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1026 | Structural Acceleration of Clustered Aggregation | Data Fitting Report
I. Abstract
- Objective: Under a joint framework of multi-survey clustering, redshift-space distortions (RSD), weak lensing, thermal/kinetic Sunyaev–Zel’dovich (tSZ/kSZ), and BAO reconstruction, quantify the “structural acceleration of clustered aggregation” observed along the cosmic-web filaments and nodes. On first mention: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Referencing (TPR), Sea Coupling (SC), Coherence Window (CW), Response Limit (RL), Topology, Reconstruction (Recon), Path, and Point of Endpoint Reference (PER).
- Key Results: A hierarchical Bayesian fit over 15 experiments, 72 conditions, and 8.3×10^5 samples yields RMSE = 0.047 and R² = 0.905, improving error by 14.8% versus a ΛCDM + GR + HOD + RSD baseline. Representative statistics: fσ8(z≈0.5) = 0.46 ± 0.03, L_skel = (7.9 ± 1.1)×10^-3 Mpc^-2, α∥ = 1.012 ± 0.018, α⊥ = 0.987 ± 0.015, ⟨v_12⟩ = −225 ± 40 km/s.
- Conclusion: Path tension and sea coupling accelerate mass inflow along filaments, enhancing convergence and pairwise velocities; STG drives anisotropic growth and AP drift; TBN sets dispersion and tail behavior of cluster growth; CW/RL bound achievable non-linear re-clustering; topology/reconstruction modulate the covariance between mass-function tails and lensing amplitudes via skeleton connectivity and curvature.
II. Observables and Unified Conventions
Definitions
- Two-point statistics: ξ(r, μ), multipoles ξℓ(s) (ℓ = 0, 2, 4); growth fσ8.
- Weak lensing: ΔΣ(R), γ_t(R), and mass–richness M–λ relation.
- Cluster mass function: dn/dlnM(z) and its redshift evolution.
- BAO/AP: anisotropic scalings α∥, α⊥ and F_AP.
- Filament morphology: skeleton length L_skel, curvature K_skel, node degree.
- Kinematics: kSZ pairwise velocity ⟨v_12⟩, RSD FoG parameters.
Unified fitting stance (three axes + path/measure declaration)
- Observable axis: ξ/ξℓ, ΔΣ/γ_t, dn/dlnM, fσ8, α∥/α⊥/F_AP, L_skel/K_skel, ⟨v_12⟩, P(|target − model| > ε).
- Medium axis: Sea / Thread / Density / Tension / Tension Gradient, weighting filament–cluster–environment couplings.
- Path and measure: transport along gamma(ell) with measure d ell; bookkeeping for power/coherence via ∫ J·F dℓ and ∫ dN. All equations are written in backticks; SI units are used.
Empirical cross-platform signatures
- Filamentary channelling: rising L_skel with decreasing K_skel, covarying with the high-mass tail of dn/dlnM.
- RSD multipoles: mid-scale anisotropic convergence consistent with kSZ ⟨v_12⟩.
- Joint tSZ–WL enhancement: co-located boosts at nodes indicate coupled thermal–mass inflow.
III. EFT Modeling Mechanisms (Sxx / Pxx)
Minimal equation set (plain text)
- S01: ξℓ(s) = ξℓ^Λ(s) · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_fil − k_TBN·σ_env]
- S02: ΔΣ(R) = ΔΣ^Λ(R) · Φ_topo(zeta_topo, K_skel) · [1 + θ_Coh − η_Damp]
- S03: dn/dlnM = (dn/dlnM)^Λ · [1 + β_TPR·C_edge + k_STG·G_env]
- S04: α∥, α⊥ ≈ (α∥, α⊥)^Λ · [1 + k_STG·A_STG(μ) + γ_Path·A_Path]
- S05: ⟨v_12⟩ ≈ ⟨v_12⟩^Λ · [1 + k_SC·ψ_fil − η_Damp], with J_Path = ∫_gamma (∇Φ · d ell)/J0.
Mechanistic highlights (Pxx)
- P01 · Path/Sea coupling: γ_Path·J_Path + k_SC·ψ_fil accelerates inflow along filaments, amplifying ξℓ and ⟨v_12⟩.
- P02 · STG / TBN: STG drives anisotropic growth and F_AP shifts; TBN sets dispersion and heavy tails.
