Opening R5 GENERAL with one quadratic term
The registered R5 low-four-bit GENERAL cases can be represented as an affine function plus at most one x2·x3 term.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
The registered R5 low-four-bit GENERAL cases can be represented as an affine function plus at most one x2·x3 term.
Why the test is meaningful
When affine form is insufficient, the next controlled algebraic class adds one quadratic monomial. AQ23 represents a Boolean function as an affine component plus x2·x3; preserving subtraction borrow is necessary because modular subtraction couples low-bit equations.
f(x)=b⊕Σᵢaᵢxᵢ⊕q(x₂∧x₃)q∈{0,1}; algebraic degree ≤2borrowᵢ₊₁ determined exactly from minuend, subtrahend and borrowᵢHow it was tested
Enumerate exact source cubes, isolate the quadratic monomial, preserve subtraction-borrow context and compile compact AQ23 programs.
What happened
All registered V17 transitions were opened by the AQ23 representation; the independent test engine reported zero errors.
Exactness and statistical controls
Every registered 16-point cube was enumerated, AQ23 programs were compiled, and an independent engine compared program output with the direct transition. The test reported zero errors.
What the result means
The low-four-bit family has controlled multiplicative complexity. This is not a claim about full SHA-256 or runtime speed.
Limitations
- The grammar permits only the registered quadratic term.
- It concerns low four bits and associated borrow.
- Controlled algebraic degree does not establish lower runtime.
Evidence trail
Exact 16-point subcube enumeration and independent AQ23 program verification.
Canonical variants
SUBENGINE-V18ASUBENGINE-V18BSUBENGINE-V18CSUBENGINE-V18DSUBENGINE-V18ESUBENGINE-V18FSUBENGINE-V18GSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.