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Appendix B Parameter Registry & Default Priors
I. Abstract & Scope
This appendix defines the unified specification for “parameter registry & default priors,” covering channels (reconnection/shear/comparators), spectrum formation & transport, GRB/FRB specifics, ToA path corrections, noise & calibration, hierarchical hyperparameters, and coding transforms. All parameters are registered in English notation with SI units (default 3 significant figures). Any ToA-related quantity is recorded in two forms with delta_form, explicitly stating path gamma(ell) and measure d ell.
II. Dependencies & References
Unified symbols & dimensions: Appendix A and Chapter 2 P12-. Channels & kinematics: Chapters 3–6 (S20-/S30-/S40-/S45-). Spectrum & transport: Chapters 7–8 (S50-/S52-). GRB/FRB: Chapters 10–11 (M62-/M64-). Simulation & benchmarks: Chapter 12 (M70-). Data/pipelines & release: Chapter 14 (I75-/M75-). Inference & falsification: Chapter 13 (M72-). API bindings: Chapter 15 (I80-*).
III. Registry Scope & Naming (Mandatory)
- Naming: parameter names use English snake_case or camelCase, aligned with text anchors; cross-chapter parameters are listed in the centralized table.
- Fields (minimum): {name, meaning, unit, dim, transform, bounds, prior, hyper, scope, see}.
- Transforms: transform ∈ {identity, log, logit}; use logit for bounded, log for strictly positive.
- Priors: U[a,b], N(μ,σ), LogU[a,b], LN(μ,σ), Beta(α,β), HalfN(σ), etc.
- ToA-related: any parameter tied to T_arr/path/measure must be under scope:"ToA", recording both forms and delta_form.
IV. Parameter Registry (Grouped)
Tab. B-1 Reconnection Channel (see S30-*)
name | meaning | unit | dim | transform | bounds | default prior | see |
|---|---|---|---|---|---|---|---|
xi_rate | reconnection rate coefficient | 1 | 1 | logit | (0,1] | Beta(2,5) | S30-1 |
u_in | inflow speed | m·s^-1 | L·T^-1 | log | (0, c_ref) | LogU[1e2,1e6] | S30-1 |
u_out | outflow speed | m·s^-1 | L·T^-1 | log | (0, c_ref) | LogU[1e3,1e7] | S30-3 |
L_sheet | sheet length | m | L | log | (1e-3,1e13) | LogU[1e0,1e9] | S30-0 |
delta_sheet | sheet thickness | m | L | log | (1e-6,1e9) | LogU[1e-3,1e6] | S30-0 |
chi_open | topological openness | 1 | 1 | logit | (0,1] | Beta(2,2) | S30-3 |
T_fil | tension magnitude | N | M·L·T^-2 | log | (1e-6,1e24) | LogU[1e0,1e15] | Core.Tension |
Theta_T | tension ratio T_fil/T_ref | 1 | 1 | log | (1e-6,1e6) | LogU[1e-3,1e3] | S30-3 |
E_cut_rec | reconnection cutoff energy | eV | E | log | (1e3,1e21) | LogU[1e6,1e20] | S30-5 |
p_eta | efficiency slope | 1 | 1 | identity | [0.5, 4] | U[0.5,4] | S30-5 |
q_rec | tension exponent | 1 | 1 | identity | [0, 2] | U[0,2] | S30-3 |
Tab. B-2 Shear Channel (see S40-*)
name | meaning | unit | dim | transform | bounds | default prior | see |
|---|---|---|---|---|---|---|---|
sigma_shear | shear strain rate | s^-1 | T^-1 | log | (1e-9,1e9) | LogU[1e-6,1e3] | S40-1 |
