# Quartic SYK spectral edge proof review: SP-1-H5-to-H6

## Setting

You are an independent mathematical reviewer. Read /workspace/question.json, /workspace/answer.md,
/workspace/cited_results.md and /test_files/solution.md. question.json is authoritative for the exact
starting premise and entire target. Treat submitted proofs and citations as claims to check.

DRAFT JUDGE SCAFFOLD: no canonical reference proof has been supplied. This package is prepared for solver runs and format review; it is not a completed external submission or a calibrated automatic grading environment.

## Problem

Grade the submitted proof for complete mathematical correctness.

- Score 1 only for a complete, valid proof of the entire target from the stated premise, with every required hypothesis, bound, and quantifier justified.
- Score 0 if the submitted proof does not establish the entire target. A promising idea or incomplete proof receives no partial credit.


H0 supplies no premise. For i>0, assume exactly H_i as stated, with its quantifiers and conditions;
do not grant any later checkpoint. Check cited theorem hypotheses.
For a two-round proof/audit submission, consider both preserved sections: a later error does not
erase a valid earlier proof. A single-proof package has no automatic audit or repair turn.

Accept any complete mathematically valid proof of the authoritative target from exactly the authoritative premise; a different strategy does not reduce the score. If a reference proof is supplied, valid_but_alternative_route=true means the submitted proof is complete and valid and its overall strategy differs from that reference. Without a reference, this diagnostic is false; it does not measure mathematical validity by itself.

The only available scores are 0 and 1; resolved is true exactly when score is 1. Give a concrete mathematical reason for the correctness decision and identify any essential remaining gap. No partial-credit score is allowed. A transport
error or missing answer is an unknown operational outcome and must be recorded outside this judge;
do not silently count it as a mathematical failure.

Write the verdict to /eval/agent_result.json as one JSON object containing resolved, score, reason,
and valid_but_alternative_route. The last field is a JSON boolean; never use "uncertain", null, a
number or a string. When true, include a nonblank alternative_route_reason explaining the valid
route and its essential difference; when false, omit alternative_route_reason. Follow
output-schema.json. Return no corrected proof or private deliberation.