35-EFT.WP.EDX.OrientedTension v1.0 | Appendix B Parameter Registry & Default Priors (OT)

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Appendix B Parameter Registry & Default Priors (OT)

I. Abstract & Scope
This appendix defines the unified specification for OT (Oriented Tension) parameter registry and default priors: covering orientation–constitutive (Λ_{ijkl}, A, K, tau_relax, D_Q), couplings (χ_* , D1, α_*, κ_s), interfaces/defects (κ_a, κ_b, K, r_core), media & effective tensors (ε_ij, μ_ij, C_eff, D_eff), EDX energy/flux kernels (K_E, etc.), and (if present) ToA-related fields. All parameters are registered in English notation with SI units; priors must respect physical feasibility and dimensional closure.

II. Dependencies & References

• Notation & units: Ch.2 P80-1/4/5/6; orientation & geometry: Ch.3 S80-1/2; constitutive & dynamics: Ch.4 S80-3/4; couplings: Ch.6 S80-5/6; EDX: Ch.7 S80-7/8; interfaces/defects: Ch.8 S80-9/10/11; numerics & APIs: Ch.10/12 (SimStack-OT, I80-*).

III. Scope & Naming Rules (mandatory)

• Naming: English snake_case/camelCase aligned with anchors; cross-chapter parameters are centrally registered.
• Minimum fields: {name, meaning, unit, dim, transform, bounds, prior, hyper, scope, see}.
• Transforms: identity | log | logit; use log for positive, logit for bounded.
• Prior families: U[a,b], N(μ,σ), LogU[a,b], LN(μ,σ), Beta(α,β), HalfN(σ), etc.
• Feasible domain: enforce positivity/objectivity/symmetry/nonnegative energy alongside unit/dimension closure.

IV. Parameter Registry (grouped)

Tab. B-1 Orientation–Constitutive (Ch.4)

Tab. B-2 Couplings (Ch.6)

Tab. B-3 Media & Effective Tensors (Ch.6)

Tab. B-4 Interfaces/Defects (Ch.8)

Tab. B-5 EDX & Flux Kernels (Ch.7)

Tab. B-6 Numerics & Instrumentation (Ch.10/12)

(Optional) Tab. B-7 ToA-Related (if present, Ch.12)

V. Hierarchical Priors & Shared Hypers (Ch.9 M80-25/27)

• Orientation–constitutive layer:
  log A ~ N(μ_A, σ_A), μ_A ~ N(0,2), σ_A ~ HalfN(1);
  log K ~ N(μ_K, σ_K), μ_K ~ N(0,2), σ_K ~ HalfN(1);
  log tau_relax ~ N(μ_τ, σ_τ), μ_τ ~ N(−2,2), σ_τ ~ HalfN(1).
• Coupling layer:
  χ_* | (σ_χ) ~ N(0, σ_χ^2), σ_χ ~ HalfN(s_0); D1 | (σ_D1) ~ N(0, σ_D1^2).
• Media-tensor layer: share hypers across material families (isotropic/transversely isotropic, etc.).

VI. Prior Coding & Feasibility (Execution)

• Enforce SPD via Cholesky/eigendecomposition (e.g., D_eff = L L^T); symmetry & traceless constraints in parameter space or via projection.
• Objectivity/symmetry through invariant bases or DoF reduction (e.g., material-symmetry constraints on Λ_{ijkl}).
• Nonnegative energy: A≥0, K≥0; positive diffusion/flux; violations are rejected or penalized.

VII. Card & Workflow Integration (I75-/I80-/M-series)

• ParameterCard: emit per this appendix; embed in ModelCard.params.
• I80 APIs: oriented_tension, couple_transport, edx_balance, simulate_ot, fit_ot read parameters and return unit/dimension-bearing results.
• M workflows: M80-39/40/41/42 and M80-31…38 consume default priors; ModelCard may override with override:true and provenance.

VIII. Dual-Form ToA Parameterization (if used, mandatory)

• Form A: T_arr = ( 1 / c_ref ) * ( ∫_{gamma(ell)} n_eff d ell ) (depends on n_eff model & path params).
• Form B: T_arr = ( ∫_{gamma(ell)} ( n_eff / c_ref ) d ell ).
  Parameter cards must list {paths = gamma(ell), measure = d ell, n_eff_model} and the delta_form policy.

IX. Templates & Examples

• Minimal ParameterCard snippet:
  {"name":"tau_relax","unit":"s","dim":"T","transform":"log","bounds":[1e-6,1e4],"prior":"LN(-2,1)","see":"S80-4"}
• Override example: in ModelCard.params, set override:true and cite the data/literature source when replacing defaults.

— This appendix establishes the baseline for OT parameter registration and priors, ensuring reproducibility, auditability, and physical consistency across chapters and implementation layers.