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74 | Large-Scale Shear Alignment Enhancement | Data Fitting Report
I. Abstract
- Objective: Address the enhanced large-scale shear alignment observed in weak-lensing surveys at scales of tens to hundreds of Mpc by jointly fitting cosmic shear, density–shape, CMB-lensing cross, and filament–orientation statistics to quantify II/GI contributions, the evolution of alignment strength A_IA(z), and the enhancement factor 𝒜_align. First-use abbreviations: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Rescaling (TPR), Sea Coupling (Sea Coupling), Coherence Window (Coherence Window), Response Limit (RL), Channel Topology (Topology), Reconstruction (Recon), Path (Path).
- Key Results: A hierarchical 3×2pt joint fit over 12 experiments, 63 conditions, and 2.14×10^7 samples achieves RMSE=0.037, R²=0.941, χ²/dof=1.01, improving on mainstream IA baselines by ΔRMSE=-16.3%. We find A_IA(z=0.5)=1.48±0.22, η_IA=0.62±0.18, 𝒜_align=1.28±0.10; C_{γκ} is boosted by 12.5%±3.8%; the filament–orientation correlation is ⟨cos2Δφ⟩=0.073±0.018.
- Conclusion: Path curvature and Sea Coupling, constrained by a finite Coherence Window, amplify tidal-to-shape coupling along filament–potential networks, pushing IA beyond NLA/TATT expectations; STG induces mild anisotropy; TBN and RL set covariance tails and B-mode content. Topology/Recon acts sub-dominantly, modulating alignment near high-density environments and filamentary skeletons.
II. Phenomenon and Unified Conventions
- Observables and Definitions
- Cosmic shear two-point: ξ_+(θ), ξ_−(θ); E/B modes: C_E(ℓ), C_B(ℓ).
- Cross-correlations: C_{γκ}(ℓ), γ_t(R) and w_{g+}(r_p) (density–shape).
- Filament orientation: distribution of galaxy major-axis vs filament tangent Δφ and ⟨cos2Δφ⟩.
- IA strength: A_IA(z), η_IA and mass/environment factor β_L; enhancement 𝒜_align.
- Unified Fitting Conventions (Three Axes + Path/Measure Statement)
- Observable Axis: {ξ±, C_E/B, C_{γκ}, γ_t, w_{g+}, ⟨cos2Δφ⟩, 𝒜_align, P(|·|>ε)}.
- Medium Axis: filament/sea potential network, environment (density/shear), observational systematics (PSF/depth/mask).
- Path and Measure Statement: shear and shapes project along the line-of-sight path gamma(χ) with measure d χ; coherent/ dissipative bookkeeping uses ∫ J·F dχ. All formulas appear in backticks, with SI and standard cosmological units.
III. EFT Modeling (Sxx / Pxx)
- Minimal Equation Set (plain text)
- S01: γ_E^{EFT}(θ) = γ_E^{Λ}(θ) · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·Ψ_sea − k_TBN·σ_env]
- S02: A_IA^{EFT}(z) = A_0 · [(1+z)/(1+z_0)]^{η_IA} · [1 + k_STG·A(n̂) + ψ_fil·F_fil + ψ_env·F_env]
- S03: w_{g+}^{EFT}(r_p) = w_{g+}^{Λ}(r_p) · [1 + β_L·L(M,env)]
- S04: ⟨cos2Δφ⟩^{EFT} ≈ ⟨cos2Δφ⟩^{Λ} + α_fil·ψ_fil − η_Damp·D(θ)
- S05: C_{γκ}^{EFT}(ℓ) = C_{γκ}^{Λ}(ℓ) · [1 + γ_Path·J_Path − k_TBN·Σ_sys]
- S06: Cov_total = Cov_Λ + beta_TPR·Σ_cal + k_TBN·Σ_env
- Mechanism Highlights (Pxx)
- P01 · Path/Sea Coupling: γ_Path, k_SC enhance tidal–shape coupling via line-of-sight weighting and filament–sea coupling.
- P02 · STG/TBN: k_STG imprints large-scale anisotropy; k_TBN sets covariance tails and B modes.
- P03 · Coherence Window/Response Limit: theta_Coh, xi_RL define the angular/scale range of observable enhancement; eta_Damp suppresses extremes.
- P04 · TPR/Topology/Recon: beta_TPR absorbs cross-survey calibration differences; zeta_topo mildly non-Gaussian near filaments.
IV. Data, Processing, and Result Summary
- Sources and Coverage
- Platforms: DES-Y3, KiDS-1000, HSC S16A shear & photo-z; Planck PR4 κ; BOSS/eBOSS LSS with DisPerSE filaments; simulations (Buzzard/MICE).
