Four studies separating whether a model is doing the mathematics or matching its surface
LOGIS is a set of studies on how language models handle mathematics, built around a single question: when a model solves a problem, is it using the structure, or recognising the shape of something it has seen before. The designs separate the two. Some seed a model with a closed formal system, glyphs and grammar and inference rules and nothing else, and let a proof checker be the only feedback, so there is no natural language to lean on. Others alter the rules so that memorised classic results become mechanically false, which a model reasoning from structure survives and a model recalling does not.
A proof-checker kernel is the only feedback signal: accepted or rejected, per line, with no interpretation of any symbol
Rule-altered arms make memorised theorems mechanically false, which separates deriving from recalling
First study complete: 33 goal-free runs across three substrates at three seeds, plus forced-engagement, a depth curve, and a syntactic-mimic baseline
Public monorepo: four study designs, pre-registered before any run