the papers everyone builds on carry proofs nobody ever stress-tested. we built a pipeline that attacks them at their weakest joint — and when a theorem fails, we don't just report it. we prove the boundary: which settings survive, which die, how fast the failure grows, and what it takes to repair it.
23 proven breaks · 2 complete correction packages
every break here survived our own adversarial checking — exact arithmetic, independent reconstruction, and formal certificates where the math allows them. a few may be independently known; we audit novelty before we claim priority.
two theorems, taken apart completely.
a widely used ai score is only valid at one setting. we classified all of them.
the formula — cited by 175 papers — is supposed to measure how related two things are, and never go below zero. we didn't find one bad case. we classified the entire family: exactly one setting survives, and at every other setting we construct exact failures, prove the smallest one possible, and show the violation grows without bound at the fastest order mathematics allows. the core certificate is verified in lean.
the violation doubles, triples, and keeps growing as the witness is squared — exact values from the amplification theorem, i(r) = r · i(1), n = 4^r. no construction can fall faster than logarithmically; this one falls logarithmically. it never comes back above zero.
the headline guarantees of random forests were proven for software nobody runs.
random forests are everywhere in statistics and machine learning. the field's headline consistency proofs quietly swap the real, finite method for an idealized one that averages over every possible tree. we constructed the exact setting where the published guarantee fails no matter how much data you add — then wrote the correction and derived the condition that actually restores the theorem.
b = 1 · θ̂ ∈ {−1,+1} — one tree, any amount of data · claimed error → 0, real error never moves