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Claude-Code-Workflow/.codex/skills/numerical-analysis-workflow/schemas/tasks-schema.md
catlog22 f389e3e6dd feat: add dynamic pipeline detection for team sessions v5 architecture 
Backend:
- Fix readLegacyFiles to handle { name, prefix }[] role format
- Add roles backfill in getEffectiveTeamMeta when meta.json exists
- Ensure pipeline_stages and roles flow correctly to API response

Team Skills:
- Add pipeline metadata initialization to all 16 team skill coordinator roles
- Each skill now reports pipeline_stages and roles to meta.json at session init

Documentation:
- Update command references and component documentation
- Add numerical-analysis-workflow skill spec
- Sync zh/en translations for commands and components
2026-03-04 14:52:07 +08:00

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Numerical Analysis Workflow — CSV Schema

Master CSV: tasks.csv

Column Definitions

Input Columns (Set by Decomposer)

Column Type Required Description Example
id string Yes Unique task identifier (T{wave}.{track}) "T2.1"
title string Yes Short task title "Mathematical Formulation"
description string Yes Detailed task description (self-contained) "Derive precise mathematical formulations..."
track_role string Yes Analysis role name "Mathematician"
analysis_dimension string Yes Analysis focus area "formula_derivation"
formula_refs string No References to formulas from earlier tasks (TaskID:formula_name;...) "T1.1:governing_eqs;T2.2:convergence_conds"
precision_req string No Required floating-point precision "double"
scope string No File/directory scope for analysis (glob) "src/solver/**"
deps string No Semicolon-separated dependency task IDs "T2.1;T2.2"
context_from string No Semicolon-separated task IDs for context "T1.1;T2.1"

Computed Columns (Set by Wave Engine)

Column Type Description Example
wave integer Wave number (1-6, fixed per diamond topology) 3
prev_context string Aggregated findings + formulas from context_from tasks (per-wave CSV only) "[T2.1] Weak form derived..."

Output Columns (Set by Agent)

Column Type Description Example
status enum pending → completed / failed / skipped "completed"
findings string Key discoveries (max 500 chars) "Identified CFL condition..."
severity_distribution string Issue counts by severity "Critical:0 High:2 Medium:3 Low:1"
latex_formulas string Key LaTeX formulas (semicolon-separated) "\\Delta t \\leq \\frac{h}{c};\\kappa(A) = \|A\|\|A^{-1}\|"
doc_path string Path to generated analysis document "docs/P3_Numerical_Stability_Report.md"
error string Error message if failed ""

Example Data

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
"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",""
"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",""
"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","","","","",""

Column Lifecycle

Decomposer (Phase 1)     Wave Engine (Phase 2)    Agent (Execution)
─────────────────────    ────────────────────     ─────────────────
id          ───────────►  id          ──────────►  id
title       ───────────►  title       ──────────►  (reads)
description ───────────►  description ──────────►  (reads)
track_role  ───────────►  track_role  ──────────►  (reads)
analysis_dimension ─────► analysis_dimension ────►  (reads)
formula_refs ──────────►  formula_refs ─────────►  (reads)
precision_req ─────────►  precision_req ─────────► (reads)
scope       ───────────►  scope       ──────────►  (reads)
deps        ───────────►  deps        ──────────►  (reads)
context_from───────────►  context_from──────────►  (reads)
                          wave         ──────────►  (reads)
                          prev_context ──────────►  (reads)
                                                    status
                                                    findings
                                                    severity_distribution
                                                    latex_formulas
                                                    doc_path
                                                    error

Output Schema (JSON)

Agent output via report_agent_job_result:

{
  "type": "object",
  "properties": {
    "id": { "type": "string", "description": "Task ID (T{wave}.{track})" },
    "status": { "type": "string", "enum": ["completed", "failed"] },
    "findings": { "type": "string", "description": "Key discoveries, max 500 chars" },
    "severity_distribution": { "type": "string", "description": "Critical:N High:N Medium:N Low:N" },
    "latex_formulas": { "type": "string", "description": "Key formulas in LaTeX, semicolon-separated" },
    "doc_path": { "type": "string", "description": "Path to generated analysis document" },
    "error": { "type": "string", "description": "Error message if failed" }
  },
  "required": ["id", "status", "findings"]
}

Discovery Types

Type Dedup Key Data Schema Description
governing_equation eq_name {eq_name, latex, domain, boundary_conditions} Governing equations found
numerical_method method_name {method_name, type, order, stability_class} Numerical methods identified
stability_issue location {location, condition_number, severity, description} Stability concerns
convergence_property method {method, rate, order, conditions} Convergence properties
precision_risk location+operation {location, operation, risk_type, recommendation} Float precision risks
performance_bottleneck location {location, operation_count, memory_pattern, suggestion} Performance bottlenecks
architecture_pattern pattern_name {pattern_name, files, description} Architecture patterns
test_gap component {component, missing_coverage, priority} Missing test coverage

Discovery NDJSON Format

{"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"}}
{"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"}}
{"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"}}
{"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"}}

Validation Rules

Rule Check Error
Unique IDs No duplicate id values "Duplicate task ID: {id}"
Valid deps All dep IDs exist in tasks "Unknown dependency: {dep_id}"
No self-deps Task cannot depend on itself "Self-dependency: {id}"
No circular deps Topological sort completes "Circular dependency detected involving: {ids}"
context_from valid All context IDs exist and in earlier waves "Invalid context_from: {id}"
Description non-empty Every task has description "Empty description for task: {id}"
Status enum status in {pending, completed, failed, skipped} "Invalid status: {status}"
Wave range wave in {1..6} "Invalid wave number: {wave}"
Track role valid track_role matches known roles "Unknown track_role: {role}"
Formula refs format TaskID:formula_name pattern "Malformed formula_refs: {value}"

Analysis Dimension Values

Dimension Used In Wave Description
domain_modeling 1 Physical/mathematical domain survey
architecture_analysis 1 Software architecture analysis
validation_design 1 Validation and benchmark strategy
formula_derivation 2 Mathematical formulation and derivation
convergence_analysis 2 Convergence theory and error bounds
complexity_analysis 2 Computational complexity analysis
method_selection 3 Numerical method selection and design
stability_analysis 3 Numerical stability assessment
performance_modeling 3 Performance prediction and modeling
implementation_analysis 4 Module-level code analysis
data_structure_review 4 Data structure and memory layout review
interface_analysis 4 API contract and interface analysis
optimization 5 Function-level performance optimization
edge_case_analysis 5 Boundary and singularity handling
precision_audit 5 Floating-point precision audit
integration_testing 6 System integration testing
benchmarking 6 Performance benchmarking
quality_assurance 6 Final quality audit and synthesis
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