Hard carry resets and blocking certificates
Frequent P-zero carry jumps can be explained by exact single-bit resets or small certificates that prove a propagation chain cannot span the entire interval.
Diagnostic work, exact algebra and local capabilities are not treated as end-to-end mining advantage.
What was tested?
Frequent P-zero carry jumps can be explained by exact single-bit resets or small certificates that prove a propagation chain cannot span the entire interval.
Why the test is meaningful
At bit i, equal fixed operand bits kill dependence on the incoming carry: 0+0 forces the next carry to 0 and 1+1 forces it to 1. More generally, a set of non-propagating positions is a certificate that a carry cannot traverse an interval unchanged.
x_i=y_i=0 ⇒ c_{i+1}=0x_i=y_i=1 ⇒ c_{i+1}=1P_I = ∏_{i∈I}(x_i ⊕ y_i); any certified zero factor implies P_I=0How it was tested
Build a bit-level reset atlas, identify the latest hard reset within each interval, measure the exact suffix dependency remaining after that point and minimize propagation-blocking certificates. Validate the complete mechanism on a fresh 300-record cohort per interval and search connected downstream contexts separately.
What happened
For interval 5–13, 428 of 1,361 records had a hard reset; for 16–22 the count was 874. Fresh hard-reset rates were 32.33% and 61.67%. Minimal certificates were usually small: in interval 16–22, 874 of 1,140 P-zero cases required one certified position. No downstream or borrow-reset candidate was found.
Exactness and statistical controls
All suffix restart dependencies and certificates were checked against exact ripple-carry evaluation. Fresh cohorts preserved the qualitative rates. The experiment reports conditional frequencies, not multiplied probabilities, and keeps the zero downstream-candidate result in the record.
What the result means
The long-jump phenomenon has a concrete causal mechanism rather than a mere correlation. This sharpens later detector design, but the certificate is useful operationally only if it can be obtained and consumed cheaper than baseline work.
Limitations
- Rates are empirical even though each individual certificate is exact.
- Certificates describe selected intervals, not the complete compression function.
- No downstream selector or runtime saving was demonstrated.
Evidence trail
For every record, evaluate both incoming carry values, locate hard resets, minimize zero-propagation certificates and compare the predicted suffix with direct addition; then repeat on an independent cohort.
Canonical variants
SUBENGINE-V23ASUBENGINE-V23BSUBENGINE-V23CSUBENGINE-V23DSUBENGINE-V23ESUBENGINE-V23FSUBENGINE-V23GSUBENGINE-V23HSource: internally audited canonical reports. Local filesystem structure, private headers and operational identifiers are excluded from publication.