Compatible uniform cut fields

Exact statement

A compatible uniform cut field over a nonempty finite alphabet contains every literal Boolean table indexed by an exact prefix length and exact future length, the diagonal law that moves one named symbol across the cut, combined bounded-future signatures, prefix-budget rectangles, global residual quotients, horizon bonds, Boolean output, and exposure-one letter actions.

StatusPrecisely stated and self-contained

External reviewNo documented external or specialist review of this FPRD result is recorded.

Context

The definition organizes all fixed-length prefix-versus-future tables of one language into one compatible object. Literal row labels and section maps retain information that a list of cut widths discards.

Definitions

The exact cell $C_{m,n}$ records $\mathbf 1[uv\in L]$ for every $u\in\Sigma^m$ and $v\in\Sigma^n$ .
Diagonal compatibility is $C_{m+1,n}(ua,v)=C_{m,n+1}(u,av)$ .
The global horizon quotient $Q_N(L)$ consists of all residual membership tables on $\Sigma^{\le N}$ .

Hypotheses and scope

The alphabet is finite and nonempty.
Axes retain literal prefix and suffix names; duplicate rows are not discarded before compatibility is checked.

Proof or evidence

The M26 specification defines the exact cells, combined signatures, finite rectangles, bonds, output, and shifted letter actions. The proof uses each component in the assembly theorems below.

Uniform cut field →

Verification notes

The definition was reconciled with the M26 specification, proof, closure audit, production interfaces, and independent malformed-artifact checks.

Limitations

Anonymous cut widths do not determine a language or the required compatibility maps.
A finite prefix rectangle is bounded evidence, not a certificate of a global plateau.

Open work

Add one complete two-letter example showing exact cut cells, a combined row, a horizon bond, and a letter action.

Notes

Literal names and section maps are essential: anonymous cut widths do not determine compatibility or a language. Finite prefix rectangles are bounded evidence and do not by themselves certify a global plateau.