Exact lazy evaluation of the B8 predicate
The exact B8 predicate can reject on the first required-bit mismatch without evaluating every demanded bit.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
The exact B8 predicate can reject on the first required-bit mismatch without evaluating every demanded bit.
Why the test is meaningful
Bitcoin proof of work compares the double-SHA-256 digest with a target. B8 is the exact predicate on the first registered target byte. Because lexicographic comparison is decided by the first unequal required bit, an evaluator may stop after a decisive mismatch; the scientific question is whether dependency resolution costs less than eagerly constructing every demanded bit.
B8(H,T) ⇔ byte₀(H) ≤ byte₀(T) under the registered boundary rulelazy decision = first i in order π with Hᵢ ≠ Tᵢwork ratio ρᵣ = E[W_lazy at Rr] / E[W_eager at Rr]How it was tested
Build demand-driven evaluators for R60 through R56, train bit order only for cost, and compare every partial decision against eager and full-suffix oracles on free and reachable cohorts.
What happened
The partial flow was exact: zero semantic mismatches and zero false rejects. Diagnostic lazy/eager work was about 25.6% at R60 and 89.6% at R56.
Exactness and statistical controls
Every lazy decision was compared with both an eager B8 evaluator and the complete suffix oracle on free-frontier and reachable Bitcoin-format cohorts. Bit order was permitted to affect work only, never semantics. Zero mismatches and zero false rejects are deterministic safety gates; the reported work ratios are descriptive measurements under the registered counter, not estimates of ASIC cycles.
What the result means
Conditional evaluation saves diagnostic semantic work near the target, but the saving contracts at earlier frontiers. These units are not native cycles or mining speedup.
Limitations
- The work counter measures semantic operations, not gates, clock cycles or joules.
- B8 is a partial target predicate and is not equivalent to full proof of work.
- A useful local ratio can disappear after state transport, scheduling and hardware overhead.
Evidence trail
Validated on fresh free-frontier and reachable Bitcoin-format samples against the golden full-round oracle.
Canonical variants
SUBENGINE-V1ASUBENGINE-V1BSUBENGINE-V1CSUBENGINE-V1DSUBENGINE-V1ESUBENGINE-V1FSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.