Decompose architecture into 28 atomic implementation tasks

Break the @alkdev/taskgraph architecture specs into dependency-ordered
implementation tasks across 8 component directories: setup, schema,
error, graph, analysis, cost-benefit, frontmatter, api, and review.
Each task has clear acceptance criteria referencing specific architecture
docs. Three review tasks serve as quality gates at critical junction
points (schemas-and-errors, graph-complete, complete-library). The
dependency graph is validated acyclic with 9 topological levels enabling
significant parallelism across independent work streams.
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---
id: graph/subgraph-and-validation
name: Implement TaskGraph subgraph and validation methods
status: pending
depends_on:
- graph/taskgraph-class
- graph/queries
- schema/input-schemas
- schema/graph-schemas
scope: narrow
risk: low
impact: component
level: implementation
---
## Description
Implement the `subgraph()` method and the three validation methods (`validateSchema`, `validateGraph`, `validate`) on `TaskGraph`.
Per [ADR-007](../../../docs/architecture/decisions/007-subgraph-internal-only.md), `subgraph` returns only edges where both endpoints are in the filtered set.
Per [errors-validation.md](../../../docs/architecture/errors-validation.md), validation methods collect issues and return arrays — never throw.
## Acceptance Criteria
- [ ] `subgraph(filter: (taskId: string, attrs: TaskGraphNodeAttributes) => boolean): TaskGraph`:
- Uses `graphology-operators.subgraph` to extract matching nodes
- Returns only edges where both endpoints are in the filtered set (internal-only) per ADR-007
- Returns a new `TaskGraph` instance (not mutating the original)
- [ ] `validateSchema(): ValidationError[]`:
- Uses TypeBox `Value.Check()` and `Value.Errors()` on each node's attributes
- Returns structured `ValidationError[]` with `type: "schema"`, `taskId`, `field`, `message`, `value`
- [ ] `validateGraph(): GraphValidationError[]`:
- Runs `findCycles()` and checks for dangling dependency references
- Returns structured `GraphValidationError[]` with `type: "graph"`, `category`, `message`, optional `details`
- Cycle category: `"cycle"` with cycle paths in `details`
- Dangling reference category: `"dangling-reference"` with the referencing task ID
- [ ] `validate(): ValidationError[]` — runs both `validateSchema()` and `validateGraph()`, returns combined array
- [ ] `ValidationError` and `GraphValidationError` interfaces defined (may be in error module or co-located)
- [ ] Unit tests: subgraph filtering, subgraph excludes external edges, validateSchema catches invalid enums, validateGraph catches cycles and dangling refs
## References
- docs/architecture/api-surface.md — validation API, subgraph
- docs/architecture/errors-validation.md — validation levels, return types
- docs/architecture/decisions/007-subgraph-internal-only.md — subgraph semantics
## Notes
> To be filled by implementation agent
## Summary
> To be filled on completion