Recursing the five-term partial BCLR tensor as square multiplication

Exact statement

Recursing the five-term partial BCLR tensor as square multiplication. the verified Run 9 tensor has mode dimensions $(3,4,4)$ , so its $k$ th tensor power has dimensions $(3^k,4^k,4^k)$ rather than the three equal mode dimensions of square matrix multiplication.

Statusrefuted by dimension audit.

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 verified Run 9 tensor has mode dimensions $(3,4,4)$ , so its $k$ th tensor power has dimensions $(3^k,4^k,4^k)$ rather than the three equal mode dimensions of square matrix multiplication.

Rejected transfers and surviving boundaries →

Verification notes

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

Limitations

the classical square route needs two complementary BCLR copies to obtain $M_{\langle3,2,2\rangle}$ and then three cyclic tensor factors to obtain $M_{\langle12,12,12\rangle}$ . Resource recurrences must be attached to that length-1000 certificate, not silently to the five-term partial gadget.

Open work

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