Expecting tensor powers of a complete direct sum to improve ASI value

Exact statement

Expecting tensor powers of a complete direct sum to improve ASI value. the powered volume sum factorizes exactly as $(\sum_i v_i^{\rho/3})^N$ , while the border-rank upper bound becomes $r^N$ . Taking roots recovers the original inequality.

Statusrefuted analytically.

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 powered volume sum factorizes exactly as $(\sum_i v_i^{\rho/3})^N$ , while the border-rank upper bound becomes $r^N$ . Taking roots recovers the original inequality.

Rejected transfers and surviving boundaries →

Verification notes

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

Limitations

laser leverage comes from zeroing/merging an overlapping partitioned power into a strategically chosen direct sum, not from powering a direct sum already in hand.

Open work

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