Height barrier for every non-boundary a=2, x=6 lift

Exact statement

Every non-boundary solution in the five-row cluster of FPRD-IC-T18 satisfies $v+y>26774635116096000$ and $N\ge42436792629504012$ . Equivalently, after writing $v=v_0+36288000r$ , $y=y_0+36288000s$ , every solution has $r+s>737837167$ .

StatusProved, but superseded by the complete nonboundary exclusion FPRD-IC-T21

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

Context

The shared periods have ratio 3/4, converting the exact equation into an unusually close one-sided approximation to (3/4)log2(3).

Proof or evidence

An exact sweep through r+s=737837167 finds 111 broad approximants. All miss fourteen row-specific correction limits by at least 0.0020764, while the correction error is below 10^-6.

One-sided approximation barrier →

Verification notes

Rational atanh-series bounds certify the logarithm intervals. The terminal C++ sweep uses integer comparisons; the modular and enclosure layers are independently reconstructed.

Limitations

This was an enormous conditional lower bound, not an exclusion; the later second-gate theorem makes the survivor set empty.
It does not extend from the five-row cluster to the other sixteen residual rows or arbitrary formulas.
No external review or novelty determination is recorded.

Open work

Do not extend the height sweep; the full second gate now excludes every lift to which this conditional bound applied.