35-EFT.WP.EDX.OrientedTension v1.0 | Chapter 11 Applications & Benchmarks

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Chapter 11 Applications & Benchmarks

I. Abstract & Scope
This chapter presents cross-domain application cases and benchmark suites for Oriented Tension: polymers/liquid crystals, fiber-reinforced composites, plasma shear, and astrophysical magnetic structures. Using the geometry–constitutive–coupling–energy (EDX) conventions defined earlier in this volume, it specifies reproducible experiments and numerical benchmarks, metrics and gates, and a unified procedure for evidence and closure auditing. All symbols use English notation in backticks; SI units apply. No ToA terms appear here.

II. Dependencies & References

• Geometry & orientation: Chapter 3 S80-1/2.
• Constitutive & dynamics: Chapter 4 S80-3/4, axioms P80-2/3/9/10.
• Metrology & calibration: Chapter 5 M80-1…4.
• Couplings & media: Chapter 6 S80-5/6.
• Energy accounting & power partition: Chapter 7 S80-7/8.
• Numerical methods & simulation: Chapter 10 (SimStack-OT). Implementation & APIs: Chapter 12 (I80-*).

III. Normative Anchors (added in this chapter)

• P80-16 (Benchmark Reproducibility Axiom): every case and benchmark must be one-click replayable under fixed seed, locked environment, and Unit/Dim closure; artifacts must carry {code_hash, data_hash, rng_state}.
• M80-39 (Case Modeling & Cardization): standardize case geometry/material/loading/observation into GeometryCard/ModelCard/MetrologyCard/PipelineCard.
• M80-40 (Benchmark Suites & Scale Tiers): define S/M/L tiers with task lists, input distributions, and acceptance gates.
• M80-41 (Acceptance & Evidence Evaluation): compute {metrics, posterior, evidence} and EDX closure residuals with a unified pass/fail procedure.
• M80-42 (Regression & Comparison): cross-version/method regression matrix and diffs, issuing compatibility reports.

IV. Body Structure

I. Background & Problem Statement

1. Application domains with strong orientation coupling include:
   • Polymers/Liquid crystals: Q_ij governs optical birefringence and viscoelastic response.
   • Fiber composites: interlayer anchoring and anisotropic acoustic/elastic propagation.
   • Plasma shear: coupling of Q_ij with B_vec alters transport tensors.
   • Astrophysical magnetism: large-scale Q_ij maps to phase speed/polarization observables.
2. Objective: with unified cards and metrics, place heterogeneous data and models into a single auditable workflow for parameter identification, model selection, and engineering prediction.

II. Key Equations & Derivations (S-series)
(No new minimal equations in this chapter; we invoke S80-* from Chapters 4–7 and the couplings of Chapter 6, giving only case-level constraints and mappings.)

• Optical birefringence (weak coupling): Δn(ê) ≈ (α_E/2) ( ê_i Q_ij ê_j ).
• Anisotropic diffusion: D_eff(ê) = D0 + D1 ( ê_i Q_ij ê_j ).
• Mechanical power: 𝒫_mech = T_fil_ij D_{ij}; energy closure per Chapter 7.

III. Methods & Flows (M-series)

1. M80-39 Case Modeling & Cardization
   • Input cards:
     1. GeometryCard.json: domain, mesh, boundaries (incl. interfaces/defects; see Chapter 8).
     2. ModelCard.json: W_orient, Λ_{ijkl}, A,K,tau_relax,D_Q, coupling params {χ_E,χ_B,χ_u,α_E,α_B,κ_s}.
     3. MetrologyCard.json: R_inst, noise, covariances, units.
     4. PipelineCard.json: DAG, thresholds, and exports.
   • Harmonization: audit Unit/Dim and see: anchors; emit CaseBundle.tar.
2. M80-40 Benchmark Suites & Scale Tiers
   • S-tier (minimal): single-physics channel, low-dim grid, analytic/semi-analytic checks.
   • M-tier (medium): two-channel coupling (e.g., EM+mechanics), moderate grids, realistic instrument kernels.
   • L-tier (comprehensive): multi-channel coupling, interfaces/defects, full chain (SimStack-OT → R_inst → synthetic observations).
   • Gates (examples, to be audited in metrics.json):
     1. SpecMAE ≤ 3%, EDX-closure ≤ 1σ;
     2. AnisoMap-PSNR ≥ 30 dB;
     3. Evidence: ΔlogZ ≥ 5 (coupled model over decoupled).
3. M80-41 Acceptance & Evidence
   • Run the PipelineCard to obtain {posterior, evidence, products, metrics}.
   • Compute EDX closure residual r_EDX with confidence bands.
   • Decide pass/fail and produce AcceptanceReport.md.
4. M80-42 Regression & Comparison
   • Fix seed and version hashes; run regression vs previous versions/baselines.
   • Emit DiffReport.md with compatibility status (bc/brk).
   • Update benchmark registry and index.

IV. Scenario Library & Benchmark Tasks (examples)

• Case A | Polymers/Liquid Crystals (Optics + Viscoelasticity): fit α_E, tau_relax from Δn(ê) and small-amplitude G*(ω).
• Case B | Fiber Composites (Acoustic/Elastic + Interfaces): invert κ_s, κ_a/κ_b from c_s(ê) and reflection/transmission coefficients.
• Case C | Plasma Shear (Transport + EM): constrain {D1, α_E, α_B} via D_eff(ê) and ray-traced phase speeds.
• Case D | Astrophysical Magnetic Structures (Polarimetry + Propagation): constrain large-scale Q_ij and couplings from polarization angle/amplitude over direction–frequency maps.

V. Validation, Criteria & Counterexamples

1. Positive criteria:
   • Across cases, “coupled/anisotropic” models achieve ΔlogZ ≥ 5 over simplified controls and pass metric gates.
   • EDX ledger closure improves; r_EDX mean near zero.
   • Strong correlations between ê_i Q_ij ê_j and directional observables.
2. Negative criteria:
   • Removing key terms (χ_*, D1, or Λ_{ijkl}) does not degrade fits/evidence.
   • Unit/Dim audits fail or anisotropy maps disagree with observations.
   • Systematic regression degradation without stabilization/explanation.
3. Contrasts:
   • Evidence/metrics across {isotropic-only, single-channel-only, full model}.
   • Impacts of {no interface/defect, with interface/defect} on propagation/transport.
   • Residual structures for {analytic kernel, realistic instrument kernel}.

VI. Deliverables & Figure List

1. Deliverables:
   • CaseBundle.tar (four cards & inputs).
   • Products/ (Q_ij, T_fil_ij, AnisotropyMaps, PowerTerms, Ledgers, synthetic/observed-aligned artifacts).
   • Posterior.zarr, Evidence.txt, metrics.json.
   • AcceptanceReport.md, DiffReport.md.
2. Figures/Tables (suggested):
   • Tab. 11-1 Scenario–channel–observable–parameter mapping.
   • Tab. 11-2 S/M/L benchmarks and gates.
   • Fig. 11-1 Direction/frequency anisotropy maps vs model.
   • Tab. 11-3 Evidence and EDX-closure statistics.
   • Fig. 11-2 Regression diffs and pass/fail matrix.