**Overall Verdict:** Strong Accept — The submission is complete, coherent, technically rigorous, safely reachable, and objectively evaluable end to end without material risk.

**Completeness Check:**
- Instruction: Complete — The PDE, finite-element space, boundary conditions, quadrature requirement, solver interface, convergence study, artifacts, and output schemas are precisely specified.
- Inputs: Complete — All four solver-visible inputs are readable, mutually consistent, and clearly separated from evaluator-only references.
- Toolchain: Complete — The Bash wrapper, TOML manifest, and lockfile define Python 3.11–3.13 with pinned NumPy and SciPy releases and compatible Linux packages.
- Reference output: Complete — The reference solver, JSON results, and nine-array NPZ artifact are internally consistent and implement the prescribed cubic-Hermite method.
- Rubric: Complete — The grader provides deterministic tiered scoring, schema and provenance validation, independent field comparison, all-mesh regeneration, and causal solve auditing.

**File and Task Reachability:**
The attachment set is `reachable`, and the end-to-end task is `reachable`. I inspected `problem_spec.md`, `python.sh`, `pyproject.toml`, `uv.lock`, `grade.py`, `EVALUATION.md`, `fem_solver.py`, `results.json`, and `reference_arrays.npz`; their downloaded byte counts match the manifest. The text files are readable ASCII or UTF-8 in their expected semantic formats. The NPZ is a 55,305-byte, unencrypted ZIP containing nine path-safe NPY members totaling 83,384 uncompressed bytes. Its arrays have the required `(7,)` and `(2561,)` shapes, numeric dtypes, expected mesh sequence, finite values except the prescribed leading EOC NaNs, exact grid, analytic solution agreement, exact error identity, and artifact/table consistency. The JSON reproduces the array errors, orders, mesh spacings, and metadata exactly. Uploaded programs were inspected statically and were not executed; no attachment was omitted, and no material tooling limitation remains. The completion path is clear: use the pinned CPU-only Python environment, implement and run `solve(n)` for seven meshes, emit the three required outputs, and evaluate them using independent numerical, provenance, dependency, and causal-assembly checks. Reference artifacts are evaluator-only and do not leak a solver-visible answer. License keys, accounts, tokens, and other credentials are not required from the contributor. Confidential, proprietary, or internal material may be evaluated as submitted evidence without requiring additional disclosure.

**Special Screening:**
None. No affirmative evidence supports AI-fabricated core evidence, a deliberately injected defect fixture, or a publicly identifiable protected benchmark answer. External public-identifiability was not independently searched because it falls outside the permitted evidence boundary.

**Recommended Changes:**
The submission already provides a valid specialized numerical-analysis workflow, reproducible reference artifacts, and unusually strong evaluation coverage. No changes are required.