mathguard — Math-Heavy Optimization for AI Code

lemmaly makes you pick the right classical algorithm. mathguard kicks in when the classical algorithm is already optimal but mathematics gives a better bound — usually by accepting bounded approximation, exploiting structure, or moving to a smarter algebraic space.

The model knows these techniques. It almost never proposes them spontaneously. mathguard fixes that.

Violating the letter of these rules is violating the spirit of the skill. A Bloom filter where the caller assumed exact answers is a production incident, not an optimization.

The Iron Law

NO APPROXIMATE STRUCTURE WITHOUT WRITTEN ε/δ AND EXPLICIT CALLER ACCEPTANCE

Probabilistic data structures (Bloom, HyperLogLog, Count-Min, MinHash/LSH, t-digest), randomized projections (JL), and lossy transforms (floating FFT) all change the answer's meaning. Before proposing one:

1. Write the error parameter the caller will see (false-positive rate, relative error, distortion bound).
2. Identify the caller and state, in one sentence, that they tolerate this kind of wrong answer.
3. If you cannot identify the caller, or they need exact (auth checks, billing, dedup keys, deduplication for correctness, anything that flows into a primary key), DO NOT propose the approximate structure. Keep classical, or escalate to a sharded/streaming exact design.