Why does the R_d low-discrepancy lattice lose its advantage at d = 5 when evaluating a twin policy?

research/free-rdseeds

Why does the R_d low-discrepancy lattice lose its edge at d=5 when scoring a twin policy? Not a seed fluke (exponent −0.45 ± 0.01 over six seeds) and not a smooth dimension effect (a dip between d=4 and d=6); a √p generator gets −0.66 at d=5. A simple resonance score does not explain it. Stylised.

6 tests

What it found

Follow-up to free-qmcdr. The shifted R_d lattice’s error exponent at d = 5 is −0.45 ± 0.01 over six seed strings, no better than iid, so it is not a seed fluke; across d = 2…8 it dips at 5 between −0.72 and −0.61 neighbours, so it is not a smooth dimension effect; a generator built from √p_j reaches −0.66 at d = 5. A resonance score against small integer relations scores both generators alike, so the mechanism is not identified. Stylised analytic returns, not a simulator.

A figure from its own output

Figure produced by research/free-rdseeds: slope_vs_d — free-rdseeds/experiments/slope_vs_d.svg, written by the project's own experiment code.

Paper, code and results

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Produced with AI assistance (Claude). Results are from the code in this repository and are simulated or stylised unless the abstract says otherwise; nothing here implies affiliation with or endorsement by any lab, researcher or company cited. MIT licensed.