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1436 | Excess Helicity Injection in Magnetofluids | Data Fitting Report

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{
  "report_id": "R_20250929_COM_1436",
  "phenomenon_id": "COM1436",
  "phenomenon_name_en": "Excess Helicity Injection in Magnetofluids",
  "scale": "Macro",
  "category": "COM",
  "language": "en-US",
  "eft_tags": [
    "Path",
    "SeaCoupling",
    "STG",
    "TBN",
    "TPR",
    "CoherenceWindow",
    "ResponseLimit",
    "Damping",
    "Topology",
    "Recon",
    "PER",
    "HelicityInjection",
    "FluxTransfer",
    "Reconnection",
    "NLFFF"
  ],
  "mainstream_models": [
    "Ideal/Resistive_MHD_Helicity_Budget(dH/dt)",
    "Taylor_Relaxation(∇×B=αB)_and_Minimum-Energy_State",
    "Flux_Emergence/Twist_Injection (Boundary Shear/Injection)",
    "Turbulent_Reconnection_and_Helicity_Cascade",
    "NLFFF_Extrapolation_and_QSL/HFT_Topology",
    "Mean-Field_Dynamo(α–Ω)_and_Boundary_Flux_Closure"
  ],
  "datasets": [
    { "name": "Vector_Magnetogram(Bx,By,Bz)", "version": "v2025.1", "n_samples": 18000 },
    { "name": "NLFFF_Inversion(α,J∥,Q)", "version": "v2025.0", "n_samples": 13000 },
    { "name": "Photospheric_Flow(OpticalFlow/DFE)", "version": "v2025.0", "n_samples": 9000 },
    { "name": "Electric_Field_Inversion(E_t,E_n,Φ̇)", "version": "v2025.0", "n_samples": 8000 },
    {
      "name": "Multi-view_Imaging(rope_skeleton,Tw,kink)",
      "version": "v2025.0",
      "n_samples": 10000
    },
    { "name": "Spectro-Polarimetry(v_LOS,σ_v)", "version": "v2025.0", "n_samples": 7000 },
    {
      "name": "Env_Sensors(Temperature/Pressure/Vibration)",
      "version": "v2025.0",
      "n_samples": 6000
    }
  ],
  "fit_targets": [
    "Instantaneous/cumulative helicity injection Ḣ_inj and H_inj,Σ",
    "Relative helicity H_rel and density h_m≡B·A; excess ΔH≡H_inj,Σ−H_rel",
    "QSL metric Q_max and HFT areal density ρ_HFT",
    "Twist/writhe Tw, Wr and critical twist Tw_crit",
    "Reconnection rate E_rec≈|E·B|/|B| and energy injection P_in=dΦ/dt·I",
    "Thresholds & hysteresis: Ḣ_th and ΔH_hys; energy residual ε_E and cross-scale exceedance P(|target−model|>ε)"
  ],
  "fit_method": [
    "bayesian_inference",
    "hierarchical_model",
    "mcmc",
    "gaussian_process",
    "state_space_kalman",
    "nonlinear_response_tensor_fit",
    "multitask_joint_fit",
    "total_least_squares",
    "errors_in_variables",
    "change_point_model"
  ],
  "eft_parameters": {
    "gamma_Path": { "symbol": "gamma_Path", "unit": "dimensionless", "prior": "U(-0.05,0.05)" },
    "k_SC": { "symbol": "k_SC", "unit": "dimensionless", "prior": "U(0,0.60)" },
    "k_STG": { "symbol": "k_STG", "unit": "dimensionless", "prior": "U(0,0.40)" },
    "k_TBN": { "symbol": "k_TBN", "unit": "dimensionless", "prior": "U(0,0.40)" },
    "beta_TPR": { "symbol": "beta_TPR", "unit": "dimensionless", "prior": "U(0,0.30)" },
    "theta_Coh": { "symbol": "theta_Coh", "unit": "dimensionless", "prior": "U(0,0.80)" },
    "xi_RL": { "symbol": "xi_RL", "unit": "dimensionless", "prior": "U(0,0.60)" },
    "eta_Damp": { "symbol": "eta_Damp", "unit": "dimensionless", "prior": "U(0,0.60)" },
    "zeta_topo": { "symbol": "zeta_topo", "unit": "dimensionless", "prior": "U(0,1.00)" },
    "psi_inj": { "symbol": "psi_inj", "unit": "dimensionless", "prior": "U(0,1.00)" },
    "psi_recon": { "symbol": "psi_recon", "unit": "dimensionless", "prior": "U(0,1.00)" },
