Add comprehensive documentation for Numerical Analysis Workflow

- Introduced agent instruction template for task assignments in numerical analysis.
- Defined CSV schema for tasks, including input, computed, and output columns.
- Specified analysis dimensions across six phases of the workflow.
- Established phase topology for the diamond deep tree structure of the workflow.
- Outlined quality standards for assessing analysis reports, including criteria and quality gates.

.codex/skill_lib/numerical-analysis-workflow/specs/quality-standards.md

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+# Quality Standards for Numerical Analysis Workflow
+
+Quality assessment criteria for NADW analysis reports.
+
+## When to Use
+
+| Phase | Usage | Section |
+|-------|-------|---------|
+| Phase 2 (Execution) | Guide agent analysis quality | All dimensions |
+| Phase 3 (Aggregation) | Score generated reports | Quality Gates |
+
+---
+
+## Quality Dimensions
+
+### 1. Mathematical Rigor (30%)
+
+| Score | Criteria |
+|-------|----------|
+| 100% | All formulas correct, properly derived, LaTeX well-formatted, error bounds proven |
+| 80% | Formulas correct, some derivation steps skipped, bounds stated without full proof |
+| 60% | Key formulas present, some notation inconsistencies, bounds estimated |
+| 40% | Formulas incomplete or contain errors |
+| 0% | No mathematical content |
+
+**Checklist**:
+- [ ] Governing equations identified and written in LaTeX
+- [ ] Weak forms correctly derived from strong forms
+- [ ] Convergence order stated with conditions
+- [ ] Error bounds provided (a priori or a posteriori)
+- [ ] CFL/stability conditions explicitly stated
+- [ ] Condition numbers estimated for key matrices
+- [ ] Complexity bounds (time and space) determined
+- [ ] LaTeX notation consistent throughout all documents
+
+### 2. Code-Theory Mapping (25%)
+
+| Score | Criteria |
+|-------|----------|
+| 100% | Every algorithm mapped to code with file:line references, data structures justified |
+| 80% | Major algorithms mapped, most references accurate |
+| 60% | Key mappings present, some code references missing |
+| 40% | Superficial mapping, few code references |
+| 0% | No code-theory connection |
+
+**Checklist**:
+- [ ] Each numerical method traced to implementing function/module
+- [ ] Data structures justified against algorithm requirements
+- [ ] Sparse matrix format matched to access patterns
+- [ ] Time integration scheme identified in code
+- [ ] Boundary condition implementation verified
+- [ ] Solver configuration traced to convergence requirements
+- [ ] Preconditioner choice justified
+
+### 3. Numerical Quality Assessment (25%)
+
+| Score | Criteria |
+|-------|----------|
+| 100% | Stability fully analyzed, precision risks cataloged, all edge cases covered |
+| 80% | Stability assessed, major precision risks found, common edge cases covered |
+| 60% | Basic stability check, some precision risks, incomplete edge cases |
+| 40% | Superficial stability mention, few precision issues found |
+| 0% | No numerical quality analysis |
+
+**Checklist**:
+- [ ] Condition numbers estimated for key operations
+- [ ] Catastrophic cancellation risks identified with file:line
+- [ ] Accumulation error potential assessed
+- [ ] Float precision choices justified (float32 vs float64)
+- [ ] Edge cases cataloged (singularities, degenerate inputs)
+- [ ] Overflow/underflow risks identified
+- [ ] Mixed-precision operations flagged
+
+### 4. Cross-Phase Coherence (20%)
+
+| Score | Criteria |
+|-------|----------|
+| 100% | All 6 phases connected, findings build on each other, no contradictions |
+| 80% | Most phases connected, minor gaps in context propagation |
+| 60% | Key connections present, some phases isolated |
+| 40% | Limited cross-referencing between phases |
+| 0% | Phases completely isolated |
+
+**Checklist**:
