EXP-049VALIDATED
Advantage Decomposition / SHA-256

B64→B72 cross-word backward capability

The target ladder can cross from B64 into digest word 5 by reconstructing the exact e63/feedforward relation and evaluating the next target byte backward from the final digest.

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 e63/feedforward from each anchored state, verify B64, test the next eight bits lazily and compare with the complete 256-bit target decision in both replicates.
01 / Question & hypothesis

What was tested?

The target ladder can cross from B64 into digest word 5 by reconstructing the exact e63/feedforward relation and evaluating the next target byte backward from the final digest.

02 / Scientific basis

Why the test is meaningful

A byte boundary crossing changes which final state word supplies target bits. SHA-256 state shifting gives a deterministic relation between late-round e63 and digest word 5; preserving that identity is necessary for a safe incremental decision.

B72 = B64 ∧ next8(word5)digest_word5 = e63 + IV5 (mod 2³²)incremental decision = first differing bit of word5 byte0
Backward bridge into word 5The e63 feedforward identity transports the comparison from B64 to B72.EXP-049 / BACKWARD BRIDGE INTO WORD 5B64conditione63 + IV5mod 2³²B720 errors
FIGURE / RESULT READINGThe e63 feedforward identity transports the comparison from B64 to B72.
03 / Method

How it was tested

Condition on exact B64 records, reconstruct e63 and digest word 5, evaluate the next byte in lazy bit order and repeat two independent 20,000-record campaigns against the full suffix.

04 / Observed result

What happened

Mean work A / B45.799 / 45.938
Median work46
Exactness errors0

Both replicates reported zero B64-condition, e63-relation and full-suffix errors. Mean incremental B72 work was 45.799 and 45.938 units, with median 46 in both. Most rejections occurred in the first few tested bits.

05 / Validation

Exactness and statistical controls

Two independent replicates exercised the cross-word identity and every final target decision. The contract explicitly classifies this as a capability, not a mining submotor.

06 / Interpretation

What the result means

V49 validates the second cross-word bridge. Exact backward comparison can continue into word 5, but the measured work has not been shown cheaper than a native complete implementation.

Limitations

  • The experiment begins from B64-conditioned records.
  • Diagnostic work units are not ASIC cycles.
  • The capability tests target compatibility; it does not generate candidates.
07 / Reproduction

Evidence trail

Recompute e63/feedforward from each anchored state, verify B64, test the next eight bits lazily and compare with the complete 256-bit target decision in both replicates.

Canonical variants

SUBENGINE-V49ASUBENGINE-V49BSUBENGINE-V49C

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