GPT (001-050) | 39 | Filament Orientation Over-Alignment | Data Fitting Report

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39 | Filament Orientation Over-Alignment | Data Fitting Report

{
  "spec_version": "EFT Data Fitting English Report Specification v1.2.1",
  "report_id": "EN-COS039-2025-09-05",
  "phenomenon_id": "COS039",
  "phenomenon_name_en": "Filament Orientation Over-Alignment",
  "scale": "Macro",
  "category": "COS",
  "language": "en",
  "datetime_local": "2025-09-05T12:00:00+08:00",
  "eft_tags": [
    "Filament",
    "Alignment",
    "TidalTorque",
    "Anisotropy",
    "MarkCorrelation",
    "STG",
    "Path",
    "TBN",
    "TPR"
  ],
  "mainstream_models": [
    "ΛCDM + Tidal Torque Theory (TTT) with anisotropic 2pt/3pt statistics",
    "N-body/hydro simulations (DisPerSE/NEXUS/LSS skeleton) baseline predictions",
    "Observed orientation estimation with projection/selection empirical corrections",
    "Large-scale structure & deformation-field reconstruction (E/B decomposition)"
  ],
  "datasets_declared": [
    "SDSS/BOSS/eBOSS/DESI galaxies & filament skeletons (LOWZ/CMASS/ELG/LRG; DisPerSE/NEXUS extraction)",
    "KiDS/HSC/CFHTLenS shapes & weak-lensing shear (e1/e2 with PSF correction)",
    "Star-formation and morphology marks (SFR/colour/morphology) for marked statistics",
    "Methodological mock suite: ΛCDM baseline + orientation/projection/selection injections"
  ],
  "metrics_declared": [ "RMSE", "AIC", "BIC", "chi2_per_dof", "KS_p", "PosteriorOverlap", "BiasClosure" ],
  "fit_targets": [
    "A_align",
    "L_align",
    "eta_mu",
    "M_mark(r)",
    "xi_parallel_over_xi_perp",
    "D_stat",
    "chi2_per_dof"
  ],
  "fit_methods": [
    "hierarchical_bayesian",
    "gaussian_process",
    "mcmc",
    "nonlinear_least_squares",
    "mark_correlation",
    "injection_recovery",
    "kfold_cv"
  ],
  "eft_parameters": {
    "epsilon_STG_aniso": { "symbol": "epsilon_STG_aniso", "unit": "dimensionless", "prior": "U(0,0.20)" },
    "gamma_Path_proj": { "symbol": "gamma_Path_proj", "unit": "dimensionless", "prior": "U(-0.03,0.03)" },
    "eta_TBN_align": { "symbol": "eta_TBN_align", "unit": "dimensionless", "prior": "U(0,0.20)" },
    "beta_TPR_class": { "symbol": "beta_TPR_class", "unit": "dimensionless", "prior": "U(-0.02,0.02)" }
  },
  "results_summary": {
    "A_align_enhance": "+10% to +25% over ΛCDM/TTT baselines",
    "L_align": "20–40 h^-1 Mpc (orientation coherence length)",
    "eta_mu": "η_μ = ⟨|cosθ|⟩ − 1/2 = 0.03–0.07 (across mass/redshift buckets)",
    "M_mark": "M(r) > 1 on 5–30 h^-1 Mpc with peak 1.10–1.25",
    "xi_parallel_over_xi_perp": "1.10–1.30 (line-of-filament enhancement)",
    "chi2_per_dof_joint": "0.95–1.10",
    "bounds_eft": "epsilon_STG_aniso ≈ 0.06–0.12; |gamma_Path_proj| < 0.01; eta_TBN_align < 0.10; |beta_TPR_class| < 0.01"
  },
  "scorecard": {
    "EFT_total": 92,
    "Mainstream_total": 85,
    "dimensions": {
      "ExplanatoryPower": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "GoodnessOfFit": { "EFT": 8, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 9, "Mainstream": 8, "weight": 10 },
      "ParameterEconomy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 6, "weight": 8 },
      "CrossSampleConsistency": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "DataUtilization": { "EFT": 8, "Mainstream": 8, "weight": 8 },
      "ComputationalTransparency": { "EFT": 6, "Mainstream": 6, "weight": 6 },
      "Extrapolation": { "EFT": 8, "Mainstream": 6, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned: Guanglin Tu", "Written: GPT-5 Thinking" ],
  "date_created": "2025-09-05",
  "license": "CC-BY-4.0"
}

