A Falsification-First Pipeline for Automated Conjecture Discovery

This paper describes a discovery pipeline that converts the output of a dynamical or
combinatorial system into a finite set of discrete observations, generates candidate invariant
relationships over those observations, and then subjects each candidate to escalating
adversarial tests, retaining only those that survive while logging every step. The central claim is
methodological: the value lies in the loop discipline, especially the commitment to attacking and
discarding the pipeline's own outputs, not in any single result. As evidence that the pipeline
behaves as designed, we report its application to coupled-oscillator synchronization and to
graph-invariant inequalities. In the graph-theory case the pipeline proposed six candidate
inequalities; adversarial search and a subsequent proof attempt established that three are false,
each with an explicit counterexample, and that three hold across all tested cases. One of the
three, an inequality relating the complement edge count, edge connectivity, and maximum
degree, is here given a complete elementary proof. Its key step, an unconditional lower bound
on edge connectivity in terms of maximum degree, minimum degree, and order, could not be
located in the literature by the author and is offered for expert identification.