+- [ ] Wave 2 formulas reference Wave 1 governing equations
+- [ ] Wave 3 algorithms justified by Wave 2 theory
+- [ ] Wave 4 implementation verified against Wave 3 pseudocode
+- [ ] Wave 5 optimization targets from Wave 3 performance model
+- [ ] Wave 5 precision requirements from Wave 2/3 analysis
+- [ ] Wave 6 test plan covers findings from all prior waves
+- [ ] Wave 6 benchmarks compare against Wave 3 predictions
+- [ ] No contradictory findings between phases
+- [ ] Discoveries board used for cross-track sharing
+
+---
+
+## Quality Gates (Per-Wave)
+
+| Wave | Phase | Gate Criteria | Required Tracks |
+|------|-------|--------------|-----------------|
+| 1 | Global Survey | Core model identified + architecture mapped + ≥1 KPI | 3/3 completed |
+| 2 | Theory | Key formulas LaTeX'd + convergence stated + complexity determined | 3/3 completed |
+| 3 | Algorithm | Pseudocode produced + stability assessed + performance predicted | ≥2/3 completed |
+| 4 | Module | Code-algorithm mapping + data structures reviewed + APIs documented | ≥2/3 completed |
+| 5 | Local | Hotspots identified + edge cases cataloged + precision risks flagged | ≥2/3 completed |
+| 6 | Integration | Test plan complete + benchmarks planned + QA report synthesized | 3/3 completed |
+
+---
+
+## Overall Quality Gates
+
+| Gate | Threshold | Action |
+|------|-----------|--------|
+| PASS | >= 80% across all dimensions | Report ready for delivery |
+| REVIEW | 70-79% in any dimension | Flag dimension for improvement, user decides |
+| FAIL | < 70% in any dimension | Block delivery, identify gaps, suggest re-analysis |
+
+---
+
+## Issue Classification
+
+### Errors (Must Fix)
+
+- Missing governing equation identification (Wave 1)
+- LaTeX formulas with mathematical errors (Wave 2)
+- Algorithm pseudocode that doesn't match convergence requirements (Wave 3)
+- Code references to non-existent files/functions (Wave 4)
+- Unidentified catastrophic cancellation in critical path (Wave 5)
+- Test plan that doesn't cover identified stability issues (Wave 6)
+- Contradictory findings between phases
+- Missing context propagation (later phase ignores earlier findings)
+
+### Warnings (Should Fix)
+
+- Formulas without derivation steps
+- Convergence bounds stated without proof or reference
+- Missing edge case for known singularity
+- Performance model without memory bandwidth consideration
+- Data structure choice not justified
+- Test plan without manufactured solution verification
+- Benchmark without theoretical baseline comparison
+
+### Notes (Nice to Have)
+
+- Additional bibliography references
+- Alternative algorithm comparisons
+- Extended precision sensitivity analysis
+- Scaling prediction beyond current problem size
+- Code style or naming convention suggestions
+
+---
+
+## Severity Levels for Findings
+
+| Severity | Definition | Example |
+|----------|-----------|---------|
+| **Critical** | Incorrect results or numerical failure | Wrong boundary condition → divergent solution |
+| **High** | Significant accuracy or performance degradation | Condition number 10^15 → double precision insufficient |
+| **Medium** | Suboptimal but functional | O(N^2) where O(N log N) is possible |
+| **Low** | Minor improvement opportunity | Unnecessary array copy in non-critical path |
+
+---
+
+## Document Quality Metrics
+
+| Metric | Target | Measurement |
+|--------|--------|-------------|
+| Formula coverage | ≥ 90% of core equations in LaTeX | Count identified vs documented |
+| Code reference density | ≥ 1 file:line per finding | Count references per finding |
+| Cross-phase references | ≥ 3 per document (Waves 3-6) | Count cross-references |
+| Severity distribution | ≥ 1 per severity level | Count per level |
+| Discovery board contributions | ≥ 2 per track | Count NDJSON entries per worker |
+| Perspective package | Present in every document | Boolean per document |