**Overall Verdict:** Strong Accept — The submission is complete, mathematically consistent, independently reproducible, objectively graded, and fully reachable with the declared toolchain.

**Completeness Check:**
- Instruction: Complete — The equation, matrix conventions, units, accepted methods, input schema, output schema, and required residual are clearly specified.
- Inputs: Complete — `scene.json` parses successfully and contains eight exact-schema motion pairs; all matrices are finite 4×4 rigid transforms with valid rotations and homogeneous bottom rows.
- Toolchain: Complete — Python 3.11 and NumPy 1.24+ provide a free, standard, single-machine implementation path without network access or specialized hardware.
- Reference output: Complete — `result.json` contains a valid rigid transform and an accurately reported residual near \(3.8\times10^{-13}\). Independent closed-form reconstruction matched its rotation and translation to numerical precision.
- Rubric: Complete — `grader.py` statically verifies schema, finite values, rigid-transform validity, equation residual, reported-residual consistency, and agreement with the reference using explicit tolerances.

**File and Task Reachability:**
The attachment set is `reachable`, and the end-to-end task is `reachable`. `SPEC.md`, `scene.json`, `result.json`, and `grader.py` were all inspected; their actual formats and byte counts match the manifest, the text is readable UTF-8, both JSON files parse successfully, and there are no containers, encrypted members, or unreviewed contents. The uploaded grader was inspected statically and was not executed, as required; independent safe numerical analysis confirmed full-rank rotational and translational systems, a unique solution, valid reference geometry, and residual consistency. The completion path is direct: read the eight motion pairs, solve for the rigid transform with NumPy, serialize `X` and `max_residual`, and evaluate the output against the supplied numerical checks. Solver-visible inputs and evaluator/reference assets are explicitly separated by manifest category. 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. There is no affirmative evidence of AI-fabricated core evidence, a public benchmark, or a synthetic defect fixture. Public-source identity was not independently searched because external lookup is outside the permitted evidence boundary.

**Recommended Changes:**
The submission already provides coherent instructions, valid data, a verified reference, and a hardened objective evaluator. No changes are required.