EXP-045VALIDATED
Advantage Decomposition / SHA-256

Exact B8→B16 target nesting

A candidate that passes the first target byte can be tested for the second byte incrementally, with total work equal to B8 work plus conditional B16 work and no decision errors.

Claim statusNO END-TO-END MINING ADVANTAGE DEMONSTRATED

Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.

Date2026-08-23
HardwareClassical exact algebraic verifier
Run scopeThree canonical variants
ReproducibilityPreserve digest byte order, run the frozen B8 engine, invoke B16 only on survivors and verify all decisions plus the conditional-cost identity against the full suffix.
01 / Question & hypothesis

What was tested?

A candidate that passes the first target byte can be tested for the second byte incrementally, with total work equal to B8 work plus conditional B16 work and no decision errors.

02 / Scientific basis

Why the test is meaningful

Bitcoin target comparison is lexicographic in digest order. The B16 predicate is nested inside B8: the second byte matters only when the first byte satisfies its boundary. Conditional evaluation is exact when earlier rejection is final.

B16 ⊂ B8E[W_nested]=E[W_B8]+P(B8)·E[W_{next byte}|B8]decision = first differing target bit
Nested target evaluationThe second byte is evaluated only for exact B8 survivors.EXP-045 / NESTED TARGET EVALUATION30,000 NONCESactual jobPASS B80.3767%PASS B160.00333%
FIGURE / RESULT READINGThe second byte is evaluated only for exact B8 survivors.
03 / Method

How it was tested

Run exact B8 then incrementally evaluate the next target byte only for B8 survivors across free, conditioned, actual-job and genesis-job cohorts. Verify the cost identity and full suffix on every record.

04 / Observed result

What happened

Actual-job B8 rate0.3767%
Actual-job B16 rate0.00333%
Exactness errors0

All lever, suffix and cost-identity errors were zero. In 30,000 actual-job nonces, B8 rate was 0.003767 and B16 rate 0.0000333; mean nested work was 46.033 versus 45.884 at B8 alone. In 60,000 free unconditional records, B8 rate was 0.00405 and B16 rate 0.0000167.

05 / Validation

Exactness and statistical controls

Several cohort types test both free and reachable behavior. The conditioned-on-B8 cohort separately measured incremental cost, while unconditional cohorts verified the total expectation identity.

06 / Interpretation

What the result means

Target nesting is an exact decision architecture and correctly concentrates later work on rare survivors. It is not a mining speedup because the baseline-equivalent implementation and full SHA cost are not yet established.

Limitations

  • Rates reflect the registered target bytes and cohorts.
  • Diagnostic work is not native hardware cost.
  • Nesting is a comparison strategy, not a method for producing better hashes.
07 / Reproduction

Evidence trail

Preserve digest byte order, run the frozen B8 engine, invoke B16 only on survivors and verify all decisions plus the conditional-cost identity against the full suffix.

Canonical variants

SUBENGINE-V45ASUBENGINE-V45BSUBENGINE-V45C

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