Superadditivity of unprimed acyclic gate networks

Exact statement

Every scalar function computed by a finite acyclic network of splitters, adders, and unprimed topplers satisfies $F(x+y)\ge F(x)+F(y)$ .

StatusProved internally by structural induction

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

Context

The invariant is stronger than the previously established sign condition and applies at arbitrary unprimed depth.

Hypotheses and scope

Finite directed acyclic network.
Unprimed topplers start in state zero; no hidden constant or preload source.
Aggregate input-count semantics only.

Proof or evidence

Coordinates are additive; addition preserves superadditivity; and $\lfloor(F(x)+F(y))/\lambda\rfloor\ge\lfloor F(x)/\lambda\rfloor+\lfloor F(y)/\lambda\rfloor$ . Structural induction proves the claim.

Superadditivity proof →

Verification notes

The full Run 8 proof and its stated model boundaries were checked. Shared subcircuits do not alter the computed function, so treeification does not change this structural induction.

Limitations

No statement is made about trace order, timing, queues, odometers, feedback networks, or primed gates.
No novelty claim is made.

Open work

Audit placement in the broader literature on floor functions and unprimed abelian gates.