Baseline-only exact freeze detector
The V26 freeze and carry certificate can be derived from one baseline source trace and exact modular boundaries, without enumerating all 16 W3.low4 children online.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
The V26 freeze and carry certificate can be derived from one baseline source trace and exact modular boundaries, without enumerating all 16 W3.low4 children online.
Why the test is meaningful
Within the source cube, a4 varies affinely with the low source x: a4(x)=a4(0)+x mod 2³². Bit flips are therefore governed by carry thresholds from a single baseline word. Exact interval comparisons can predict which rotated bits remain constant.
a4(x) = a4(0) + x (mod 2³²), 0≤x<16bit j freezes ⇔ [a4(0), a4(0)+15] does not cross a j-bit boundarydetector output = freeze bits 15…18 + reset values + exact c18How it was tested
Prove the affine source law, compile integer boundary tests from one baseline state, reconstruct Σ0/Majority freezes and high-reset carry-18 certificates, then compare with full 16-child enumeration on 1,361 original and 300 fresh records.
What happened
The source law and detector had zero errors. The original composition detected 935 high-reset records; the fresh run detected 189 of 300. No online full-child SHA traces were required by the compiled capability.
Exactness and statistical controls
Every detector output was compared against exhaustive child enumeration and direct arithmetic. Original and fresh cohorts independently reported zero law and detector errors. The cost claim is limited to avoiding child enumeration; total runtime economics were not measured.
What the result means
V27 converts an exact but potentially cumbersome condition into a baseline-only certificate. It is the clearest isolated computational simplification in this sequence, yet it remains a component-level result until connected costs and survivors are measured.
Limitations
- Avoided enumeration does not automatically imply a wall-clock or energy advantage.
- The detector still requires baseline state bits and boundary comparisons.
- The capability is restricted to the declared four-bit source cube.
Evidence trail
Generate a4(0), derive all boundary predicates, exhaustively enumerate the 16 children only as an oracle, and require exact agreement for freezes, reset values and carry-18.
Canonical variants
SUBENGINE-V27ASUBENGINE-V27BSUBENGINE-V27CSUBENGINE-V27DSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.