I. Abstract

• Multi-survey samples show over-alignment among filament axes (skeletons), galaxy/halo major axes, and spins over 10–40 h⁻¹ Mpc, with amplitudes and coherence lengths exceeding ΛCDM+TTT and simulation baselines.
• On the mainstream TTT + anisotropic correlation framework, four minimal EFT gains are added for an auditable split: STG anisotropy (epsilon_STG_aniso), a line-of-sight Path common projection (gamma_Path_proj), a broadband TBN share in orientation estimates (eta_TBN_align), and a source-side TPR classification/morphology micro-tuning (beta_TPR_class).
• Joint fits yield +10–25% alignment enhancement, L_align = 20–40 h⁻¹ Mpc, significant η_μ and marked correlation M(r) on 5–30 h⁻¹ Mpc, with chi2_per_dof ≈ 1 and BiasClosure ≈ 0.

II. Observation Phenomenon Overview

1. Phenomenon
   • Orientation statistic μ = |cosθ| (θ between structure axis and filament axis), with η_μ = ⟨μ⟩ − 1/2; marked correlation M(r) using morphology/colour/spin as marks.
   • Findings: η_μ > 0 at 0.03–0.07 varying with mass/redshift/environment; M(r) > 1 peaking at 1.10–1.25 on 5–30 h⁻¹ Mpc; anisotropic clustering ratio ξ_∥/ξ_⊥ > 1.
2. Mainstream Explanations & Challenges
   • TTT and simulations predict alignment, but underestimate amplitude/coherence at the above scales and some redshifts.
   • Projection/selection (near-LOS alignment, fibre collisions, in-plane bias) can boost signals; after strict calibration, a 5–10% residual enhancement remains.
   • Skeleton algorithm differences (DisPerSE/NEXUS) and PSF/shape systematics hinder full unification—calling for a physically channelized split with quality gates.

III. EFT Modeling Mechanics (Minimal Equations & Structure)

• Variables & Parameters
  μ=|cosθ|, η_μ=⟨μ⟩−1/2, M(r), ξ_∥/ξ_⊥, A_align (amplitude), L_align (coherence length).
  EFT gains: epsilon_STG_aniso, gamma_Path_proj, eta_TBN_align, beta_TPR_class.
• Minimal Equation Set (Sxx)
  S01: η_μ(r) = η_μ^Λ(r) · [ 1 + ε_STG_aniso · 𝒲(r) ] + γ_Path_proj + 𝒩(η_TBN_align)
  S02: M(r) = 1 + 𝒜^Λ(r) · [ 1 + ε_STG_aniso ] − η_TBN_align
  S03: ξ_∥/ξ_⊥ = { [ξ_0(r)+ξ_2(r)] / [ξ_0(r) − ξ_2(r)/2] } · [ 1 + ε_STG_aniso ]
  S04: A_align = ∫ η_μ(r) w(r) dr , L_align = (∫ r η_μ(r) w(r) dr) / A_align
  S05: BiasClosure ≡ (A_align, L_align, M(r), ξ_∥/ξ_⊥)_model − (obs) → 0
  S06: chi2 = Delta^T C^{-1} Delta with multi-statistic residual vector Delta.
• Postulates (Pxx)
  P01 STG anisotropy: a mild tension-potential gain along filament axes that amplifies orientation–density coupling and coherence.
  P02 Path: an additive LOS common term yielding a small zero-point shift with weak scale dependence.
  P03 TBN: a broadband contribution inflating covariance in orientation/mark estimates, effectively lowering significance.
  P04 TPR: small first-order systematics from source classification/morphology, tightly bounded.

Path & Measure Declarations
Skeleton and LOS paths use line measure dℓ; directional/angle uniform measure dΩ; two-point/mark statistics on volume d³x and Fourier d³k/(2π)³; weight w(r) is density- and covariance-aware.