L_grad | gradient scale | m | L | log | (1e-3,1e13) | LogU[1e0,1e9] | S40-0 |
delta_shear | layer thickness | m | L | log | (1e-6,1e9) | LogU[1e-3,1e6] | S40-0 |
Delta_u | velocity contrast | m·s^-1 | L·T^-1 | log | (1e1, c_ref) | LogU[1e2,1e7] | S40-1 |
chi_aniso | anisotropy factor | 1 | 1 | logit | (0,1] | Beta(2,2) | S40-3 |
p_sh | gain exponent | 1 | 1 | identity | [1,3] | U[1,3] | S40-3/6 |
E_cut_sh | coherence cutoff | eV | E | log | (1e3,1e21) | LogU[1e6,1e19] | S40-5 |
p_coh | coherence roll-off slope | 1 | 1 | identity | [0.5,4] | U[0.5,4] | S40-5 |
Tab. B-3 Transport & Losses (see S52-*)
name | meaning | unit | dim | transform | bounds | default prior | see |
|---|---|---|---|---|---|---|---|
D0 | diffusion amplitude | m^2·s^-1 | L^2·T^-1 | log | (1e-6,1e20) | LogU[1e6,1e15] | S52-0 |
delta_D | diffusion energy index | 1 | 1 | identity | [0,2] | U[0,2] | S52-* |
k_rad | radiative-loss coefficient | s^-1·eV^-1 | T^-1·E^-1 | log | (1e-40,1e-10) | LogU[1e-30,1e-12] | S52-5 |
div_u | flow divergence (∇·u_adv) | s^-1 | T^-1 | identity | [-1,1] | N(0,0.1) | S52-5 |
k_coll | collisional-loss coeff. | s^-1 | T^-1 | log | (1e-30,1e-6) | LogU[1e-25,1e-8] | S52-5 |
k_ion | ionization-loss coeff. | s^-1 | T^-1 | log | (1e-30,1e-6) | LogU[1e-25,1e-8] | S52-5 |
L_esc | escape scale | m | L | log | (1e2,1e23) | LogU[1e5,1e21] | S52-3 |
kappa_esc | escape geometry factor | 1 | 1 | log | (1e-3,1e3) | LogU[1e-2,1e2] | S52-3 |
Tab. B-4 Spectrum Formation & Injection (see S50-*)
name | meaning | unit | dim | transform | bounds | default prior | see |
|---|---|---|---|---|---|---|---|
alpha_inj | injection spectral index | 1 | 1 | identity | [1,3.5] | N(2.2,0.3) | S50-* |
Q0_Z | injection normalization (by charge) | s^-1 | T^-1 | log | (1e-30,1e10) | LogU[1e-10,1e5] | M60-3 |
E0 | reference energy | eV | E | log | (1e3,1e12) | LogU[1e6,1e9] | S50-* |
R_br | rigidity break | V | E·Q^-1 | log | (1e6,1e16) | LogU[1e8,1e15] | M60-3 |
E_max | maximum energy | eV | E | log | (1e6,1e22) | LogU[1e9,1e21] | S50-7 |
Tab. B-5 GRB (see M62-*)
name | meaning | unit | dim | transform | bounds | default prior | see |
|---|---|---|---|---|---|---|---|
A_rec0(t_k) | reconnection amplitude (window k) | s^-1 | T^-1 | log | (1e-6,1e3) | LogU[1e-4,1e1] | M62-3 |
A_sh0(t_k) | shear amplitude (window k) | s^-1 | T^-1 | log | (1e-6,1e3) | LogU[1e-4,1e1] | M62-3 |
C_geom(t_k) | geometry factor | 1 | 1 | log | (1e-3,1e3) | LogU[1e-2,1e2] | S62-2 |
C_prop(t_k) | propagation factor | 1 | 1 | log | (1e-3,1e3) | LogU[1e-2,1e2] | S62-2 |
Tab. B-6 FRB (see M64-*)
name | meaning | unit | dim | transform | bounds | default prior | see |
|---|---|---|---|---|---|---|---|
DM_MW | Milky Way DM | m^-2 | L^-2 | log | (1e14,1e23) | LogU[1e16,1e22] | S64-3/7 |
DM_IGM | IGM DM | m^-2 | L^-2 | log | (1e15,1e25) | LogU[1e18,1e24] | S64-3/7 |
