Shared boundary lock for the a=2, x=6 cluster

Exact statement

For the five residual rows of $9P(v)(64+3^y)+1=2^N$ inherited from FPRD-IC-T17, every solution satisfies $v\equiv v_0\pmod{36288000}$ , $y\equiv y_0\pmod{36288000}$ , and $N\equiv12\pmod{48384000}$ , where $(v_0,y_0)$ is its displayed boundary residue. Twelve simultaneous multiplicative-order quotients preserve exactly one lift of each row.

StatusProved and independently reconstructed; superseded as a frontier by FPRD-IC-T21

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

Context

Five of the 21 residual rows share x=6 and N congruent to 12. Their base residues encode only the two factorizations 9·7·65+1 and 9·5·91+1.

Proof or evidence

The prime chain 19,41,61,151,101,251,271,541,631,29,751,811 expands the common periods while retaining exactly the five base rows at every stage.

Shared five-row boundary lock →

Verification notes

Independent C++ and Python implementations reconstruct every intermediate period and assert that no extra simultaneous lift survives.

Limitations

The theorem by itself locks rather than excludes nonzero lifts; FPRD-IC-T21 supplies the stronger exclusion.
It concerns five rows of one normalized positive-type-II branch.
No external review or novelty determination is recorded.

Open work

Retain as an exact intermediate theorem; do not extend this lock after FPRD-IC-T21 closes every nonboundary lift.