Generic B8–B32 word-7 target family

What was tested?

The B8→B16 nesting rule generalizes byte by byte through B24 and B32 while the comparison remains inside digest word 7.

Why the test is meaningful

SHA-256 feedforward maps the relevant late-round state word to digest word 7 by an exact modular identity. Each additional target byte is another lexicographic refinement conditioned on all previous bytes.

How it was tested

Compile a width-generic word-7 contract, evaluate three consecutive byte transitions and reproduce each transition on two independent 20,000-record conditioned cohorts with full-suffix checks.

What happened

All previous/next relation and suffix errors were zero. Replicate A continue rates were 0.405%, 0.390% and 0.360% for 8→16, 16→24 and 24→32; mean incremental next-byte work was 39.827, 37.707 and 37.985 units. Replicate B independently passed.

Exactness and statistical controls

Two frozen replicates evaluated all three widths. Counts and work were reported per boundary; no rate multiplication was used to claim a complete target probability.

What the result means

V46 validates a generic exact family through one digest word. The next width crosses into word 6 and requires additional state, so the capability boundary is explicit.

Limitations

• The contract stops at B32.
• Conditioned rates are not unconditional mining probabilities.
• No SHA-equivalent hardware economics were measured.

Evidence trail

For each width, condition on the previous predicate, evaluate exactly one new byte, compare against the full digest target relation and repeat with independent records.

Canonical variants

Source: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.