K/P/G attribution at carry 20
The exact source of carry-21 regeneration can be separated into Generate at bit 20 and the product of Propagate with incoming carry, revealing which primitive restores x3 complexity.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
The exact source of carry-21 regeneration can be separated into Generate at bit 20 and the product of Propagate with incoming carry, revealing which primitive restores x3 complexity.
Why the test is meaningful
The K/P/G identity is a causal decomposition of a carry bit. G20 creates carry independently; P20·c20 transmits prior complexity. Comparing these exact components is more informative than correlating only the final carry mask.
c21 = G20 ∨ (P20 ∧ c20)G20=u20∧v20P20=u20⊕v20How it was tested
Compute exact masks for G20, P20, c20 and their product, attribute x3-containing monomials at each stage and repeat fixed survivor/non-survivor summaries on original and fresh cohorts.
What happened
K/P/G recomposition was exact with zero semantic errors for 1,361 original and 300 fresh records. The atlas localized regeneration between the direct-generate and propagated-carry products but did not yield an independent selector or mining advantage.
Exactness and statistical controls
The OR/XOR-equivalent carry truth table was checked lane by lane against direct addition. Original and fresh reports preserve every component, preventing post-hoc selection of whichever term looked favorable.
What the result means
V35 identifies the arithmetic channel by which canceled structure can return. It supports mechanistic understanding and subsequent consumer tests, not faster hashing.
Limitations
- Component attribution does not prove controllability.
- Group means may vary with the registered context distribution.
- The cost of computing K/P/G masks was not compared with native SHA-256.
Evidence trail
Derive G20 and P20 from the exact operands, reconstruct c21 for every lane, verify equality with the direct oracle and repeat x3 attribution on the untouched fresh cohort.
Canonical variants
SUBENGINE-V35ASUBENGINE-V35BSUBENGINE-V35CSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.