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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.
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# Numerical Analysis Workflow — CSV Schema
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## Master CSV: tasks.csv
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### Column Definitions
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#### Input Columns (Set by Decomposer)
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| Column | Type | Required | Description | Example |
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|--------|------|----------|-------------|---------|
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| `id` | string | Yes | Unique task identifier (T{wave}.{track}) | `"T2.1"` |
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| `title` | string | Yes | Short task title | `"Mathematical Formulation"` |
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| `description` | string | Yes | Detailed task description (self-contained) | `"Derive precise mathematical formulations..."` |
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| `track_role` | string | Yes | Analysis role name | `"Mathematician"` |
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| `analysis_dimension` | string | Yes | Analysis focus area | `"formula_derivation"` |
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| `formula_refs` | string | No | References to formulas from earlier tasks (TaskID:formula_name;...) | `"T1.1:governing_eqs;T2.2:convergence_conds"` |
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| `precision_req` | string | No | Required floating-point precision | `"double"` |
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| `scope` | string | No | File/directory scope for analysis (glob) | `"src/solver/**"` |
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| `deps` | string | No | Semicolon-separated dependency task IDs | `"T2.1;T2.2"` |
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| `context_from` | string | No | Semicolon-separated task IDs for context | `"T1.1;T2.1"` |
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#### Computed Columns (Set by Wave Engine)
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| Column | Type | Description | Example |
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|--------|------|-------------|---------|
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| `wave` | integer | Wave number (1-6, fixed per diamond topology) | `3` |
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| `prev_context` | string | Aggregated findings + formulas from context_from tasks (per-wave CSV only) | `"[T2.1] Weak form derived..."` |
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#### Output Columns (Set by Agent)
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| Column | Type | Description | Example |
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|--------|------|-------------|---------|
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| `status` | enum | `pending` → `completed` / `failed` / `skipped` | `"completed"` |
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| `findings` | string | Key discoveries (max 500 chars) | `"Identified CFL condition..."` |
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| `severity_distribution` | string | Issue counts by severity | `"Critical:0 High:2 Medium:3 Low:1"` |
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| `latex_formulas` | string | Key LaTeX formulas (semicolon-separated) | `"\\Delta t \\leq \\frac{h}{c};\\kappa(A) = \\|A\\|\\|A^{-1}\\|"` |
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| `doc_path` | string | Path to generated analysis document | `"docs/P3_Numerical_Stability_Report.md"` |
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| `error` | string | Error message if failed | `""` |
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---
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### Example Data
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```csv
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id,title,description,track_role,analysis_dimension,formula_refs,precision_req,scope,deps,context_from,wave,status,findings,severity_distribution,latex_formulas,doc_path,error
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"T1.1","Problem Domain Survey","Survey governing equations and mathematical models. Identify PDE types, boundary conditions, conservation laws, and physical domain.","Problem_Domain_Analyst","domain_modeling","","","src/**","","","1","completed","Identified Navier-Stokes equations with k-epsilon turbulence model. Incompressible flow assumption. No-slip boundary conditions.","Critical:0 High:0 Medium:1 Low:2","\\rho(\\frac{\\partial v}{\\partial t} + v \\cdot \\nabla v) = -\\nabla p + \\mu \\nabla^2 v","docs/P1_Domain_Survey.md",""
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"T2.1","Mathematical Formulation","Derive precise mathematical formulations using LaTeX. Transform governing equations into weak forms suitable for FEM discretization.","Mathematician","formula_derivation","T1.1:governing_eqs","","src/**","T1.1","T1.1","2","completed","Weak form derived for NS equations. Galerkin formulation with inf-sup stable elements (Taylor-Hood P2/P1).","Critical:0 High:0 Medium:0 Low:1","\\int_\\Omega \\mu \\nabla u : \\nabla v \\, d\\Omega - \\int_\\Omega p \\nabla \\cdot v \\, d\\Omega = \\int_\\Omega f \\cdot v \\, d\\Omega","docs/P2_Mathematical_Formulation.md",""
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"T3.2","Numerical Stability Report","Analyze numerical stability of selected algorithms. Evaluate condition numbers, error propagation characteristics, and precision requirements.","Stability_Analyst","stability_analysis","T2.1:weak_forms;T2.2:convergence_conds","double","src/solver/**","T2.1;T2.2","T2.1;T2.2","3","pending","","","","",""
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```
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---
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### Column Lifecycle
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```
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Decomposer (Phase 1) Wave Engine (Phase 2) Agent (Execution)
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───────────────────── ──────────────────── ─────────────────
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id ───────────► id ──────────► id
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title ───────────► title ──────────► (reads)
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description ───────────► description ──────────► (reads)
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track_role ───────────► track_role ──────────► (reads)
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analysis_dimension ─────► analysis_dimension ────► (reads)
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formula_refs ──────────► formula_refs ─────────► (reads)
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precision_req ─────────► precision_req ─────────► (reads)
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scope ───────────► scope ──────────► (reads)
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deps ───────────► deps ──────────► (reads)
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context_from───────────► context_from──────────► (reads)
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wave ──────────► (reads)
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prev_context ──────────► (reads)
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status
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findings
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severity_distribution
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latex_formulas
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doc_path
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error
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```
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---
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## Output Schema (JSON)
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Agent output via `report_agent_job_result`:
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```json
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{