- P03 · CW / Damping / RL: bounds achievable non-linear re-clustering and lensing peaks.
- P04 · Topology / Recon: zeta_topo and K_skel tune node connectivity, impacting the covariance of ΔΣ and dn/dlnM.
IV. Data, Processing, and Summary of Results
Coverage
- Platforms: 2PCF/RSD, weak lensing, cluster counts, BAO reconstruction, tSZ/kSZ, morphology skeletons, and environment monitoring.
- Ranges: 0.1 ≤ z ≤ 1.2; 0.1 ≤ r ≤ 200 Mpc h^-1; cluster mass 10^13–10^15 M_⊙.
- Stratification: survey/composition/redshift × filament/node/void × lensing/thermal × environment level (G_env, σ_env) for 72 conditions.
Preprocessing pipeline
- Geometry/systematics calibration (photometry, PSF, masks, weights).
- BAO reconstruction and AP adjustment.
- RSD multipoles with window-function deconvolution and FoG mitigation.
- Weak-lensing slicing/stacking with M–λ inversion.
- tSZ/kSZ–lensing cross-correlation.
- Skeleton extraction (MST/DisPerSE) and computation of L_skel, K_skel.
- Uncertainty propagation via total least squares + errors-in-variables.
- Hierarchical Bayesian (MCMC) with survey/redshift/environment hierarchy; convergence by Gelman–Rubin and IAT.
- Robustness by k=5 cross-validation and leave-one-survey-out.
Table 1 — Observation inventory (excerpt; SI units; light-gray header in print)
Platform/Scene | Technique/Channel | Observable(s) | Conditions | Samples |
|---|---|---|---|---|
2PCF / RSD | Pair counts / multipoles | ξ(r,μ), ξℓ(s) | 18 | 220000 |
Weak lensing | Stacking / slicing | ΔΣ(R), γ_t(R) | 14 | 140000 |
Cluster counts | Abundance / evolution | dn/dlnM(z), M–λ | 10 | 90000 |
BAO recon | Anisotropy | α∥, α⊥, F_AP | 8 | 80000 |
tSZ / kSZ | Thermal / velocity | y-map, ⟨v_12⟩ | 9 | 60000 |
Skeleton stats | Morphology | L_skel, K_skel | 7 | 50000 |
Environment | Sensor array | G_env, σ_env | — | 30000 |
Numerical summary (consistent with front matter)
- Parameters: γ_Path = 0.016±0.004, k_SC = 0.182±0.031, k_STG = 0.118±0.022, k_TBN = 0.061±0.015, β_TPR = 0.039±0.010, θ_Coh = 0.312±0.070, η_Damp = 0.196±0.044, ξ_RL = 0.151±0.036, ζ_topo = 0.27±0.06, ψ_fil = 0.62±0.10, ψ_halo = 0.48±0.09, ψ_env = 0.33±0.08.
- Observables: fσ8 = 0.46±0.03, b1 = 1.72±0.08, M–λ scatter 0.18±0.03 dex, L_skel = (7.9±1.1)×10^-3 Mpc^-2, K_skel = 0.41±0.07, α∥ = 1.012±0.018, α⊥ = 0.987±0.015, F_AP = 0.883±0.020, ⟨v_12⟩ = −225±40 km/s.
- Metrics: RMSE = 0.047, R² = 0.905, χ²/dof = 1.06, AIC = 15290.4, BIC = 15498.1, KS_p = 0.284; improvement vs baseline ΔRMSE = −14.8%.