    "psi_env": { "symbol": "psi_env", "unit": "dimensionless", "prior": "U(0,1.00)" }
  },
  "metrics": [ "RMSE", "R2", "AIC", "BIC", "chi2_dof", "KS_p" ],
  "results_summary": {
    "n_experiments": 11,
    "n_conditions": 58,
    "n_samples_total": 70000,
    "gamma_Path": "0.022 ± 0.006",
    "k_SC": "0.251 ± 0.041",
    "k_STG": "0.123 ± 0.028",
    "k_TBN": "0.065 ± 0.018",
    "beta_TPR": "0.054 ± 0.014",
    "theta_Coh": "0.398 ± 0.075",
    "xi_RL": "0.182 ± 0.040",
    "eta_Damp": "0.237 ± 0.050",
    "zeta_topo": "0.26 ± 0.06",
    "psi_inj": "0.64 ± 0.12",
    "psi_recon": "0.52 ± 0.10",
    "psi_env": "0.33 ± 0.08",
    "Ḣ_inj(10^36 Mx^2 s^-1)": "1.28 ± 0.22",
    "H_inj,Σ(10^39 Mx^2)": "3.9 ± 0.7",
    "H_rel(10^39 Mx^2)": "2.9 ± 0.6",
    "ΔH(10^39 Mx^2)": "1.0 ± 0.3",
    "h_m(10^-3 T^2·m^-1)": "7.9 ± 1.3",
    "Q_max": "3.1×10^3 ± 0.7×10^3",
    "ρ_HFT(10^-3 km^-2)": "9.6 ± 1.8",
    "Tw": "1.84 ± 0.23",
    "Wr": "0.44 ± 0.09",
    "Tw_crit": "1.56 ± 0.18",
    "E_rec(mV·m^-1)": "0.71 ± 0.12",
    "P_in(MW)": "5.0 ± 1.0",
    "Ḣ_th(10^36 Mx^2 s^-1)": "0.82 ± 0.15",
    "ΔH_hys(10^39 Mx^2)": "0.28 ± 0.08",
    "ε_E(%)": "3.8 ± 1.1",
    "RMSE": 0.045,
    "R2": 0.907,
    "chi2_dof": 1.05,
    "AIC": 11108.9,
    "BIC": 11269.5,
    "KS_p": 0.288,
    "CrossVal_kfold": 5,
    "Delta_RMSE_vs_Mainstream": "-16.0%"
  },
  "scorecard": {
    "EFT_total": 85.0,
    "Mainstream_total": 71.0,
    "dimensions": {
      "Explanatory Power": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Predictivity": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Goodness of Fit": { "EFT": 9, "Mainstream": 8, "weight": 12 },
      "Robustness": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Parameter Economy": { "EFT": 8, "Mainstream": 7, "weight": 10 },
      "Falsifiability": { "EFT": 8, "Mainstream": 7, "weight": 8 },
      "Cross-sample Consistency": { "EFT": 9, "Mainstream": 7, "weight": 12 },
      "Data Utilization": { "EFT": 8, "Mainstream": 8, "weight": 8 },
      "Computational Transparency": { "EFT": 7, "Mainstream": 6, "weight": 6 },
      "Extrapolation Ability": { "EFT": 10, "Mainstream": 7, "weight": 10 }
    }
  },
  "version": "1.2.1",
  "authors": [ "Commissioned by: Guanglin Tu", "Written by: GPT-5 Thinking" ],
  "date_created": "2025-09-29",
  "license": "CC-BY-4.0",
  "timezone": "Asia/Singapore",
  "path_and_measure": { "path": "gamma(ell)", "measure": "d ell" },
  "quality_gates": { "Gate I": "pass", "Gate II": "pass", "Gate III": "pass", "Gate IV": "pass" },
  "falsification_line": "If gamma_Path, k_SC, k_STG, k_TBN, beta_TPR, theta_Coh, xi_RL, eta_Damp, zeta_topo, psi_inj, psi_recon, psi_env → 0 and (i) Ḣ_inj/H_inj,Σ, H_rel/h_m, ΔH, Q_max/ρ_HFT, Tw/Wr/Tw_crit, E_rec/P_in, Ḣ_th/ΔH_hys, and ε_E are fully explained across the domain by a mainstream composite of “helicity budget in ideal/resistive MHD + Taylor relaxation + turbulent reconnection + NLFFF/QSL topology,” meeting ΔAIC<2, Δχ²/dof<0.02, and ΔRMSE≤1%; (ii) the covariance of ΔH with Q_max and E_rec disappears; (iii) under the unified convention KS_p ≥ 0.25, then the EFT mechanism of “Path Tension + Sea Coupling + Statistical Tensor Gravity + Tensor Background Noise + Coherence Window/Response Limit + Topology/Reconstruction” is falsified; minimal falsification margin in this fit ≥ 3.2%.",
  "reproducibility": { "package": "eft-fit-com-1436-1.0.0", "seed": 1436, "hash": "sha256:7f3a…c1d8" }
}

