ANF cancellation attribution in Σ0 lane 0
The attenuation observed at Σ0(a5) lane 0 can be attributed exactly to cancellation among rotated input monomials rather than described only by an aggregate complexity score.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
The attenuation observed at Σ0(a5) lane 0 can be attributed exactly to cancellation among rotated input monomials rather than described only by an aggregate complexity score.
Why the test is meaningful
Because XOR is addition in GF(2), the same ANF monomial appearing an even number of times across rotated inputs cancels exactly. Attribution tracks provenance of each term, distinguishing retained a5[22] structure from complexity imported by a5[2] and a5[13].
Σ0(a5)[0]=a5[2]⊕a5[13]⊕a5[22]α_S(out)=α_S(2)⊕α_S(13)⊕α_S(22)retention(a5[22]) = |N22 ∩ Nout| / |N22|How it was tested
Build exact ANFs for the three source lanes and their XOR, label each nonlinear monomial by origin, measure union, cancellation and retention, then compare actual survivor and non-survivor groups in original and fresh cohorts.
What happened
All 1,361 original and 300 fresh records had zero semantic errors. Original retention differed by −0.008 between survivors and non-survivors; fresh retention differed by +0.054, reversing direction. Mean union size was slightly lower for survivors in both cohorts, but by only 0.089 and 0.157 monomials.
Exactness and statistical controls
Truth-table reconstruction verified every ANF. Original and untouched fresh cohorts were compared using the same fixed measures. Because the retention direction changed, the experiment limits its claim to exact attribution and empirical contrasts.
What the result means
Cancellation can be measured precisely, but it does not yield a stable survivor-specific simplification. The attenuation is distributed among imported and canceled terms rather than explained by a reproducible retention rule.
Limitations
- Mean monomial differences are descriptive without a preregistered selector.
- ANF size does not equal circuit latency.
- Four-variable source cubes capture a local interface only.
Evidence trail
Derive ANFs by exact Möbius transform, tag all nonlinear terms by input lane, reconstruct the output truth table and repeat retention/union summaries on the untouched fresh split.
Canonical variants
SUBENGINE-V31ASUBENGINE-V31BSUBENGINE-V31CSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.