Opening the coarse GENERAL grammar
States labeled GENERAL by a coarse grammar may still admit exact, structured low-bit representations.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
States labeled GENERAL by a coarse grammar may still admit exact, structured low-bit representations.
Why the test is meaningful
GENERAL was a label produced by a coarse grammar, not a theorem of irreducibility. Any Boolean output on a finite low-bit source cube has a unique truth table and a unique algebraic normal form, so opaque cases can be opened exactly by exhaustive enumeration.
f:{0,1}⁴→{0,1}f(x)=⊕_{S⊆{0,1,2,3}} a_S∏_{i∈S}x_iANF coefficients obtained by Möbius transform of the truth tableHow it was tested
Replace the opaque label with truth-table and algebraic-normal-form analysis on registered low-bit source cubes.
What happened
Previously opaque cases were decomposed into explicit exact structures, enabling more precise downstream experiments.
Exactness and statistical controls
Every point of each registered source subcube was enumerated and the reconstructed form was required to equal the direct output. Exhaustive equality is stronger than a sampled fit but remains local to the four-bit cube.
What the result means
GENERAL described a limitation of the grammar, not proof of cryptographic randomness or irreducibility.
Limitations
- The result concerns registered low-bit cubes.
- ANF size can grow rapidly with dimension.
- Algebraic visibility is not synonymous with computational advantage.
Evidence trail
Exact enumeration within every registered source subcube.
Canonical variants
SUBENGINE-V13ASUBENGINE-V13BSUBENGINE-V13CSUBENGINE-V13DSUBENGINE-V13ESUBENGINE-V13FSUBENGINE-V13GSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.