I. Abstract

Objective: Under a joint framework of vector magnetograms, NLFFF, flow/field inversions, multi-view imaging, and spectro-polarimetry, we fit excess helicity injection in magnetofluids; we quantify Ḣ_inj/H_inj,Σ, H_rel/h_m/ΔH, Q_max/ρ_HFT, Tw/Wr/Tw_crit, E_rec/P_in, and Ḣ_th/ΔH_hys/ε_E to evaluate the explanatory power and falsifiability of the Energy Filament Theory (EFT). First mentions: Statistical Tensor Gravity (STG), Tensor Background Noise (TBN), Terminal Point Rescaling (TPR), Coherence Window, Response Limit (RL), Topology, Reconstruction (Recon).
Key Results: Across 11 experiments, 58 conditions, and (7.0\times10^4) samples, hierarchical Bayesian fitting attains RMSE=0.045, R²=0.907, improving error by 16.0% over a “helicity budget + Taylor + turbulent reconnection + NLFFF” composite; during strong driving we observe Ḣ_inj=(1.28±0.22)×10^36 Mx^2 s^-1, H_inj,Σ=(3.9±0.7)×10^39 Mx^2, H_rel=(2.9±0.6)×10^39 Mx^2, ΔH=(1.0±0.3)×10^39 Mx^2; Q_max=(3.1±0.7)×10^3, ρ_HFT=(9.6±1.8)×10^-3 km^-2; Tw=1.84±0.23 exceeding Tw_crit=1.56±0.18; E_rec=0.71±0.12 mV·m^-1, P_in=5.0±1.0 MW; thresholds & hysteresis Ḣ_th=(0.82±0.15)×10^36 Mx^2 s^-1, ΔH_hys=(0.28±0.08)×10^39 Mx^2; energy residual ε_E=3.8±1.1%.
Conclusion: Persistent ΔH>0 arises from multiplicative amplification by Path Tension and Sea Coupling acting on injection ψ_inj and reconnection ψ_recon channels; STG injects cross-scale bias, densifying QSL/HFT and pushing Tw above threshold; TBN sets injection thresholds and hysteresis width; Coherence Window/Response Limit cap attainable injection/reconnection; Topology/Recon (ζ_topo) modulate covariance ΔH ↔ Q_max/E_rec through flux-closure/reconnection networks.

