FOCUSED PRIORITY AND OVERLAP CHECK
9 November2026. Bounded source comparison, not a priority certification.

The authoring agent completed this live check after the separate hostile
reviewer's initial read/search call returned no content before interruption.
The hostile review therefore must not be described as an independent fresh
web search. Its provided-text assessment is recorded separately.

Queries actually completed by the authoring agent:
1. "Boolean" "order thinning" torsion
2. "two-bit" "poset" "torsion"
3. "signed incidence" "Smith" Zaslavsky
4. "poset" "two-bit" "Mobius" (query used the umlaut spelling)
5. "order thinning" "signed"
6. "Boolean" "thinning" "Z/2"

Returned results included the B-Theory parent reading copy and general
signed-graph, cellular-homology and unrelated uses of thinning. No independent
exact Boolean realization was identified in these returned results. This is
a narrow terminology-dependent search with noisy results; it cannot establish
that no such realization exists under other terminology. Search snippets
were not used as authority for any theorem.

Primary texts reopened and relevant sections inspected on9 November2026:

https://www.b-theory.com/manuscripts-html/binary-order-thinning/
Theorem4.2 and Section7 retain the one-bit recognition theorem and seven-state
integral-neutral noncollapse. Our result is an additional restricted two-bit
classification plus a torsion witness, not a refutation or replacement.

https://arxiv.org/html/1303.3083
Zaslavsky SectionsIV.B-IV.C give row switching, column reorientation and the
characteristic-dependent incidence rank. Those are antecedents to Lemma1
and Proposition3, for which the addendum supplies its own short integer proof.

https://arxiv.org/html/2105.05388v2
Contreras and Andrew R.Tawfeek Example4.9 explicitly uses the Mobius strip
with its boundary as root and relativeH1=Z/2. It is the closest geometric
antecedent identified. The addendum attributes it and isolates the extra
poset/two-bit/(C) realization constraint.

Additional inherited primary-source comparison, preserved from4 November:
Zaslavsky Signed graphs1982, Sections8A-8B,
https://doi.org/10.1016/0166-218X(82)90033-6
Bernardi-Klivans, Directed rooted forests in higher dimension,
https://arxiv.org/html/1512.07757v4
These account for classical signed incidence and rooted-forest/fitting-
orientation technology. No first claim for those methods is defensible.

POSITIONING
The differentiated content is the explicit nine-state Boolean realization,
its full integral certificate and degree-two map, and the exact scope of the
restricted recognition criterion. It warrants consideration as a technical
addendum to the existing paper. It does not by itself establish standalone
paper novelty or publication priority. Avoid 'first', 'smallest', 'new theory
of signed graphs', and any implication that Mobius-strip torsion is new.

The operational examples strengthen existing scope warnings; they do not
retract the parent manuscripts' stated formal theorems. The exclusiveK2,2
secondary-map target is not the same realizability problem.