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"type": "object",
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"properties": {
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"id": { "type": "string", "description": "Task ID (T{wave}.{track})" },
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"status": { "type": "string", "enum": ["completed", "failed"] },
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"findings": { "type": "string", "description": "Key discoveries, max 500 chars" },
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"severity_distribution": { "type": "string", "description": "Critical:N High:N Medium:N Low:N" },
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"latex_formulas": { "type": "string", "description": "Key formulas in LaTeX, semicolon-separated" },
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"doc_path": { "type": "string", "description": "Path to generated analysis document" },
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"error": { "type": "string", "description": "Error message if failed" }
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},
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"required": ["id", "status", "findings"]
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}
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```
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---
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## Discovery Types
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| Type | Dedup Key | Data Schema | Description |
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|------|-----------|-------------|-------------|
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| `governing_equation` | `eq_name` | `{eq_name, latex, domain, boundary_conditions}` | Governing equations found |
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| `numerical_method` | `method_name` | `{method_name, type, order, stability_class}` | Numerical methods identified |
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| `stability_issue` | `location` | `{location, condition_number, severity, description}` | Stability concerns |
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| `convergence_property` | `method` | `{method, rate, order, conditions}` | Convergence properties |
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| `precision_risk` | `location+operation` | `{location, operation, risk_type, recommendation}` | Float precision risks |
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| `performance_bottleneck` | `location` | `{location, operation_count, memory_pattern, suggestion}` | Performance bottlenecks |
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| `architecture_pattern` | `pattern_name` | `{pattern_name, files, description}` | Architecture patterns |
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| `test_gap` | `component` | `{component, missing_coverage, priority}` | Missing test coverage |
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### Discovery NDJSON Format
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```jsonl
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{"ts":"2026-03-04T10:00:00Z","worker":"T1.1","type":"governing_equation","data":{"eq_name":"Navier-Stokes","latex":"\\rho(\\frac{\\partial v}{\\partial t} + v \\cdot \\nabla v) = -\\nabla p + \\mu \\nabla^2 v","domain":"fluid_dynamics","boundary_conditions":"no-slip walls"}}
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{"ts":"2026-03-04T10:05:00Z","worker":"T2.2","type":"convergence_property","data":{"method":"Galerkin FEM","rate":"optimal","order":"h^{k+1}","conditions":"quasi-uniform mesh"}}
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{"ts":"2026-03-04T10:10:00Z","worker":"T3.2","type":"stability_issue","data":{"location":"src/solver/assembler.rs:142","condition_number":"1e12","severity":"High","description":"Ill-conditioned stiffness matrix"}}
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{"ts":"2026-03-04T10:15:00Z","worker":"T5.3","type":"precision_risk","data":{"location":"src/solver/residual.rs:87","operation":"subtraction of nearly equal values","risk_type":"catastrophic_cancellation","recommendation":"Use compensated summation or reformulate"}}
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```
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---
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## Validation Rules
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| Rule | Check | Error |
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|------|-------|-------|
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| Unique IDs | No duplicate `id` values | "Duplicate task ID: {id}" |
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| Valid deps | All dep IDs exist in tasks | "Unknown dependency: {dep_id}" |
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| No self-deps | Task cannot depend on itself | "Self-dependency: {id}" |
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| No circular deps | Topological sort completes | "Circular dependency detected involving: {ids}" |
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| context_from valid | All context IDs exist and in earlier waves | "Invalid context_from: {id}" |
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| Description non-empty | Every task has description | "Empty description for task: {id}" |
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| Status enum | status in {pending, completed, failed, skipped} | "Invalid status: {status}" |
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| Wave range | wave in {1..6} | "Invalid wave number: {wave}" |
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| Track role valid | track_role matches known roles | "Unknown track_role: {role}" |
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| Formula refs format | TaskID:formula_name pattern | "Malformed formula_refs: {value}" |
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### Analysis Dimension Values
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| Dimension | Used In Wave | Description |
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|-----------|-------------|-------------|
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| `domain_modeling` | 1 | Physical/mathematical domain survey |
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| `architecture_analysis` | 1 | Software architecture analysis |
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| `validation_design` | 1 | Validation and benchmark strategy |
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| `formula_derivation` | 2 | Mathematical formulation and derivation |
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| `convergence_analysis` | 2 | Convergence theory and error bounds |
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| `complexity_analysis` | 2 | Computational complexity analysis |
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| `method_selection` | 3 | Numerical method selection and design |
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| `stability_analysis` | 3 | Numerical stability assessment |
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| `performance_modeling` | 3 | Performance prediction and modeling |
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| `implementation_analysis` | 4 | Module-level code analysis |
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| `data_structure_review` | 4 | Data structure and memory layout review |
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| `interface_analysis` | 4 | API contract and interface analysis |
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| `optimization` | 5 | Function-level performance optimization |
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| `edge_case_analysis` | 5 | Boundary and singularity handling |
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| `precision_audit` | 5 | Floating-point precision audit |
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| `integration_testing` | 6 | System integration testing |
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| `benchmarking` | 6 | Performance benchmarking |
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| `quality_assurance` | 6 | Final quality audit and synthesis |
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