EXP-027VALIDATED
Advantage Decomposition / SHA-256

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.

Claim statusNO END-TO-END MINING ADVANTAGE DEMONSTRATED

Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.

Date2026-08-14
HardwareClassical exact algebraic verifier
Run scopeFour canonical variants
ReproducibilityGenerate 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.
01 / Question & hypothesis

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.

02 / Scientific basis

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 c18
Baseline-only exact freeze detectorVisual reading of the published metrics and gates for EXP-027; it summarizes the registered result, not a mining advantage.EXP-027 / BASELINE-ONLY EXACT FREEZE DETECTORLAW ERRORS0DETECTOR ERRORS0ONLINE CHILD TRACES0
FIGURE / RESULT READINGVisual reading of the published metrics and gates for EXP-027; it summarizes the registered result, not a mining advantage.
03 / Method

How 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.

04 / Observed result

What happened

Law errors0
Detector errors0
Online child traces0

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.

05 / Validation

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.

06 / Interpretation

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.
07 / Reproduction

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-V27D

Source: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.