feat(evals): add near-field template experiment

docs/exec-plans/completed/20260612-boxcode-nearfield-template-experiment.md

@@ -0,0 +1,71 @@
+# Box-Code Near-Field Template Experiment
+
+## Objective
+
+Evaluate whether folded-decomposition charts can support reusable near-field
+template corrections for box-code and Volumential-style workflows.
+
+## Scope
+
+- Derive the mapped-kernel form for a 2D fan folded piece.
+- Focus the near-field form on point targets in physical space.
+- Identify singular factors that can be separated from smooth geometry payloads.
+- Frame the reuse hypothesis as a functional expansion in smooth metric fields
+  `M(z)`, not just as raw runtime geometry data.
+- Add a small analytic experiment driver with deterministic tests.
+- Document feasibility limits and the next CUTKIT/Volumential boundary.
+
+## Non-Goals
+
+- No production Volumential integration in this branch.
+- No CAD dependency for the first prototype.
+- No claim that arbitrary cut shapes have finite exact correction tables.
+
+## Acceptance Criteria
+
+- The derivation states the mapped self-interaction form and its split.
+- The derivation records the point-target form, target/source geometry taxonomy,
+  and measurement criteria from issue 61.
+- The prototype records a point-target template experiment with a direct
+  high-order reference value.
+- Tests check the experiment against an analytic or independently computed
+  invariant.
+- Documentation explains whether the idea is feasible and what data must remain
+  runtime geometry payload.
+
+## Completed Checklist
+
+- [x] Read issue 61 and repository orientation docs.
+- [x] Work through the 2D fan-map singularity derivation.
+- [x] Add an experiment module or script for the near-field template prototype.
+- [x] Add tests for the prototype invariants.
+- [x] Update docs and doc index if new documentation is added.
+- [x] Run targeted tests and `make dev`.
+- [x] Move this plan to completed with outcomes.
+
+## Outcomes
+
+- The near-field template idea is feasible as a CUTKIT experiment: singular and
+  nearly singular folded-piece interactions can be expressed on fixed template
+  domains.
+- The reusable singular part is a template-space log singular model. The metric
+  field `M(z) = DT(z)^T DT(z)` and higher-order terms are smooth geometry data.
+- The practical reuse hypothesis is that a functional expansion in `M(z)` and
+  smooth-remainder data covers the folded-decomposition cases with few modes.
+- The first prototype covers analytic straight fan maps, point-target
+  integrals, a log-kernel scale-law check, and a diagonal metric-remainder
+  sample.
+
+## Validation
+
+- `uv run --extra dev python -m pytest tests/evals/test_nearfield_templates.py tests/test_script_wrappers.py`
+- `uv run --extra dev python scripts/run_nearfield_template_experiment.py --order 6`
+- `make dev`
+
+## Remaining Risks
+
+- Template corrections may be reusable only after parameterized compression, not
+  as shape-independent lookup tables.
+- Self-interaction singular quadrature may need specialized rules beyond the
+  first direct high-order reference prototype.
+- Curved analytic pieces and adjacent-piece cases still need follow-up coverage.

docs/index.md

@@ -23,6 +23,7 @@ Repository-local documentation is the system of record for CUTKIT.
 - `docs/cad-box-batch-interface.md`: consumer-facing CAD object-or-arrays clip/integrate interface
 - `docs/volumential-handoff.md`: CUTKIT far/near primitive handoff contract for volumential workflows
 - `docs/meshmode-cut-overlay.md`: meshmode cut-overlay contract and validation semantics
+- `docs/nearfield-template-experiments.md`: folded fan near-field template derivation and prototype
 - `docs/poisson-benchmarks.md`: Poisson-oriented benchmark usage and profiles
 - `docs/poisson-galerkin-solver.md`: immersed Poisson Galerkin solve + validation workflow
 - `docs/formdsl-parity-benchmarks.md`: shared IGA + DG-SEM formdsl parity benchmark usage