Store the law, discard the data — at1 ruletier
For a law-governed signal — a trend plus a dominant periodicity — you don’t need to keep the samples. at1 ruletierkeeps only the generator and a residual certificate, then regenerates the signal on demand within a certified bound: 1,261× smaller on a real certified trend+periodic signal. The certificate is issued only if its bound covers held-out data, and the tool refuses to certify a signal that isn’t law-governed— a random walk fails the gate. A certificate that can’t fail is no certificate.
Use it
# 1) store only the generator + a holdout-validated residual certificate
at1 ruletier store signal.csv -o signal.at1rule
# CERTIFIED (explained_var=0.992, holdout_coverage=0.999, q99.9 bound=2.67); 1261.8x reduction
# a random walk? -> REFUSED to certify (not law-governed)
# 2) regenerate on demand, guaranteed within the certified bound
at1 ruletier regenerate signal.at1rule -o out.csv
# 3) re-check the certificate
at1 ruletier verify signal.at1ruleWhat it guarantees
- Bounded reconstruction — every regenerated value lies within the q99.9 residual bound.
- Holdout-tested — the certificate must cover held-out data before it is issued.
- Refuses noise — an unlawful signal is rejected rather than falsely certified.
The certificate is statistical (a q99.9 bound), not an absolute guarantee — it needs enough samples to pin the periodicity, covers one law family (trend + sine) today, and stores lossless for the uncovered tail. For an exact, byte-identical generator, use generator discovery instead.