameter-free, substrate-counting normalisation, Hubble Frontier Fields, dark matter, gauge-safe linearisation, weak lensing, cluster lensing, Quantum Traction Theory, strong lensing, Abell 2744, substrate-occupancy, HFF, modified gravity

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
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