A Universal Odd Divisor for Single-Domino Constraints

What is this paper trying to establish?

Does one universal odd divisor survive when any single domino is required or forbidden?

The central idea.

Identifies a common odd divisor retained when any one domino location is required or forbidden on an even square board. Integral matrix reduction separates odd denominators from the remaining factor of two.

What changes if the method holds?

The theorem would extend the divisibility phenomenon from a special diagonal to every single location while sharply excluding simultaneous multi-constraint cases.

Where scrutiny should concentrate.

The paper identifies the following points as the highest-value targets for independent review.

1. 01
   Integral equivalence of the signed grid matrix and the Kronecker-sum operator.
2. 02
   Symmetric/alternating decomposition, cyclicity in characteristic two, and denominator control.
3. 03
   Sign-correct single-edge counts, exact scope of Pachter’s assertion, and exclusions for multiple simultaneous constraints.