Exact periodic lift lock for the first two complementary minimum layers

Exact statement

In the normalized complementary $f=1$ and split- $(2,0)$ $f=2$ branches, impose $m=\min(b,y,g)\in\{1,2\}$ . Of the 32 canonical minimum strata, nine are empty. Every state in the other 23 lies on one of 40 exact periodic lift graphs with common coordinate period $P=20{,}652{,}025{,}680$ . Twenty-nine graphs are rooted at seventeen proper harmless presentations and eleven at nine improper rational boundary identities. Every noncontrol proper solution therefore has output exponent $N\ge P$ .

StatusProved without exponent bounds; independently reconstructed

External reviewNo documented external or specialist review of these FPRD results is recorded.

Context

The two valuation laws fix K+f-h modulo 18 when the least ternary exponent is one or two. Exact minimum masks and the quadratic-reciprocity gate leave 32 canonical strata before odd-prime quotients.

Proof or evidence

A 26-prime CRT-compatible quotient leaves exactly 40 terminal graphs at common period 20,652,025,680. Centering each graph gives either a genuine small presentation or an exact improper rational boundary identity; nine strata have no graph at all.

Complementary minimum-layer lift lock →

Verification notes

Independent Python and C++20 implementations reproduce every stage count, the 40-row terminal hash, all centered roots, the minimum six-one excess of the proper controls, and the resulting output-height bound.

Limitations

The 40 lift graphs are not proved to contain only their centered roots.
This classifies two minimum layers of two complementary branches, not the complete normalized grammar or arbitrary expression trees.
No external review or novelty determination is recorded.

Open work

Use the next 3-adic digit and an archimedean descent on the eleven boundary-rooted lift graphs; do not merely enlarge the order-modulus period.