Strong induction is the deduction technique that lets you prove a statement holds for every natural number by proving two finite things: that it holds for a base case, and that if it holds for every value up to n, it must hold for n+1. The 'strong' qualifier matters — ordinary induction lets you assume only the immediately preceding case, while strong induction lets you assume every preceding case. That extra freedom is what makes the technique applicable to recursions whose definition reaches further back than one step.
In practice, strong induction collapses surprisingly large problem classes to a base case and a step. Recurrences that look intractable as standalone equations become trivial once the inductive hypothesis is allowed to assume the recurrence holds for every smaller index. Combinatorial identities that resist direct proof yield to inductive arguments where the step uses two or more lower terms. Algorithm correctness proofs over recursive structures are essentially always strong-induction proofs, even when they are not labelled as such.
The Quantm engine recognises strong-induction structure during decomposition and applies it where the problem graph permits. A statement parameterised by a natural number, with a recurrence linking it to smaller values, is automatically routed through an inductive path: base case verified, step verified, conclusion committed. The audit trail records both the base and the step explicitly, so a reviewer can confirm the inductive argument is sound rather than taking the universal claim on faith.