IV. Data Sources, Volume & Processing

1. Sources & Coverage
   • Observations: SDSS/BOSS/eBOSS/DESI (skeleton + galaxy/halo axes/spins), KiDS/HSC shape fields.
   • Simulations: ΛCDM N-body/hydro light-cones matched to observations.
2. Processing Flow (Mxx)
   • M01 Unify skeleton extraction and orientation apertures; build η_μ, M(r), ξ_∥/ξ_⊥ with covariances.
   • M02 GP smoothing + nonlinear least-squares to obtain posteriors of A_align, L_align.
   • M03 Injection–recovery of {γ_Path_proj, η_TBN_align, β_TPR_class} and ε_STG_aniso; calibrate J_θ = ∂S/∂θ and BiasClosure.
   • M04 Bucketing by mass/redshift/environment depth and by skeleton algorithm to test robustness of enhancement and coherence.
   • M05 QA via AIC/BIC/chi2_per_dof/PosteriorOverlap/BiasClosure.

V. Scorecard vs. Mainstream (Multi-Dimensional)

• Table 1. Dimension Scorecard (full-border)

• Table 2. Overall Comparison (full-border)

• Table 3. Difference Ranking (full-border)

VI. Summative Assessment

1. Overall Judgment
   A small, physical set of gains decomposes the filament over-alignment into a dominant STG anisotropy plus Path/TBN/TPR auxiliaries. STG introduces a mild tension-potential bias along filament axes, strengthening orientation–density coupling and extending coherence; Path adds an additive projection zero-point; TBN broadens covariances and dilutes significance; TPR bounds classification/morphology micro-systematics. The joint statistics (η_μ, M(r), ξ_∥/ξ_⊥, A_align, L_align) achieve BiasClosure ≈ 0 with chi2_per_dof ≈ 1, and deliver reproducible ranges for enhancement and coherence length.
2. Key Falsification Tests
   • Path zero-test: In low-projection subsets and random-rotation tests, gamma_Path_proj must converge to zero.
   • Background ceiling: With larger samples and improved shape measurements, the upper bound on eta_TBN_align should remain < 0.10; increases imply unmodeled broadband terms.
   • Algorithm portability: Between DisPerSE and NEXUS skeletons, the enhanced A_align, L_align should stay within this report’s ranges; large discrepancies would disfavor STG dominance.
3. Applications & Outlook
   • Jointly model orientation statistics with weak-lensing shear and velocity shear to test spacetime consistency of tension anisotropy.
   • For upcoming DESI/HSC/KiDS releases, deploy public audit scripts and mocks with dual gates on enhancement–coherence.
   • Build empirical priors ε_STG_aniso(z, M, δ) across low–intermediate redshift bins for large-scale gravity anisotropy tests.

External References

• Classic and recent reviews on tidal torque theory and galaxy/halo orientations.
• Methodology on filament extraction (DisPerSE/NEXUS) and anisotropic two-point/marked correlations.
• Studies of shape measurement, PSF correction, and projection/selection impacts on orientation statistics.
• N-body/hydro baselines and observation–simulation comparisons for alignment and coherence scales.
• Latest progress on weak-lensing–skeleton and velocity-shear cross-statistics.

Appendix A — Data Dictionary & Processing Details

• Fields & Units
  μ=|cosθ|: dimensionless; η_μ: dimensionless; M(r): dimensionless; ξ_∥/ξ_⊥: dimensionless; A_align: dimensionless; L_align: h^-1 Mpc; D_stat: dimensionless; chi2_per_dof: dimensionless.
• Processing & Calibration
  Unified skeleton and orientation definitions (major axis/spin/shape); PSF/shear-calibrated shape fields; marks (colour/SFR/morphology) with completeness/selection weights; covariances from bootstrap + simulations; injections of {γ_Path_proj, η_TBN_align, β_TPR_class, ε_STG_aniso} for identifiability and bias assessment.

Appendix B — Sensitivity & Robustness Checks

• Prior Sensitivity
  Posterior centers of A_align, L_align, η_μ, M(r) are stable under loose vs. informative priors; the eta_TBN_align ceiling shows mild sensitivity to shape-measurement systematics without altering conclusions.
• Partition & Swap Tests
  Consistent results across mass/redshift/environment depth and across skeleton algorithms; after train/validation swaps, BiasClosure and key parameters show no systematic drift.
• Injection–Recovery
  Injections of {ε_STG_aniso, γ_Path_proj, η_TBN_align, β_TPR_class} recover nearly linearly; when γ_Path_proj = 0 is injected, recovered significance is null, supporting the zero-test.