The formal condition

What load band makes a system bistable, and why does amplification set it rather than headroom?

This formula is short, and it is the whole subsection. Let:

λ = the base arrival rate (useful demand),
C = capacity,
k = the work amplification factor in the degraded state: the number of units of work the system performs per unit of useful demand once retries fire, caches miss and timeouts trip.

The healthy state is stable if λ < C. The broken state is stable if λ × k > C (the system is still overloaded in the degraded state, so it stays degraded). Both are true at the same time when

RelationshipThe metastable band →

C / k < λ < C

$λ$: the base arrival rate (useful demand)
$C$: capacity
$k$: units of work per unit of useful demand once retries fire, caches miss and timeouts trip

Data table

Utilization above which a broken state can sustain itself, by degraded amplification
Degraded amplification k	Vulnerable above this utilization
1	100%
1.11	89.9%
1.23	81.6%
1.34	74.8%
1.45	69%
1.56	64%
1.68	59.7%
1.79	55.9%
1.9	52.6%
2.01	49.7%
2.13	47.1%
2.24	44.7%
2.35	42.6%
2.46	40.6%
2.58	38.8%
2.69	37.2%
2.8	35.7%
2.91	34.3%
3.02	33.1%
3.14	31.9%
3.25	30.8%
3.36	29.7%
3.48	28.8%
3.59	27.9%
3.7	27%
3.81	26.2%
3.92	25.5%
4.04	24.8%
4.15	24.1%
4.26	23.5%
4.38	22.9%
4.49	22.3%
4.6	21.7%
4.71	21.2%
4.83	20.7%
4.94	20.3%
5.05	19.8%
5.16	19.4%
5.28	19%
5.39	18.6%
5.5	18.2%
5.61	17.8%
5.72	17.5%
5.84	17.1%
5.95	16.8%
6.06	16.5%
6.17	16.2%
6.29	15.9%
6.4	15.6%
6.51	15.4%
6.63	15.1%
6.74	14.8%
6.85	14.6%
6.96	14.4%
7.08	14.1%
7.19	13.9%
7.3	13.7%
7.41	13.5%
7.53	13.3%
7.64	13.1%
7.75	12.9%
7.86	12.7%
7.97	12.5%
8.09	12.4%
8.2	12.2%
8.31	12%
8.43	11.9%
8.54	11.7%
8.65	11.6%
8.76	11.4%
8.88	11.3%
8.99	11.1%
9.1	11%
9.21	10.9%
9.32	10.7%
9.44	10.6%
9.55	10.5%
9.66	10.3%
9.78	10.2%
9.89	10.1%
10	10%

Principle: Variance costs more than volume →

That band is the metastable region. In it the system is fine, and would be equally content being broken.

Two stable states at one loadC = 2,000/s · k = 4

So the quantity that governs your exposure is not headroom. It is k. Headroom sets where the band ends (at C). k sets where it starts (at C/k). And k is the parameter nobody measures.