R4.T2 mod 16 affine decomposition
R4.T2 low four bits can be classified into exact affine context formulas over the registered source.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
R4.T2 low four bits can be classified into exact affine context formulas over the registered source.
Why the test is meaningful
Modulo 16, only the four least significant result bits and their internal carries matter. An affine representation over GF(2) contains a constant and degree-one source terms; exhaustive truth-table comparison determines exactly which contexts belong to that class.
T2_low4(x)=b⊕a₀x₀⊕a₁x₁⊕a₂x₂⊕a₃x₃x∈{0,1}⁴, so each context has 16 pointsaffine ⇔ every ANF coefficient of degree ≥2 is zeroHow it was tested
Enumerate each 16-point source cube, derive affine candidates and reject any formula with a truth-table mismatch.
What happened
Exact affine decompositions were compiled for the qualifying contexts and verified exhaustively within each cube.
Exactness and statistical controls
Candidate formulas were evaluated on all 16 inputs of every registered context; any single mismatch rejected the affine classification. The test therefore has no sampling error within a cube.
What the result means
Low-bit affine structure is a reusable capability, not a statement about the full 32-bit word or final target.
Limitations
- Only T2 modulo 16 is classified.
- Qualifying contexts do not imply the full word is affine.
- Context identification and downstream carry cost remain.
Evidence trail
Exhaustive 16-point checks for each published context formula.
Canonical variants
SUBENGINE-V14ASUBENGINE-V14BSUBENGINE-V14CSUBENGINE-V14DSUBENGINE-V14ESUBENGINE-V14FSUBENGINE-V14GSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.