Opening the R5 Σ0 / Maj complexity wall
Global low-bit complexity at R5 can be localized into carry boundaries and conditional Majority branches instead of treated as one opaque wall.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
Global low-bit complexity at R5 can be localized into carry boundaries and conditional Majority branches instead of treated as one opaque wall.
Why the test is meaningful
SHA-256 T2 combines Σ0 rotations with Majority and modular addition. Rotation is linear over GF(2), Majority is nonlinear, and the addition carry introduces further products. Decomposing these sources separately localizes complexity without claiming that any one local simplification survives the complete round.
Σ0(x)=ROTR²(x)⊕ROTR¹³(x)⊕ROTR²²(x)Maj(x,y,z)=(x∧y)⊕(x∧z)⊕(y∧z)T2=Σ0(a)+Maj(a,b,c) (mod 2³²)How it was tested
Build exact Σ0 and Maj atlases, decompose carry boundaries, search conditional context selectors and verify the compiled capability contracts.
What happened
The internal decomposition and test engine completed exactly. Some side-capability signals were retained as descriptive candidates only.
Exactness and statistical controls
Exact atlases and compiled contracts were compared with direct round computation on every registered source subcube. Side signals remained explicitly descriptive because independent formalization and operational replication were absent.
What the result means
The complexity wall is better localized, but it remains the main obstacle. Conditional signals do not redirect the research line or imply mining advantage.
Limitations
- The decomposition localizes but does not eliminate nonlinear complexity.
- Side signals are hypotheses, not validated selectors.
- The economic and full-SHA verdict remains open.
Evidence trail
Exact within registered source subcubes; context candidates remain empirical until independently formalized.
Canonical variants
SUBENGINE-V20ASUBENGINE-V20BSUBENGINE-V20CSUBENGINE-V20DSUBENGINE-V20ESUBENGINE-V20FSUBENGINE-V20GSUBENGINE-V20HSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.