K/P/G carry transfer and long-jump irrelevance
Carry propagation across selected A5 intervals can be represented by exact Kill/Propagate/Generate transfer states, and an interval with identically zero propagation makes its incoming carry irrelevant.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
Carry propagation across selected A5 intervals can be represented by exact Kill/Propagate/Generate transfer states, and an interval with identically zero propagation makes its incoming carry irrelevant.
Why the test is meaningful
Binary addition admits an exact three-state transfer algebra. For a bit interval I, K means the interval forces carry-out 0, G forces carry-out 1 and P transmits the incoming carry. Composition is associative, so long intervals can be summarized without replaying every incoming-carry case.
c_out = G_I ∨ (P_I ∧ c_in)P_I ≡ 0 ⇒ c_out = G_I(K,P,G)_{I∪J} = (K,P,G)_J ∘ (K,P,G)_IHow it was tested
Construct an exact A5 interval-transfer atlas, prove the long-jump condition, compile a class-conditioned low-four-bit Majority shell and search R6 contexts for selectors. Repeat prevalence measurements in independent fresh samples; keep borrow-based enrichment as a separate non-authoritative scout.
What happened
Carry transfer and the Majority shell were exact. In 1,361 original records, P was identically zero in 1,273 cases (93.53%) for interval 5–13 and 1,140 cases (83.76%) for interval 16–22. Fresh fractions were 88.8% and 83.2% over 250 records per interval. No jump-context or borrow-jump candidate survived.
Exactness and statistical controls
The implication P≡0⇒incoming-carry irrelevance is a theorem, while its prevalence is empirical. The prevalence was therefore repeated on fresh cohorts rather than extrapolated. Exact transfer and shell identities passed independent replay; candidate searches returned zero.
What the result means
V22 establishes a genuine local capability: some carry inputs are provably irrelevant over particular intervals. It does not show that detecting or consuming the condition costs less than hashing, and it produced no connected R6 selector.
Limitations
- Prevalence depends on the studied context distribution.
- A frequent exact condition can still be expensive to detect.
- Local carry skipping is not a complete SHA-256 work reduction.
Evidence trail
Rebuild K/P/G states bit by bit, compose them over both registered intervals, verify both incoming carries against direct addition, then repeat the P-zero rates on a separately generated cohort.
Canonical variants
SUBENGINE-V22ASUBENGINE-V22BSUBENGINE-V22CSUBENGINE-V22DSUBENGINE-V22ESUBENGINE-V22FSUBENGINE-V22GSUBENGINE-V22HSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.