Methods note · September 28 reviewed source · Reading copy 1
Brian Theory
A complete four-operator example shows how the permitted tests, their polynomial degree, the chosen coordinates and zero handling change exact operator identification.
Exact original 14-page PDF and self-contained TeX. The source date field is blank and preserved. The source package establishes the September 28 revision date. Extracted text may lose equations; use the PDF and TeX for mathematics.
Read or download PDF · Exact source ZIP · TeX · Extracted text · Bounded verification code and results · Version record
For F(x,y)=x+y+xy, the nonzero score patterns give AND, the two projections and XNOR. In the original positive-magnitude coordinates, no finite linear-sign library suffices; degree two or three needs three fixed tests; degree four or higher needs two. Reciprocal coordinates change the degree restriction. Three truth-table coordinate probes are still necessary in the deterministic adaptive worst case.
Correspondence Matrices concerns faithful representations. This note asks how an operator can actually be identified under declared observation rules. Observable Answers treats the broader distinction between information, test selection and legal execution. These are related contracts, not one theorem or an implementation speedup. Finite-Jet studies a complementary continuous-realization question.
Later internal source comparison identified close antecedents in Averkov (2009), Polynomial Representations and Averkov–Bey, polynomial descriptions of polygonal regions. Boundary-factor and polynomial-description methods should not be treated as new here. The note is offered as a focused worked synthesis, without historical-priority clearance. Its unchanged bibliography describes the CM/LM companion as unpublished at drafting time; the current public parent is linked above.
This copy is the reviewed September 28 methods note. A complete October 13 extended working draft adds weighted boundary codes, connected chamber graphs and joint-box/composition certificates. Those later results are not part of this PDF and require their own release preparation and review binding. They are not claimed as missing research.
Internal same-assistant reviews and bounded exact checks do not establish external human peer review, historical priority or physical/cognitive validation.