Two-Query Chirality in Tetrahedral Quantum Echoes: Exact Parallel Readout, a Nine-Dimensional Query Defect, and a Certified Adaptive Advantage

Strengths

• Theorem 6.1 uses only purification and bilinearity in two uses of the unknown qubit unitary to place every causal output in a fixed linear image of a 1+3+5 dimensional feature space, yielding the clean 9/24 cap.
• Equations (12)-(16) provide a constructive deterministic comb, exact spectrum and partial trace, positive orbit weights, and an exact scalable-frame identity; the quotient-field program rechecked all 24 states and the full KCK=K relation.
• Theorem 5.1 optimizes arbitrary parallel inputs including retained references by a symmetry-complete singlet/triplet marginal, and the q=1/2 solution shows explicitly why two Bell pairs are suboptimal.
• Corollary 7.3 turns the point separation into an open pulse interval using a uniform derivative bound, and the manuscript clearly distinguishes ordinary causal memory from indefinite causal order.

Weaknesses

• Theorem 4.2 says the covariant seed operators satisfy primal completeness, but the appendix supplies only the block table and scalar reduction rather than explicit seed matrices for general pulse z; a reader must reconstruct the representation-theoretic SDP details.
• The collision-completeness appendix invokes Sturm isolation and exact filtering, whereas the supplied word audit uses nroots and numerical tolerance for the final physical roots and class grouping. This leaves the exact table less reproducible than the central causal certificate.
• The public layout does not match README_SUPPLIED.md: the scripts are in src/replay rather than verification, and the claimed manuscript source, bibliography, claim ledger, submission sheet, and compiled source PDF are not included at the paths required by package_release.py.
• The literature check confirms that sequential advantage outside group ensembles was already known; the paper's priority claim therefore depends on its architecture-specific exact synthesis, for which no exhaustive search was performed.

Potential errors

• The all-pulse Bell-square optimum depends on reducing the compound geometrically uniform discrimination SDP to one orbit weight and blockwise scalar domination. The displayed argument is plausible, but I did not independently reconstruct every attaining primal operator beyond the q=1/2 numerical fixture.
• The collision table's exact completeness cannot be inferred from the executed tolerance-based classifier alone. A missed near-multiple eliminant root would affect the generic-distinctness claim, although the adaptive optimum at the isolated q=1/2 point is separately certified.
• The README's replay commands and package helper cannot be followed literally on the supplied tree. This is a release-integrity error, not a mathematical counterexample to Theorem 7.2.

Strong novelty candidates

• The exact global parallel formula for all pulses after optimization over arbitrary ancillary inputs, including the non-Bell optimum at q=1/2.
• The fixed-trace nine-dimensional causal query defect and its exact saturation by a rational deterministic comb with positive chiral orbit weights.
• The closed-form strict adaptive-versus-parallel separation for a concrete non-group unitary ensemble, extended to an explicit open pulse interval.

Unresolved material objections

None reported.

Strengths

• Proposition 2.1 and equations (1)-(4), pp. 3-4: direct Pauli multiplication confirms the common half trace, both E formulas and v1*v2*v3=0 for all 24 symbolic words.
• Theorems 4.2 and 5.1, pp. 4-5: optimizing a weighted orbit-average square root yields the scalar clamp; singlet/triplet symmetry exhausts parallel marginals, including retained references.
• Theorem 6.1, p. 6: a fixed linear image of quadratic oracle coordinates cannot increase span. Fixed scalar and vector norm impose one homogeneous relation; the d/24 pure-state bound is valid and need not be attainable generally.
• Lemma 7.1 and Theorem 7.2, pp. 6-7: the executed rational-arithmetic verifier checks normalization, Hermiticity, A4 covariance, representative rows of KCK=K, and exact positive weight intervals. Covariance covers all 576 entries.
• Appendix C, p. 11: the six Kraus operators satisfy completeness and reproduce 2*Xi in the actual execution, providing a constructive channel rather than merely an abstract feasibility assertion.
• Corollary 7.3, p. 8: the eight-generator norm bound and two-query hybrid derivative bound give a valid conservative Lipschitz radius for a fixed tester against the optimized parallel value.
• Section 8 and Appendix D: an independent exact polynomial-GCD check of all 276 pairs reproduces the three finite nonnegative-t collision factors and class sizes; t=1 gives three projective classes of size eight.

Weaknesses

• Appendix A, p. 10, promises an explicit attaining primal but supplies strong-duality prose instead. Display the weighted square-root measurement and the orbit KKT conditions, including zero-weight and rank-deficient limits.
• The equivalent copies 3V and 3E cannot be discarded from the dual merely because the unweighted average is block diagonal. The required fact is that every orbit-weighted twirl has zero off-diagonal intertwiner; the seed orthogonality proves this but the optimization argument should say so.
• Appendix B, p. 10: relative to Bell-square, nonscalar squared norms scale by 4(1-a)/3, since Bell-square has a=1/4. The stated factor 1-a suppresses this normalization; the displayed K and final formulas do include the necessary factor.
• Section 9 and Appendix D distinguish exact algebra from floating-point diagnostics appropriately, but the machine word audit uses numerical root filtering, not a stored exact Sturm certificate. The independent GCD audit supplies separate corroboration.
• README_SUPPLIED.md and package_release.py reference absent paper/, verification/, release metadata and compiled-PDF paths. The actual release build fails immediately. Scientific scripts at their supplied paths remain runnable.
• No noise model, laboratory resource analysis, or unrestricted causal optimum away from q=1/2 is supplied. The paper correctly excludes these extensions.
• Source comparison is bounded: selected primary references were inspected, not the entire bibliography or worldwide priority. Incidental ratings metadata returned by a prerequisite search is disclosed in the verification record and was excluded as evidence.

Potential errors

• Proposition 4.1, p. 4: "It is never a tight frame on that support" is false at z=0. All Bell-square outputs coincide, so their average has spectrum {1} on a one-dimensional support and is tight. The discriminant argument assumes the V block is occupied. Restrict the assertion to generic rank-nine support.
• Section 4 writes v dot Q(v)=3*v1*v2*v3, whereas Appendix A defines Q with sqrt(2), giving 3*sqrt(2)*v1*v2*v3. The common zero makes this a normalization typo without effect on decoupling.

Strong novelty candidates

• The exact two-orbit chiral-energy clamp combined with optimization over the singlet weight, Theorems 4.2 and 5.1.
• The rational causal normalization and positive scalable-frame weights attaining 9/24 at q=1/2, with an explicit six-Kraus realization and a certified open interval.

Unresolved material objections

None reported.