DM_host | host DM (source frame) | m^-2 | L^-2 | log | (1e14,1e23) | LogU[1e16,1e22] | S64-7 |
DM_loc | local DM | m^-2 | L^-2 | log | (1e13,1e22) | LogU[1e15,1e21] | S64-7 |
RM_* | RM components | rad·m^-2 | rad·L^-2 | identity/log | (−1e7,1e7) | N(0,1e4) | S64-4/7 |
tau_scat0 | scattering amplitude | s | T | log | (1e-7,1e2) | LogU[1e-5,1e1] | S64-5 |
alpha_scat | scattering frequency index | 1 | 1 | identity | [2,6] | U[2,6] | S64-5 |
D_dep | depolarization factor | 1 | 1 | logit | (0,1] | Beta(2,2) | S64-6 |
Tab. B-7 ToA/Path Corrections & Noise
name | meaning | unit | dim | transform | bounds | default prior | see |
|---|---|---|---|---|---|---|---|
gamma_Path | path-correction strength | 1 | 1 | log | (1e-6,1e2) | LogU[1e-3,1e1] | falsification |
sigma_spec | spectral noise ratio | 1 | 1 | logit | (0,1) | Beta(2,20) | M72-1 |
sigma_timing | timing noise | s | T | log | (1e-6,1e1) | LogU[1e-5,1e-1] | M72-1 |
calib_gain | instrument gain calibration | 1 | 1 | log | (1e-1,1e1) | LN(0,0.2) | I75-/M75- |
delta_form | ToA form flag | — | — | — | {A,B} | (record field) | S50-9/S52-8 |
V. Hierarchical Priors & Shared Hyperparameters (see M72-2)
- alpha_inj | (μ_α, σ_α) ~ N(μ_α, σ_α), with shared hyperparameters μ_α ~ N(2.2,0.5), σ_α ~ HalfN(0.5).
- E_max | (μ_E, σ_E) ~ LN(μ_E, σ_E), with μ_E ~ N(ln 1e18, 2), σ_E ~ HalfN(2).
- Transport family {D0, delta_D} hierarchical: log D0 ~ N(μ_D0, σ_D0), with μ_D0 ~ N(ln 1e13,3), σ_D0 ~ HalfN(2).
- FRB path decomposition: DM_k ~ LN(μ_k, σ_k); (μ_k, σ_k) modeled by sky/z subgroups.
VI. Prior Coding & Transform Rules (Enforcement)
- Positive parameters → log; bounded → logit; others → identity; sampling domain matches bounds.
- All priors must be unit/dimension consistent; if physical bounds conflict, restrict to the narrowest feasible interval.
- Compatibility: ModelCards may override defaults, but must record override:true and source within the card.
VII. Card & Workflow Integration (I75-/I80-/M70-/M72-)
- ParameterCard: emit per this appendix and embed into ModelCard.params.
- APIs: I80-1/2/3/4/6 read parameters and return unit/dimension-bearing results.
- Simulation & Fitting: SimStack (M70-) instantiates from ParameterCard; inference flows (M72-) start from defaults and write back {posterior, evidence} in deliverables.
VIII. Dual-Form ToA Parameterization (Mandatory Template)
- Form A: T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff d ell ) (depends on n_eff model parameters and path parameters).
- Form B: T_arr = ( ∫_{gamma(ell)} ( n_eff / c_ref ) d ell ).
Both forms must list {paths = gamma(ell), measure = d ell, n_eff_model} in the ParameterCard and define the delta_form recording policy.
IX. Figures & Lists (This Appendix)
- Tabs B-1…B-7: parameter registry & default priors (grouped).
- Templates: minimal ParameterCard fields & example; dual-form ToA recording checklist; hierarchical prior schematic.
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/