**Overall Verdict:** Accept — The task is complete, objectively verifiable, and end-to-end reachable; only non-material difficulty metadata is inconsistent with the attached evidence.

**Completeness Check:**
- Instruction: Complete — The specification clearly defines all three optimization instances, the exact certificate and witness schema, resource constraints, and required output.
- Inputs: Complete — The polynomial input contains three valid five-variable degree-six instances with 61, 68, and 66 unique terms; the basis contains 56 unique exponent vectors in the required order.
- Toolchain: Complete — The offline Python, NumPy, and SciPy workflow is legally available, compatible with the stated environment, and demonstrated within the stated single-machine resource budget.
- Reference output: Complete — The reference contains all required fields for all three instances. Each matrix is symmetric and positive definite, satisfies all 462 coefficient identities exactly, clears its target, and has an exact witness gap below \(10^{-5}\).
- Rubric: Complete — The evaluator provides deterministic structure, identity, positive-definiteness, tightness, witness, and minimum-over-instances scoring with meaningful full, partial, and failure outcomes.

**File and Task Reachability:**
The attachment set is `reachable`, and the end-to-end task is `reachable`. The inspected files were `polynomials.json`, `basis.json`, `problem_spec.md`, `solution_multi.json`, `solver_report_multi.json`, `evaluate.py`, `solve_all.py`, `reference_solver.py`, `sos_common.py`, and `DIFFICULTY.md`. All manifest files were readable, matched their declared byte counts and broad formats, and contained no archives, encryption barriers, or undisclosed dependencies. All JSON parsed successfully; uploaded source was inspected as text and not executed. No content remains unreviewed, and no tooling limitation affected the assessment. Solver-visible inputs are separated by manifest role from reference and evaluator assets. The completion path is clear: read the polynomial and basis inputs, construct three exact certificates and rational witnesses, write `output/solution.json`, and evaluate it through exact integer and rational checks. 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 a screening label; public-benchmark identifiability could not be externally corroborated within the permitted evidence boundary.

**Recommended Changes:**
The mathematical task, reference certificates, and evaluator are ready. No material changes are required. As non-blocking cleanup, align the submitted “<1%” difficulty estimate and model label with `DIFFICULTY.md`, which explicitly supports a 10–20% tier from three GPT-5-based trials and states that the evidence cannot justify a sub-1% estimate.