Carry regeneration after cancellation
Any suppression attributed to x3 may be erased when modular addition regenerates nonlinear terms through carry, so the next connected carry frontier must be profiled exactly.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
Any suppression attributed to x3 may be erased when modular addition regenerates nonlinear terms through carry, so the next connected carry frontier must be profiled exactly.
Why the test is meaningful
XOR can cancel ANF terms, but integer addition introduces products through its carry recurrence. Thus a simpler operand bit does not guarantee a simpler sum bit. Carry regeneration is the mechanism that must be tested before propagating a local Boolean claim.
s_i=u_i⊕v_i⊕c_ic_{i+1}=(u_i∧v_i)∨(c_i∧(u_i⊕v_i))regenerated term = absent before carry composition, present after exact additionHow it was tested
Follow the x3-attributed components into the connected modular addition, construct exact carry-regeneration truth tables and compare nonlinear support for actual survivor/non-survivor groups in original and fresh cohorts.
What happened
The connected carry profiles were reconstructed with zero semantic errors over 1,361 original and 300 fresh records. Carry regenerated part of the locally suppressed structure; the synthesis did not authorize a simplified end-to-end branch.
Exactness and statistical controls
Every post-carry mask was matched to direct addition. The same predefined summaries were produced for 545/816 original and 111/189 fresh survivor splits. No favorable aggregate was converted into a selector.
What the result means
The experiment confirms why local XOR simplification is fragile: nonlinear complexity can re-enter through carry immediately. This is a boundary result that prevents overclaiming from V31–V33.
Limitations
- The profile is tied to one connected frontier and source cube.
- Nonlinear support remains a representational proxy.
- No measured computational advantage survived the carry stage.
Evidence trail
Start from exact component masks, execute the full ripple recurrence lane by lane, tag regenerated monomials and compare the result against direct modular addition on both cohorts.
Canonical variants
SUBENGINE-V34ASUBENGINE-V34BSUBENGINE-V34CSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.