Assuming a globally chained copy-optimal relay preserves logarithmic depth

Exact statement

Assuming a globally chained copy-optimal relay preserves logarithmic depth. applying a per-wire fan-out-two caterpillar to the fully expanded Strassen DAG and ordering relay leaves by the scalar schedule attains the minimum buffer count, but exact expansions through five levels have critical depth $1+\frac32k(k+3).$ A raw value traverses longer relay chains at successive recursion levels.

Statusrefuted for the tested consumer-order construction.

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

applying a per-wire fan-out-two caterpillar to the fully expanded Strassen DAG and ordering relay leaves by the scalar schedule attains the minimum buffer count, but exact expansions through five levels have critical depth $1+\frac32k(k+3).$ A raw value traverses longer relay chains at successive recursion levels.

Rejected transfers and surviving boundaries →

Verification notes

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

Limitations

copy optimality alone is not a compositional depth receipt; the local reset/provenance structure is load-bearing.

Open work

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