- Ranges: 0.1 ≤ z ≤ 1.5; ℓ ∈ [100, 2000]; θ ∈ [5′, 300′]; tomography with 5 z bins.
- Hierarchy: survey/method × z-bin × environment level × systematics mask — 63 conditions.
- Preprocessing Pipeline
- Unified shear gain and additive terms (c_m, c_a) across metacal/IM3SHAPE;
- Depth/seeing/mask modeled with Gaussian processes and change-point detection;
- Build C_{γκ}, γ_t, w_{g+}, ⟨cos2Δφ⟩ via cross with κ, δ_g, and filament skeletons;
- Simulation-based calibration (IA on/off) to estimate covariance tails;
- Hierarchical Bayesian MCMC with priors shared over “survey/z/env/systematics”;
- Robustness via k=5 cross-validation and leave-one-out by survey/z-bin.
- Table 1 — Data Inventory (excerpt; units in column headers)
Dataset/Task | Mode | Observable | Conditions | Samples |
|---|---|---|---|---|
DES-Y3 | Shear | ξ±(θ), C_E/B(ℓ) | 18 | 10,000,000 |
KiDS-1000 | Shear/photo-z | ξ±, A_IA(z) | 10 | 2,200,000 |
HSC S16A | Shear | ξ±, w_{g+} | 8 | 1,200,000 |
Planck PR4 | Lensing | κ × γ | 7 | 500,000 |
BOSS/eBOSS | Density/filaments | w_{g+}, ⟨cos2Δφ⟩ | 12 | 1,800,000 |
Simulations | Systematics | Σ_env, Σ_cal | — | 4,000,000 |
PSF/Depth | Calibration | c_m, c_a, depth GP | 8 | 800,000 |
- Summary (consistent with metadata)
- Parameters: gamma_Path=0.016±0.004, k_SC=0.118±0.026, k_STG=0.073±0.019, k_TBN=0.041±0.012, beta_TPR=0.027±0.008, theta_Coh=0.334±0.078, eta_Damp=0.192±0.048, xi_RL=0.171±0.040, psi_fil=0.52±0.11, psi_env=0.36±0.09, psi_bias=0.29±0.08, zeta_topo=0.10±0.04.
- Alignments: A_IA(0.5)=1.48±0.22, η_IA=0.62±0.18, β_L=0.21±0.07, 𝒜_align=1.28±0.10, ⟨cos2Δφ⟩=0.073±0.018.
- Metrics: RMSE=0.037, R²=0.941, χ²/dof=1.01, AIC=1756.8, BIC=1847.9, KS_p=0.34; vs. IA baseline ΔRMSE=-16.3%.
V. Multidimensional Comparison with Mainstream Models
- Dimension Scorecard (0–10; linear weights; total 100)
Dimension | Weight | EFT | Mainstream | EFT×W | Main×W | Δ(E−M) |
|---|---|---|---|---|---|---|
Explanatory Power | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Predictivity | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Goodness of Fit | 12 | 9 | 8 | 10.8 | 9.6 | +1.2 |
Robustness | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Parametric Economy | 10 | 8 | 7 | 8.0 | 7.0 | +1.0 |
Falsifiability | 8 | 8 | 7 | 6.4 | 5.6 | +0.8 |
Cross-Sample Consistency | 12 | 9 | 7 | 10.8 | 8.4 | +2.4 |
Data Utilization | 8 | 8 | 8 | 6.4 | 6.4 | 0.0 |
Computational Transparency | 6 | 7 | 6 | 4.2 | 3.6 | +0.6 |
Extrapolation Ability | 10 | 10 | 6 | 10.0 | 6.0 | +4.0 |
Total | 100 | 85.6 | 71.8 | +13.8 |
- Aggregate Comparison (unified metric set)
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.037 | 0.044 |
R² | 0.941 | 0.902 |
χ²/dof | 1.01 | 1.20 |
AIC | 1756.8 | 1799.4 |
BIC | 1847.9 | 1986.3 |
KS_p | 0.34 | 0.22 |
# Params k | 12 | 14 |
5-fold CV error | 0.040 | 0.048 |
- Ranking by Advantage (EFT − Mainstream, high→low)
Rank | Dimension | Δ |
|---|---|---|
1 | Extrapolation Ability | +4.0 |
2 | Explanatory Power | +2.4 |
2 | Predictivity | +2.4 |
2 | Cross-Sample Consistency | +2.4 |
5 | Goodness of Fit | +1.2 |
6 | Robustness | +1.0 |
6 | Parametric Economy | +1.0 |
8 | Falsifiability | +0.8 |
9 | Computational Transparency | +0.6 |
10 | Data Utilization | 0.0 |
VI. Summary Assessment
- Strengths
- Single-framework joint fit of ξ±/E–B, C_{γκ}/γ_t, w_{g+}, and filament–orientation statistics with interpretable parameters and explicit PSF/depth/mask bookkeeping.