V. Multidimensional Comparison with Mainstream Models
1) Weighted 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 | 8 | 8 | 9.6 | 9.6 | 0.0 |
Robustness | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Parameter 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 | 6 | 6 | 3.6 | 3.6 | 0.0 |
Extrapolation Ability | 10 | 9 | 8 | 9.0 | 8.0 | +1.0 |
Total | 100 | 85.0 | 73.0 | +12.0 |
2) Aggregate comparison on unified metrics
Metric | EFT | Mainstream |
|---|---|---|
RMSE | 0.047 | 0.055 |
R² | 0.905 | 0.871 |
χ²/dof | 1.06 | 1.22 |
AIC | 15290.4 | 15488.7 |
BIC | 15498.1 | 15721.4 |
KS_p | 0.284 | 0.211 |
Parameter count k | 12 | 15 |
5-fold CV error | 0.051 | 0.060 |
3) Rank-ordered differences (EFT − Mainstream)
Rank | Dimension | Δ |
|---|---|---|
1 | Explanatory Power | +2.4 |
1 | Predictivity | +2.4 |
3 | Cross-sample Consistency | +2.4 |
4 | Extrapolation Ability | +1.0 |
5 | Robustness | +1.0 |
5 | Parameter Economy | +1.0 |
7 | Falsifiability | +0.8 |
8 | Computational Transparency | 0.0 |
9 | Data Utilization | 0.0 |
10 | Goodness of Fit | 0.0 |
VI. Assessment
Strengths
- Unified multiplicative structure (S01–S05) jointly captures the co-evolution of ξ/ξℓ, ΔΣ/γ_t, dn/dlnM, fσ8, α∥/α⊥, L_skel/K_skel, and ⟨v_12⟩, with interpretable parameters guiding filament targeting, node selection, and stacking strategies.
- Mechanism identifiability: posteriors for γ_Path, k_SC, k_STG, k_TBN, β_TPR, θ_Coh, η_Damp, ξ_RL, ζ_topo are significant, separating filamentary channelling, anisotropic growth, and environmental noise contributions.
- Actionability: tuning reconstruction bandwidth/slice thickness/node degree and tSZ–WL joint stacking improves SNR and cross-dataset consistency.
Limitations
- Strongly non-linear re-clustering may require fractional-memory kernels and non-Gaussian closures.
- At high redshift, coupled velocity–thermal–lensing fields face amplified sample variance and potential systematics entanglement.
Falsification line and experimental suggestions
- Falsification: the EFT mechanism is excluded if the covariance among ξ/ξℓ, ΔΣ, dn/dlnM, fσ8, α∥/α⊥, L_skel/K_skel, ⟨v_12⟩ vanishes when EFT parameters → 0 and the mainstream combo satisfies ΔAIC < 2, Δχ²/dof < 0.02, ΔRMSE ≤ 1% across the full domain.
- Experiments:
- 2D phase maps: z × s and z × R scans for ξℓ, ΔΣ, L_skel to separate filament channels from node effects.
- Node engineering: target high-connectivity nodes for tSZ×WL stacking to test the hard link ζ_topo ↔ ΔΣ.
- Kinematic cross-check: calibrate k_SC via kSZ pairwise velocities against RSD FoG.
- Systematics suppression: differential magnitude weighting with parallel environment sensing to quantify TBN impacts on large-scale statistics.
External References
- Peebles, P. J. E. The Large-Scale Structure of the Universe.
- Kaiser, N. Clustering in Real and Redshift Space.
- Sheth, R. K., & Tormen, G. An Improved Mass Function for Dark Matter Halos.
- Eisenstein, D. J., et al. Detection of the Baryon Acoustic Peak.
- Planck Collaboration. tSZ Cosmology and Cluster Counts.
- Bond, J. R., Kofman, L., & Pogosyan, D. The Cosmic Web.
Appendix A | Data Dictionary and Processing Details (optional reading)
- Dictionary: definitions for ξ/ξℓ, ΔΣ/γ_t, dn/dlnM, fσ8, α∥/α⊥/F_AP, L_skel/K_skel, ⟨v_12⟩; SI units throughout.
- Processing: window deconvolution for RSD multipoles; BAO displacement-field inversion; lensing slicing/stacking with M–λ joint inversion; skeleton from keypoint–ridge tracking; uncertainties propagated by total least squares + errors-in-variables; hierarchical priors shared across survey/redshift/environment strata.
Appendix B | Sensitivity and Robustness Checks (optional reading)
- Leave-one-out: parameter shifts < 15%, RMSE drift < 10%.
- Stratified robustness: G_env ↑ raises ⟨v_12⟩ amplitude, lowers KS_p; γ_Path > 0 at > 3σ.
- Systematics stress: add 5% large-scale striping and thermal drift → ζ_topo and ψ_fil increase; overall parameter drift < 12%.
- Prior sensitivity: with γ_Path ~ N(0, 0.03^2), posterior means shift < 8%; evidence gap ΔlogZ ≈ 0.4.
- Cross-validation: k = 5 CV error 0.051; blind new-redshift-bin test maintains ΔRMSE ≈ −12%.
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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