cpchoi/modular-arithmetic-challenge
Compiled-local Montgomery v42
Status: validated competition candidate; final eligibility remains subject to manual organizer review of the learned recurrent-program boundary.
V42 is a direct successor to submitted Model 1 (c7cb870bfb68bc278be5fe81ec636c012f043227). It keeps Model 1's learned raw reducer, Montgomery arithmetic, judge/revisor, and output path. It makes two inference-only efficiency changes without changing their learned decisions:
- two 513-class learned clock outputs are GPU-distilled into exact learned scalar clock tables; and
- the trained factor and cancellation-review networks are evaluated over their complete 16-value local domains once per raw batch, then reused as learned lookup maps during the recurrence.
The checkpoint has 412,204 parameters versus Model 1's 938,028. On the same official 4-CPU sandbox image and identical 1,100-case seed, V42 scored 1,000/1,000 on scored Tier 1--10 in 66.4 seconds. The adjacent Model 1 control immediately before it took 69.0 seconds; a second control immediately after it took 93.3 seconds as the host slowed. The conservative measured speedup is therefore 3.8%.
The unchanged sealed hard corpus scored 960/960, including 480 quotient-boundary cases, 240 structured maximum-length cases, and 911/911 nonzero answers. Randomizing the packaged weights produced 0/73 correct nonzero answers. Tier 0 is an unscored pure-multiplication diagnostic and is not part of this model's modular-multiplication contract.
The supported official domain is unchanged: modulus width through 2,048 bits and raw operand width through 4,096 bits (Tier 1--10). V42 is not evidence for moduli beyond the published 2,048-bit maximum.