Treating a direct-sum batch schedule as the asymptotic sum inequality

Exact statement

Treating a direct-sum batch schedule as the asymptotic sum inequality. the explicit batch DAG computes independent products. A block-diagonal embedding still omits dense cross-block products. The multiplicity-to- $\omega$ inference is supplied by Schönhage's separate asymptotic tensor theorem, not by an ordinary topological schedule of the batch.

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 explicit batch DAG computes independent products. A block-diagonal embedding still omits dense cross-block products. The multiplicity-to- $\omega$ inference is supplied by Schönhage's separate asymptotic tensor theorem, not by an ordinary topological schedule of the batch.

Rejected transfers and surviving boundaries →

Verification notes

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

Limitations

distinguish executable direct-sum extraction from the asymptotic transformation that converts its border-rank bound into a dense matrix exponent.

Open work

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