Corrected inner-T2 carry certificate
The dominant bit-18 freeze can be reconstructed from the inner carry of Σ0(a4)+Maj4, and the original source-predicate shortcut must be rejected if independent review does not support it.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
The dominant bit-18 freeze can be reconstructed from the inner carry of Σ0(a4)+Maj4, and the original source-predicate shortcut must be rejected if independent review does not support it.
Why the test is meaningful
For T2=Σ0(a4)+Maj(a4,b4,c4), output bit 18 is determined by the two bit-18 operands and the carry entering that position. A correct certificate must reconstruct this carry exactly; correlation with source labels is insufficient.
T2[18] = Σ0(a4)[18] ⊕ Maj4[18] ⊕ c18c18 = exact K/P/G composition over bits 0…17certificate validity ⇔ reconstructed T2[18] equals direct T2[18] on every laneHow it was tested
Preserve the failed original V25 in provenance, reopen the problem at the inner T2 carry, construct exact K/P/G atlases and reset pathways, and run a fresh 300-record reconstruction. Compile capability contracts only after the corrected path passes.
What happened
The original source-clause result was not promoted. In the corrected run, reconstruction errors were zero. Inner hard resets occurred in 1,305 of 1,361 original records and 290 of 300 fresh records; 1,104 of 1,129 original constant carries and 250 of 253 fresh constant carries were explained by hard-restart suffixes.
Exactness and statistical controls
This is explicitly a corrected experiment. The canonical record retains the invalidated direction, names V24 as the authoritative parent and requires independent post-package review. Exact reconstruction was checked on original and fresh cohorts; no mining claim was issued.
What the result means
The corrected mechanism explains most constant carry-18 cases through a real arithmetic pathway. Scientific value comes partly from rejecting the earlier shortcut and replacing it with a testable certificate.
Limitations
- A few globally constant carries lack an individual hard-reset explanation.
- The fresh cohort contains 300 records and does not establish universal prevalence.
- Connected survivor economics and independent external review remain pending.
Evidence trail
Start from the authoritative V24 state, rebuild the inner carry atlas without using the rejected clause as a selector, verify direct reconstruction and repeat the 300-record fresh test.
Canonical variants
SUBENGINE-V25ASUBENGINE-V25BSUBENGINE-V25R-ASUBENGINE-V25R-BSUBENGINE-V25R-CSUBENGINE-V25R-DSUBENGINE-V25R-ESUBENGINE-V25R-FSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.