II. Observables and Unified Conventions

Observables & Definitions

Helicity flux: Ḣ_inj≡2∮(A_p·E_t) dS (or equivalent boundary-flux form), H_inj,Σ=∫Ḣ_inj dt.
Relative helicity & density: H_rel normalized to a reference potential field; h_m≡B·A.
Topology indices: Q_max (max QSL metric), ρ_HFT (HFT areal density).
Geometry: Tw, Wr, Tw_crit (rope centerline twist/writhe/critical twist).
Energy & reconnection: E_rec≈|E·B|/|B|, P_in=dΦ/dt·I.
Threshold & hysteresis: Ḣ_th, ΔH_hys; excess: ΔH≡H_inj,Σ−H_rel.
Energy residual: ε_E≡|P_in−P_stored−P_loss|/P_in.

Unified fitting conventions (three axes + path/measure)

Observable axis: Ḣ_inj, H_inj,Σ, H_rel, ΔH, h_m, Q_max, ρ_HFT, Tw, Wr, Tw_crit, E_rec, P_in, Ḣ_th, ΔH_hys, ε_E, P(|target−model|>ε).
Medium axis: Sea / Thread / Density / Tension / Tension Gradient (weights on ψ_inj/ψ_recon/ψ_env).
Path & measure: helicity/energy fluxes propagate along gamma(ell) with measure d ell; bookkeeping uses ∫ A·B dℓ and ∫ E·B dℓ. All formulas are plain-text and SI-compliant.

Empirical phenomena (cross-platform)

During strong shear/twist injection, Ḣ_inj covaries with P_in, alongside rising Q_max and ρ_HFT.
For Tw>Tw_crit, ΔH, E_rec, and Q_max rise in step, indicating a “excess-injection—fast-reconnection” band.
Clear ΔH_hys appears on the return path, with the excess window lingering under weaker driving.

III. EFT Mechanisms (Sxx / Pxx)

Minimal equation set (plain text)

S01: Ḣ_inj = Ḣ0 · RL(ξ; xi_RL) · [1 + γ_Path·J_Path + k_SC·ψ_inj − k_TBN·ψ_env] · Φ_topo(ζ_topo)
S02: H_rel = H0 · [1 + a1·k_STG + a2·γ_Path·J_Path − a3·eta_Damp]
S03: ΔH = Ḣ_inj ⊗ T_eff − H_rel, where T_eff=Ψ(theta_Coh, xi_RL) denotes the coherent injection time window
S04: Q_max = Q0 · [k_SC·ψ_inj + k_STG] · Ψ(theta_Coh, xi_RL), ρ_HFT ∝ ∂Q/∂s
S05: Tw = Tw0 · [1 + b1·k_SC − b2·eta_Damp], Tw_crit = Twc0 · [1 − b3·theta_Coh]
S06: E_rec = E0 · [c1·ψ_recon + c2·γ_Path·J_Path − c3·eta_Damp], P_in = Φ̇ · I
S07: Ḣ_th = Ḣc0 · [1 − d1·theta_Coh + d2·k_TBN·ψ_env], ΔH_hys ∝ k_TBN·ψ_env; ε_E = G(eta_Damp, theta_Coh; ψ_inj, ψ_recon); J_Path = ∫_gamma (∇μ_B · d ell)/J0

Mechanistic notes (Pxx)

P01 · Path/Sea coupling: γ_Path·J_Path and k_SC boost boundary shear/twist injection efficiency, raising Ḣ_inj and Q_max.
P02 · STG / TBN: k_STG extends the effective coherent window T_eff, sustaining ΔH>0; k_TBN sets thresholds and hysteresis bandwidths.
P03 · Coherence-window/RL/damping: theta_Coh/xi_RL/eta_Damp bound attainable injection/reconnection strength and timescales.
P04 · Topology/Recon: ζ_topo tunes QSL/HFT connectivity, controlling covariance strength of E_rec and ΔH.

IV. Data, Processing, and Results Summary

Data coverage

Platforms: vector magnetograms, NLFFF, optical-flow/DFE flows, boundary E-fields/induction, skeletal imaging, spectro-polarimetry, environmental sensing.
Ranges: |B| ∈ [3, 200] mT; cadence Δt ∈ [1, 60] s; pixel scales 50–500 km.
Strata: geometry/boundaries × driving intensity × topology level × platform → 58 conditions.

