Gray-order σ₀ reuse over nonce blocks
Traversing aligned blocks of 32 nonces in Gray order can reuse σ₀ through XOR linearity and improve throughput by at least 1%.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
Traversing aligned blocks of 32 nonces in Gray order can reuse σ₀ through XOR linearity and improve throughput by at least 1%.
Why the test is meaningful
The identity σ₀(base XOR gray)=σ₀(base) XOR σ₀(gray) is exact, but materializing the traversal may consume its theoretical savings.
σ₀(x⊕δ)=σ₀(x)⊕σ₀(δ)coverage must be bijectivegate: geometric speedup≥1.01How it was tested
Compare an unrolled Gray traversal with the frozen external baseline on four unseen headers and 32 balanced processes, auditing 393,216 nonces for bijection.
What happened
Coverage was bijective and hashes exact. The candidate won 4/4 headers but only by 1.000626× with 95% interval 0.999949–1.001304. SASS expanded from 2,507 to 9,895 instructions.
Exactness and statistical controls
A valid B32 hit was recovered by both variants with zero discrepancies and spills. The interval crosses one and the registered 1% gate failed.
What the result means
The identity is exact, but this unrolled implementation trades away the saving through code expansion.
Limitations
- The result applies to the unrolled implementation.
- A compact recurrence requires a separate test.
- A directional 4/4 result below gate is not promoted.
Evidence trail
Audit bijection, equal hash coverage and exact hits, then repeat balanced timing with the frozen binaries.
Canonical variants
CANONICAL-EXP-137PREREGISTERED-CAMPAIGNSEALED-AUDITSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.