EXP-053VALIDATED
Advantage Decomposition / SHA-256

R59 predecessor transport

The digest-word-5 target relation can be transported exactly to an R59 predecessor interface using a fixed affine identity and only four reduced T1 primitives.

Claim statusNO END-TO-END MINING ADVANTAGE DEMONSTRATED

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

Date2026-08-23
HardwareClassical exact algebraic verifier
Run scopeThree canonical variants
ReproducibilityRecompute the four T1 terms and IV5 feedforward, verify the identity on generic/reachable states and audit 5,000 records per action in two replicates.
01 / Question & hypothesis

What was tested?

The digest-word-5 target relation can be transported exactly to an R59 predecessor interface using a fixed affine identity and only four reduced T1 primitives.

02 / Scientific basis

Why the test is meaningful

SHA-256 round updates and feedforward are modular additions. For the anchored route, the canonical transport contract expresses digest word 5 as predecessor state a59 plus the compiled late-round contribution T1_62 and fixed initialization word IV5; evaluating that compiled contribution uses four reduced T1 primitives.

digest_word5 = a59 + T1_62 + IV5 (mod 2³²)reduced evaluation path: 4 T1 primitives = 52 diagnostic unitsaction strata={ACCEPT,DEFER,REJECT}
R59 predecessor transportThe canonical affine identity uses a compiled four-T1 reduced evaluation path.EXP-053 / R59 PREDECESSOR TRANSPORTa59predecessorT1_62 + IV5compiled termDIGEST WORD 50 errors
FIGURE / RESULT READINGThe canonical affine identity uses a compiled four-T1 reduced evaluation path.
03 / Method

How it was tested

Derive the affine predecessor identity, verify constant invariance on generic and reachable states, stratify 15,000 records equally across the three actions and repeat the entire package independently.

04 / Observed result

What happened

Records per replicate15,000
Reduced T1 terms4
Identity errors0

Each replicate contained 5,000 ACCEPT, 5,000 DEFER and 5,000 REJECT records. Affine, reachable, constant-invariance, B64, stratum and action-safety errors were all zero. The reduced interface used four T1 terms and 52 diagnostic primitive-work units.

05 / Validation

Exactness and statistical controls

Balanced strata prevent the dominant reject class from hiding failures in rarer actions. Two independent replicates verified both generic identities and reachable anchored states.

06 / Interpretation

What the result means

V53 transports an exact target relation one predecessor step with a compact expression. It is a representation capability, not proof that computing the predecessor fiber is cheaper than forward SHA-256.

Limitations

  • The 52-unit count is not a native benchmark.
  • Balanced strata are deliberately not natural prevalence estimates.
  • Only one anchored predecessor interface is covered.
07 / Reproduction

Evidence trail

Recompute the four T1 terms and IV5 feedforward, verify the identity on generic/reachable states and audit 5,000 records per action in two replicates.

Canonical variants

SUBENGINE-V53ASUBENGINE-V53BSUBENGINE-V53C

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