The composed system, certified as one system.
ProvenOur published stability certificate carried one item marked pending in its own claims ledger: the guarantee for the whole assembled system over time, rather than for each layer separately. That item is now a machine-checked theorem in Lean 4. The system provably forgets its starting condition at an exact rate, so containment is temporary by mathematics rather than by promise, and its internal load is provably proportional to what it is given. Under sustained recovery that load settles to an explicit level at an explicit rate. The analysis also exposed a small standing bias in our own coupling design, active whenever presence is absent. We stated it inside the theorem rather than folding it into a constant. We then drove the exact production code against the certified bound with 25,000 randomized inputs and found zero violations.
