Energy Filament Theory · EFT Full KB
04_ClusterLensMass: cluster-scale extension window
V30-30.9 · F 证据节 / 显影节 ·
30.9 pushes V30 beyond galaxy scale into a cluster lensing–gas-fraction extension window: using four manually matched weak-lensing M500c–fgas pairs, one Gaussian fgas likelihood with weighted least squares on both sides, an EFT constant fit fgas(M, z) = f₀ against the standard power-law fgas(M, z) = f₀ · (M500c / Mp)^α · E(z)^β, and an enhanced robustness layer built from four leave-one-out subsets, e_fgas ×0.5/×2, and Mp = 4/5/6×10¹⁴ M☉, the report finds baseline ΔAICc ≈ −1.16 and ΔBIC ≈ −1.38 and keeps |ΔIC| < 2 with unchanged sign across all perturbations, so the section serves as a publication-level enhanced equivalence ledger and outward scale extension rather than a new closure spine.
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Keywords: Energy Filament Theory, EFT, cluster lensing, gas fraction, M500c, fgas, scale_extension_window, robustness grid, equivalence band, galaxy-to-cluster bridge, route back to closure spine
Section knowledge units
thesis
30.9 is the scale_extension_window of Volume 30. On four manually confirmed cluster pairs of weak-lensing mass and gas fraction, the source compares an EFT constant fit with the standard power-law scaling model under one small-sample fair-comparison frame. The baseline table gives ΔAICc ≈ −1.16 and ΔBIC ≈ −1.38, both inside the report’s |ΔIC| < 2 equivalence band. So this section does not establish a unique cluster-mass law; its report-bounded job is to extend V30 outward in scale and show that uniqueness also fails on the cluster lensing–gas-fraction chain.
mechanism
The comparison frame is compact and auditable. The data artifact is cluster_lensing_fgas.csv with four entries {z, M500c, e_M500c, fgas, e_fgas}, using weak-lensing M500c and gas fractions at r500. Both models are evaluated in one Gaussian likelihood in fgas with weights 1 / e_fgas² and weighted least squares. The Energy Filament Theory (EFT) side is the constant model fgas(M, z) = f₀ with 0 < f₀ < 0.3, while the standard side is f₀ · (M500c / Mp)^α · E(z)^β with baseline Mp = 5×10¹⁴ M☉ and priors 0 < f₀ < 0.3, −1 < α < 1, −1 < β < 1. Because n = 4 is extremely small, the source uses deterministic optimization rather than full MCMC.
evidence
The numerical verdict is modest but stable. The EFT constant fit reports AICc ≈ −22.67 and BIC ≈ −22.46 with f₀ ≈ 0.12, while the standard power-law reports AICc ≈ −21.51 and BIC ≈ −21.08. That gives ΔAICc ≈ −1.16 and ΔBIC ≈ −1.38, which the source reads as statistical equivalence rather than a unique standard-model win. The enhanced layer then repeats the test across four leave-one-out subsets, a global e_fgas rescaling by ×0.5 and ×2, and pivot-mass shifts from 5×10¹⁴ to 4×10¹⁴ and 6×10¹⁴ M☉. In every case |ΔIC| stays below 2 and the sign does not flip.
boundary
The strength of 30.9 is robustness under a tiny sample, not breadth. The report keeps shared data, one likelihood, and symmetric priors visible, but it still works with only four clusters and explicitly avoids full MCMC. So the section is publication-level enhanced in a small-sample sense, not a global cluster-cosmology pipeline. It should therefore not be inflated into a universal cluster-baryon mechanism or a replacement for 30.1’s closure grammar. Its narrower claim is that, on this independent weak-lensing–gas-fraction chain, the standard dark-matter explanation is not uniquely selected.
interface
The source keeps its artifacts explicit: cluster_lensing_fgas.csv, fit_table.csv, report_step2.md, the bilingual report docx, and the PowerShell run command. It also notes a simple external sanity check: mean fgas ≈ 0.12 sits below the global baryon fraction f_b ≈ 0.157, so neither side is pushed into an obviously unphysical regime. Inside Volume 30, 30.9 should be read as the outward scale-extension bridge from 30.2’s galaxy scaling and 30.6’s late-time growth toward the cluster regime, before routing back to the 30.1 RC-GGL closure spine as an extension test rather than a replacement trunk.