Assuming cyclic tensor duality preserves a chosen addition SLP

Exact statement

Assuming cyclic tensor duality preserves a chosen addition SLP. a cyclic mode permutation preserves the rank-ten tensor decomposition, but it moves the output recombination map into an input-form role and transposes another input map into the output role. The displayed linear SLP costs therefore change across the $(3,2,2)$ , $(2,2,3)$ , and $(2,3,2)$ factors.

Statusrefuted for the declared BCLR realization.

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

a cyclic mode permutation preserves the rank-ten tensor decomposition, but it moves the output recombination map into an input-form role and transposes another input map into the output role. The displayed linear SLP costs therefore change across the $(3,2,2)$ , $(2,2,3)$ , and $(2,3,2)$ factors.

Rejected transfers and surviving boundaries →

Verification notes

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

Limitations

algebraic symmetry is not automatically an executable resource symmetry; transform and recount the actual linear circuits.

Open work

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