PUBLIC REVIEW SUMMARY
Terminal response and worst-case bounded-run switching near a parabolic critical branch
Review date: 7 November 2026. Website packaging: 8 November 2026.

This is a summary, not a reproduction of private review working records.
Two independent AI reviews assessed the complete supplied manuscript source,
including a mathematical review and a hostile review. A separate scoped
editorial and literature review assessed positioning, claims, and antecedents.
The reviews are not human peer review, formal verification, external
endorsement, or certification of historical priority.

Outcome and corrections
The mathematical and hostile reviews identified no fatal mathematical error,
substantive counterexample, or unresolved substantive proof gap under the
stated hypotheses. Required minor revisions clarified the following:
1. The local equations apply at prestates with positive threshold deficit.
2. Adaptive selection between the two specified maps is covered pathwise;
   changed maps, injected disturbances, and noisy recurrences are not covered.
3. The leakage counterexample preserves leading weighted terms, not the
   ordinary multivariate Taylor jet. Both modified maps are now explicit.
4. Reproducibility claims distinguish exact algebra, bounded exhaustive
   checks, syntactic source checks, analytic proof, and production checks.
Targeted mathematical, hostile, and editorial closure reviews found these
requested corrections resolved. No required review correction remained open.

Substantive scrutiny
The reviews examined the critical-branch existence and uniqueness argument,
compatible radius choices, drift remainder estimates, schedule-uniform
terminal transfer, positivity and crossing, the direction and legality of
finite-word exchanges, fixed-block convergence, and the complete infinite-tail
bound. They found the tail estimate sufficient to justify the order of limits;
fixed-block convergence alone would not have sufficed. The reported six energy
coefficients, nine drift cancellations, and scaled ODE identities are also
covered by the executable checker included here.

Adversarial limitations retained
The class is restrictive: exact critical initialization, quadratic flatness,
a shared second-coordinate update, omission of first-coordinate contraction,
and terminal freezing. It is not a general theorem for monotone switching,
approximate critical starts, parameter-uniform limits, physical systems,
cognition, or disturbances fed into the dynamics. The exponent and zeta factor
follow from the proved transfer and complete-tail estimates and are not
presented as novel general methods. A general dynamics journal could judge
the work too narrow despite correct proofs; it is positioned as a focused
research note. Human specialist assessment of significance, priority, author
metadata, and any journal requirements remains outstanding.

Prior work and search limits
The prototype's critical geometry has a direct antecedent in Jamieson and
Merino (2018), DOI 10.1186/s13662-018-1595-x. The manuscript transparently
attributes the earlier Casasayas-Fontich-Nunes result through that inspected
later source; the original paper was not independently obtained. Cufi-Cabre
and Fontich (2021), DOI 10.3934/dcds.2021053, supplies finite-regularity context.
Angeli and Sontag (2003), DOI 10.1109/TAC.2003.817920, and Lomeli, Meiss and
Ramirez-Ros (2008), DOI 10.1088/0951-7715/21/3/007, are broader comparison and
perturbation-sum precedents, not proofs of this terminal switching result.
The bounded search found no exact duplicate of the stated combination, but
cannot certify priority or exhaust the literature.

Evidence and access limits
The full-source reviews assessed supplied source rather than independently
retrieving or hashing the disk files, and did not execute the verification
script or compiler. Targeted closure reviews assessed the supplied revisions
and relied on reported preservation of theorem and proof content. The reviewed
round-03 source hash was
27ff79930679ebfa78e54a9b68f88dba4cae148fc4b6fdbfe268d878f9d98c4a.
The later production source changes title/layout, one inline-to-display
format, bibliography layout, and production-status wording. Production checks
record the mathematical statements and proof content as unchanged, except
for that equation-format change. Exact production source SHA-256:
504294811725f5c51923738a912122b6db2e03fc19f5dbfc268fdfd4cc5b97ce.
Exact PDF SHA-256:
6e5c0a23d5861e4d752e7b5f976b4139592e4f1d2cbc6be856b404f1c8b510cd.
Compilation and all eight page inspections are recorded separately in the
production receipt. Fresh public-package source/algebra checks are recorded
in validation/public_release_validation.json. Their compiled=false field
means that checker does not compile TeX; it does not negate the production
receipt. No new human review or priority certification is claimed.
