Carry-state semantic factors
Explicit carry state can factor contextual behavior that appears opaque in a coarse word-level representation.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
Explicit carry state can factor contextual behavior that appears opaque in a coarse word-level representation.
Why the test is meaningful
Word-level modular addition hides the carry state that couples adjacent bit positions. Exposing carry converts an opaque mapping into an exact recurrence, allowing contexts with identical carry behavior to share a factor without approximating the sum.
sᵢ=xᵢ⊕yᵢ⊕cᵢcᵢ₊₁=(xᵢ∧yᵢ)∨(cᵢ∧(xᵢ⊕yᵢ))factor = exact transition (xᵢ,yᵢ,cᵢ)↦(sᵢ,cᵢ₊₁)How it was tested
Expose registered carry variables, group exact transition behavior by carry context and compare factored outputs against direct modular arithmetic.
What happened
Carry-aware factors passed the registered exactness tests across six variants.
Exactness and statistical controls
Factored outputs and carry transitions were compared with direct 32-bit modular addition across all registered contexts and variants. Exact equality, rather than correlation of class labels, was required.
What the result means
Carry state is useful semantic context. Its storage, discovery and dispatch cost still prevents an operational conclusion.
Limitations
- Explicit carry metadata consumes storage and routing.
- Factors are scoped to the registered operand contexts.
- Representation economy is not yet an operational benchmark.
Evidence trail
Direct modular-addition oracle comparison with frozen factor definitions.
Canonical variants
SUBENGINE-V6ASUBENGINE-V6BSUBENGINE-V6CSUBENGINE-V6DSUBENGINE-V6ESUBENGINE-V6FSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.