Lazy frontier ladder from R55 to R52

What was tested?

The exact lazy mechanism remains valid before R56, while measured savings reveal where dependency cost begins to dominate.

Why the test is meaningful

Moving the observation frontier backward exposes more SHA-256 dependencies. At each earlier round, the first requested target bit depends on additional schedule, Choice, Majority, rotation and modular-addition terms. A correct phase diagram therefore compares lazy and eager evaluation at the same frontier and on the same records rather than comparing raw runtimes across different programs.

How it was tested

The frozen V1 evaluator was extended through R55, R54, R53 and R52. For every frontier, 6,000 free-validation and 2,000 reachable-Bitcoin records were evaluated with the same bit order, eager byte baseline and full suffix oracle. Operation-level provenance counted demanded schedule, Ch, Maj, Σ0, Σ1, T1, T2 and word-bit evaluations; partial prefix motors were also checked against the golden B8 decision.

What happened

All frontier comparisons were exact: total false rejects and full-decision mismatches were zero. On reachable records, diagnostic savings declined from 9.33% at R55 to 7.34% at R54, 6.04% at R53 and 5.14% at R52; the earlier R56 reference was 10.38%. At R52, mean lazy work was 5,676.476 units versus 5,984 eager units, showing that the lever remains exact while dependency resolution consumes most of the eager byte cost.

Exactness and statistical controls

Each frontier used paired records: W_lazy and W_eager were measured on the same state, so the relevant contrast is within-record rather than an unpaired population mean. Free and reachable cohorts were reported separately. The preregistered 5% materiality gate was passed at R52 only for the matched diagnostic consumer; the canonical report explicitly forbids interpreting 5.14% as SHA-256 or mining speedup.

What the result means

The lever persists but becomes more expensive to resolve earlier. The measured ratios motivate transport research, not a speedup claim.

Limitations

• Diagnostic work units are implementation-specific and are not native instructions or energy.
• The experiment evaluates B8 selectivity, not the complete 256-bit target.
• Per-job setup, memory traffic, dispatch and ASIC integration are outside this phase diagram.

Evidence trail

Recreate each frozen frontier, evaluate 6,000 free and 2,000 reachable records per frontier with identical bit order, retain reject-stage counts, and require zero lazy/eager, eager/oracle and false-reject discrepancies before comparing paired work totals.

Canonical variants

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