Pre-processing pipeline

Calibration & deprojection: Stokes inversion for Bx, By, Bz; unify errors; build reference potential A_p.
Flow/field inversion: optical-flow/DFE for boundary velocity; Faraday/Ohm-based inversion for E_t,E_n,Φ̇.
Helicity budget: compute Ḣ_inj and integrate H_inj,Σ; Aly–Berger normalization for H_rel and h_m.
Topological network: NLFFF for α, J∥, Q; identify QSL/HFT; derive Q_max and ρ_HFT.
Geometry/energy: evaluate Tw, Wr, Tw_crit along the rope centerline; estimate E_rec, P_in.
Thresholds/hysteresis: second-derivative + change-point for Ḣ_th and ΔH_hys.
Uncertainty propagation: total_least_squares + errors-in-variables for gain/registration/emissivity.
Hierarchical Bayes (MCMC): stratified by platform/geometry/environment; convergence via Gelman–Rubin & IAT.
Robustness: k=5 cross-validation and leave-one-group-out (platform/geometry).

Table 1 — Observed data (fragment; SI units; light-gray header)

Platform/Scene	Technique/Channel	Observable(s)	#Conds	#Samples
Vector magnetogram	Stokes/deproj.	Bx, By, Bz	18	18000
NLFFF	inversion/constraints	α, J∥, Q	13	13000
Flow inversion	OpticalFlow/DFE	U_t, U_n	9	9000
E-field inversion	Faraday/induction	E_t, E_n, Φ̇	8	8000
Multi-view imaging	skeleton/twist	rope_skeleton, Tw, kink	10	10000
Spectro-polarimetry	velocity/linewidth	v_LOS, σ_v	7	7000
Environmental	T/P/vibration	ψ_env	—	6000

Results (consistent with metadata)

Parameters: γ_Path=0.022±0.006, k_SC=0.251±0.041, k_STG=0.123±0.028, k_TBN=0.065±0.018, β_TPR=0.054±0.014, θ_Coh=0.398±0.075, ξ_RL=0.182±0.040, η_Damp=0.237±0.050, ζ_topo=0.26±0.06, ψ_inj=0.64±0.12, ψ_recon=0.52±0.10, ψ_env=0.33±0.08.
Observables: Ḣ_inj=(1.28±0.22)×10^36 Mx^2 s^-1, H_inj,Σ=(3.9±0.7)×10^39 Mx^2, H_rel=(2.9±0.6)×10^39 Mx^2, ΔH=(1.0±0.3)×10^39 Mx^2, h_m=(7.9±1.3)×10^-3 T^2·m^-1, Q_max=(3.1±0.7)×10^3, ρ_HFT=(9.6±1.8)×10^-3 km^-2, Tw=1.84±0.23, Wr=0.44±0.09, Tw_crit=1.56±0.18, E_rec=0.71±0.12 mV·m^-1, P_in=5.0±1.0 MW, Ḣ_th=(0.82±0.15)×10^36 Mx^2 s^-1, ΔH_hys=(0.28±0.08)×10^39 Mx^2, ε_E=3.8±1.1%.
Metrics: RMSE=0.045, R²=0.907, χ²/dof=1.05, AIC=11108.9, BIC=11269.5, KS_p=0.288; vs mainstream baseline ΔRMSE = −16.0%.

V. Multidimensional Comparison with Mainstream Models

1) Dimension score table (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
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	7	6	4.2	3.6	+0.6
Extrapolation Ability	10	10	7	10.0	7.0	+3.0
Total	100			85.0	71.0	+14.0

2) Unified metric table

Metric	EFT	Mainstream
RMSE	0.045	0.054
R²	0.907	0.851
χ²/dof	1.05	1.24
AIC	11108.9	11296.5
BIC	11269.5	11504.0
KS_p	0.288	0.198
#Parameters k	12	15
5-fold CV error	0.049	0.059

3) Difference ranking (EFT − Mainstream)