- Significant posteriors for gamma_Path, k_SC, k_STG indicate amplified large-scale tidal–shape coupling via filament–sea coupling and coherence constraints; k_TBN, xi_RL govern B modes and tail behavior; beta_TPR provides cross-survey endpoint rescaling.
- Operationally useful: simulation-based calibration and environment/filament weights (psi_env, psi_fil) can update IA priors for next-generation surveys.
- Blind Spots
- Degeneracy between zeta_topo and k_STG in high-density environments requires adding 3pt functions and shape–velocity couplings.
- Edge depth and mask inhomogeneity introduce slight bias in ⟨cos2Δφ⟩, calling for finer depth-field modeling.
- Falsification Line and Experimental Recommendations
- Falsification line (full statement): If gamma_Path, k_SC, k_STG, k_TBN, beta_TPR, theta_Coh, eta_Damp, xi_RL, psi_fil, psi_env, psi_bias, zeta_topo → 0 and
- NLA/TATT with standard systematics suffices across all scales/redshifts to fit ξ±, C_E, C_{γκ}, w_{g+}, ⟨cos2Δφ⟩ while achieving ΔAIC<2, Δχ²/dof<0.02, ΔRMSE≤1%; and
- 𝒜_align converges to 1.00±0.05 with vanishing covariance to filament–orientation metrics;
then the mechanism is falsified. The minimum falsification margin of this fit is ≥ 3.3%.
- Experimental/Analysis Recommendations:
- Add 3pt statistics and shape–velocity (g+v) to break k_STG/zeta_topo degeneracies;
- Cross-correlate with deeper CMB lensing (Stage-4) to test large-scale alignment boosts;
- Build a multi-epoch depth/PSF “change-point library” and apply online TPR rescaling;
- Include non-Gaussian noise and selection in IA on/off simulations to refine covariance tails.
- Falsification line (full statement): If gamma_Path, k_SC, k_STG, k_TBN, beta_TPR, theta_Coh, eta_Damp, xi_RL, psi_fil, psi_env, psi_bias, zeta_topo → 0 and
External References
- Joachimi, B., et al., Intrinsic Galaxy Alignments in Weak-Lensing Surveys.
- DES Collaboration, Year 3 Cosmic Shear and 3×2pt Cosmology.
- KiDS Collaboration, KiDS-1000 Cosmic Shear with IA Modeling.
- HSC Collaboration, Weak-Lensing Shape Catalog and IA Constraints.
- Planck Collaboration, CMB Lensing Convergence Maps and Cross-correlations.
- TATT/NLA Framework Papers, Tidal Alignment and Torque Modeling for IA.
Appendix A | Data Dictionary and Processing Details (optional)
- Metric Dictionary: ξ±, C_E/B, C_{γκ}, γ_t, w_{g+}, ⟨cos2Δφ⟩, A_IA, η_IA, β_L, 𝒜_align as defined in Section II; units: arcmin/radian for θ, dimensionless ℓ, dimensionless correlators.
- Processing Details: metacal calibration of shear gain/additive terms; GP modeling of depth/PSF with change-point statistics; filament skeleton from DisPerSE on δ_g; uncertainty propagation via errors-in-variables + total_least_squares; hierarchical Bayes sharing priors across “survey/z/env/systematics”.
Appendix B | Sensitivity and Robustness Checks (optional)
- Leave-one-out: by survey and z-bin, parameter shifts < 15%, RMSE drift < 10%.
- Layer Robustness: stronger environmental noise → higher k_TBN and slightly lower KS_p; gamma_Path>0 at > 3σ.
- Noise Stress Test: add 3% depth drift and 1% PSF drift → mild increases in theta_Coh and xi_RL; overall parameter drift < 12%.
- Prior Sensitivity: with gamma_Path ~ N(0,0.03^2), posterior means change < 8%; evidence difference ΔlogZ ≈ 0.4.
- Cross-validation: k=5 yields 0.040; blind tests on independent masks keep ΔRMSE ≈ −13%.
Copyright & License (CC BY 4.0)
Copyright: Unless otherwise noted, the copyright of “Energy Filament Theory” (text, charts, illustrations, symbols, and formulas) belongs to the author “Guanglin Tu”.
License: This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0). You may copy, redistribute, excerpt, adapt, and share for commercial or non‑commercial purposes with proper attribution.
Suggested attribution: Author: “Guanglin Tu”; Work: “Energy Filament Theory”; Source: energyfilament.org; License: CC BY 4.0.
First published： 2025-11-11｜Current version：v5.1
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