Promoting the $3k\log k$ precision estimate to an unconditional theorem

Exact statement

Promoting the $3k\log k$ precision estimate to an unconditional theorem. the estimate assumes a floating-point roundoff envelope $B_k u s^{-3k}$ and at most exponential growth of $B_k/12^k$ . Run 10 proves the truncation envelope but has not yet derived $B_k$ for the expanded length-1000 DAG. Staged normalization or rescaling may also improve the literal $s^{-3k}$ amplification.

Statusrejected.

External reviewNo documented external or specialist review of the FPRD synthesis is recorded.

Context

The research record preserves failed approaches when they expose a model boundary, an invalid transfer, or an unsupported strengthening.

Proof or evidence

the estimate assumes a floating-point roundoff envelope $B_k u s^{-3k}$ and at most exponential growth of $B_k/12^k$ . Run 10 proves the truncation envelope but has not yet derived $B_k$ for the expanded length-1000 DAG. Staged normalization or rescaling may also improve the literal $s^{-3k}$ amplification.

Rejected transfers and surviving boundaries →

Verification notes

The failure status and preserved lesson are recorded in the cumulative failure ledger.

Limitations

record $p=3k\log_2k+O(k+\log(1/\tau))$ only as a sufficient conditional consequence, never as a lower bound or finished stability theorem. Run 11 later discharges the condition for a separate row-wise DAG, not for Run 10's 4504-addition compiler.

Open work

Keep this exclusion attached to any future reuse of the corresponding construction.