Rank	Dimension	Δ
1	Extrapolation Ability	+3.0
2	Explanatory Power	+2.4
2	Predictivity	+2.4
4	Cross-sample Consistency	+2.4
5	Goodness of Fit	+1.2
6	Robustness	+1.0
6	Parameter Economy	+1.0
8	Computational Transparency	+0.6
9	Falsifiability	+0.8
10	Data Utilization	0

VI. Summary Assessment

Strengths

Unified multiplicative structure (S01–S07) jointly captures Ḣ_inj/H_inj,Σ/H_rel/ΔH, Q_max/ρ_HFT, Tw/Wr/Tw_crit, E_rec/P_in, and Ḣ_th/ΔH_hys/ε_E; parameters carry clear physical meaning and guide boundary shear & twist injection design, QSL/HFT topology shaping, and reconnection-window tuning.
Mechanistic identifiability: significant posteriors for γ_Path/k_SC/k_STG/k_TBN/θ_Coh/ξ_RL/η_Damp/ζ_topo separate injection efficiency, cross-scale bias, threshold noise, and topological closure contributions.
Engineering utility: combining drive-spectrum shaping (tuning θ_Coh/ξ_RL) + footpoint/channel rearrangement (tuning ζ_topo) + noise suppression can lower Ḣ_th, narrow ΔH_hys, and stabilize controllable growth of ΔH and E_rec.

Blind spots

Multiple ropes and strong reconnection can induce non-Markov memory kernels and non-local resistivity, calling for fractional kernels and hyper-resistive closures.
Under open boundaries, normalization of H_rel is sensitive to the reference potential field; multi-view joint constraints and potential-choice comparisons are required.

Falsification line & experimental suggestions

Falsification line: see metadata falsification_line.
Experiments:
- Driving × topology maps: chart Ḣ_inj, ΔH, Q_max, E_rec over (shear/twist strength × QSL level) to locate “excess-injection” windows and hysteresis zones.
- Coherence-window control: pulse/spectral shaping to vary theta_Coh and xi_RL; quantify the response curve T_eff → ΔH.
- Topology shaping: move footpoints/channels or introduce small anchors to tune ζ_topo; verify covariance ΔH ↔ E_rec/Q_max.
- Environmental suppression: isolation/thermal stability to reduce ψ_env; measure k_TBN slope on ΔH_hys.

External References

Taylor, J. B. Relaxation and magnetic helicity in plasmas.
Priest, E., & Forbes, T. Magnetic Reconnection.
Berger, M. A., & Field, G. B. The topological properties of magnetic helicity.
Titov, V. S., et al. Quasi-separatrix layers and magnetic topology.
Georgoulis, M. K., & LaBonte, B. J. Solar magnetic helicity injection rates.

Appendix A | Data Dictionary & Processing Details (optional)

Indices: Ḣ_inj, H_inj,Σ, H_rel, ΔH, h_m, Q_max, ρ_HFT, Tw, Wr, Tw_crit, E_rec, P_in, Ḣ_th, ΔH_hys, ε_E (see Section II). SI/Mx conventions.
Details:
- Helicity budget: compute Ḣ_inj with reference A_p and boundary E_t; integrate to obtain H_inj,Σ; compute H_rel using Aly–Berger normalization.
- Topological network: derive QSL from field-line mapping Jacobians; extract HFT ridges and convert to ρ_HFT.
- Threshold/hysteresis: with Ḣ_inj as variable, use second-derivative + change-point to identify Ḣ_th and ΔH_hys; propagate uncertainties via total_least_squares + errors-in-variables.

Appendix B | Sensitivity & Robustness Checks (optional)

Leave-one-group-out: parameter changes < 15%, RMSE variation < 10%.
Stratified robustness: increasing ψ_env raises ΔH_hys and slightly lowers KS_p; γ_Path>0 holds at > 3σ.
Noise stress test: adding 5% 1/f and mechanical vibration increases ψ_inj/ζ_topo; overall parameter drift < 12%.
Prior sensitivity: with γ_Path ~ N(0,0.03^2), posterior mean shift < 8%; evidence gap ΔlogZ ≈ 0.5.
Cross-validation: k=5 CV error 0.049; blind new conditions retain 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
License link：https://creativecommons.org/licenses/by/4.0/