High-reset Σ0 freeze frontier
For bits 15–18, Σ0(a4) freezes exactly when one low rotated source bit freezes, because the other rotated source bits and Majority inputs are already constant in the registered context.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
For bits 15–18, Σ0(a4) freezes exactly when one low rotated source bit freezes, because the other rotated source bits and Majority inputs are already constant in the registered context.
Why the test is meaningful
SHA-256 uses Σ0(x)=ROTR²(x)⊕ROTR¹³(x)⊕ROTR²²(x). At a fixed output bit, each rotation selects one source bit. If two selected bits are context constants, variability reduces exactly to the third source bit; the resulting operand freeze can then compose with an inner hard reset.
Σ0(x)[i] = x[(i+2) mod 32] ⊕ x[(i+13) mod 32] ⊕ x[(i+22) mod 32]for i∈{15,16,17,18}: freeze(Σ0(a4)[i]) ⇔ freeze(a4[i−10])high reset + constant suffix K/P/G ⇒ exact c18How it was tested
Derive the rotated-source correspondence at bits 15–18, verify constancy of the two companion source bits and all Majority inputs, compose each hard reset with the suffix program and repeat on 300 fresh records.
What happened
All finite-scope theorem checks had zero errors. The original cohort contained 935 high resets and the fresh cohort 219; every one produced a constant suffix. Six exact suffix programs covered the fresh records, with zero identity errors.
Exactness and statistical controls
The rotation identity and reset composition were checked exactly, not estimated. Fresh prevalence was recorded separately from the original cohort. Runtime economics remained explicitly pending.
What the result means
A broad-looking Σ0 condition collapses to a one-source-bit frontier inside the registered context. This is an exact local simplification and a useful detector prerequisite, not evidence that the total SHA-256 path is cheaper.
Limitations
- The theorem has finite registered scope and depends on inherited constants.
- Six suffix programs still require dispatch.
- No online detector or energy measurement was benchmarked.
Evidence trail
Recompute all rotation indices, verify source-bit constancy, enumerate both source-bit values and compare the composed carry certificate with direct T2 evaluation on original and fresh cohorts.
Canonical variants
SUBENGINE-V26ASUBENGINE-V26BSUBENGINE-V26CSUBENGINE-V26DSUBENGINE-V26ESource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.