Knowledge decay may not be a slope. It may be a cliff you cannot climb back up.

Knowledge stores are usually described as decaying smoothly. Notes go stale at some rate, so the health metric is a level: what fraction is out of date, how old the average fact is. Cleanup is then a maintenance chore you can do whenever.

There is a different possibility worth testing, and it changes what you would measure.

The claim. Staleness may not degrade a store's usefulness linearly. It may hold, and then fold — because stale facts reinforce each other. A stale fact that gets retrieved is more likely to be cited, and a stale fact that gets cited is more likely to be written into the next summary, which is then retrieved. Past some fraction, that loop wins. If so, the useful variable is not the stale level but the distance to the point where the loop takes over.

What we measured, and exactly what it was. We built the smallest model with that feedback in it — a standard minority-tipping template where each item's state depends on its neighbours' states, with coupling J=2.0 and a small external pull h=0.15 — and swept the stale fraction. Two numbers came out:

• the model flips discontinuously at a stale fraction of 33.4%, not gradually;
• the recovery edge is 0% — within the model's dynamics, removing stale content after the flip does not restore the healthy state at any level short of removing all of it. Full hysteresis, width 33.4 points.

The threshold is not the alarming part, and the run's own verdict says so: ROBUST. A third of a store has to be stale before anything tips, which is a long way from where a maintained store lives. If the finding were only "there is a cliff at 33%", the honest response would be to stop worrying about it.

The other number is the one worth attention. A recovery edge of 0% says the two directions are not symmetric — the fraction you can safely carry on the way up is not the fraction that gets you back down. Under smooth decay those are the same quantity and cleanup timing is purely a matter of cost. Here they are not, and cleanup after the flip is close to useless. That is an operational difference even for a store that never goes near 33%.

This is a model result, not a measurement of any real system. Nothing here says a production knowledge base behaves this way. It says that if the reinforcement loop is present at all, smooth-decay intuitions are the wrong ones, and it gives a concrete shape to look for.

Why it is worth the trouble. The two readings imply opposite operational advice. Under smooth decay, cleanup scales with how much staleness you have, and doing it later costs proportionally more. Under a fold, cleanup before the threshold is cheap and cleanup after it barely works — so the money is in prevention and in knowing your distance to the edge, not in periodic tidying. Those are different products.

The falsifierThis dies if usefulness in a real store degrades smoothly and reversibly: sweep the stale fraction in a live retrieval system, measure answer quality, and if the curve is a straight-ish line and cleaning up recovers what decay cost, there is no fold and the smooth model was right all along.

What would change our mind, including something that already argues against us. We have separately measured that a memory layer with correction machinery — retiring superseded facts, refusing to resurrect them — does not beat a plain keep-everything store on answer accuracy at matched retrieval budget: 0.593 versus 0.592, no separation, and that was the third independent null pointing the same way. If corrections mattered as much as a hysteresis story implies, that difference should have shown up somewhere. It has not, in anything we have run.

The honest reconciliation is that this model predicts a regime — high stale fraction, strong reinforcement — and our accuracy tests may simply never have entered it. That is a testable statement rather than a save, and the test is the falsifier above. Until someone runs it on a live store, this is a shape worth looking for and not a finding to act on.

Prior art, since none of the machinery is ours: fold bifurcations, hysteresis and critical transitions are textbook dynamical systems, and the early-warning-signal literature on approaching thresholds long predates us. What we contribute is the mapping onto knowledge decay and a runnable minimal model with the numbers above.