Resilience and Cascades

PXS promises no price. The design notes argue that it fails gently rather than suddenly: it has no cliff to fall from and no tightly coupled web to carry a collapse. This page tests that argument with two ideas, resilience and self-organised criticality, and with the chain's own numbers.

Resilience

C. S. Holling (1973) separated two properties that are easy to confuse. Stability is a system's tendency to return to an equilibrium after a disturbance. Resilience is its ability to absorb disturbances and still keep the same relationships between its parts. A useful picture is a ball in a landscape of valleys. Each valley is a basin of attraction; the ridges between valleys are thresholds; a push that carries the ball over a ridge leaves it in a different regime.

Walker, Holling, Carpenter and Kinzig (2004) gave resilience four aspects. Applied to PXS on 2026-10-06:

The thresholds are on Chain Parameters; the numbers behind the first three rows are on Haircut, Corridor and Settlement.

One regime or two

A defended peg has two basins. In one, the peg holds. In the other, it has broken, and returning from there is costly when it is possible at all.

PXS's conversion value has one. Above a collateral ratio of 7/3, the haircut factor is 1. Below it, the factor falls in a straight line, and when the ratio recovers, it rises back along the same line. There is no separate state to fall into. The print stop is a step, not a slope, but it too reverses as soon as the debt ratio falls below 20%, because the chain recomputes the print rate in every block.

A market price is another matter. What the protocol defines is the conversion value. A market can still leave it far behind: SBD closed at 13.76 US dollars on 2017-12-19 and at 0.52 on 2019-11-13, while its conversion delivered about a dollar and about 70 cents (From SBD to PXS). A market can also lose its buyers. PXS has no market yet, so none of this has been observed for it.

How much dilution the haircut allows

Conversions out of PXS create PIXA. Without a limit, converting every PXS after a collapse in PIXA's value would create PIXA in proportion to the collapse. The haircut limits each hour's price: at the corrected price, all PXS outside the treasury is worth exactly 3/7 of all PIXA (the haircut).

The limit applies to each hourly price. As conversions burn PXS and add PIXA, the next hour's limit relaxes. The haircut slows dilution and reduces its total; it does not end it.

Self-organised criticality

Per Bak, Chao Tang and Kurt Wiesenfeld (1987) described systems that drive themselves to a critical state. Their example is a sandpile built one grain at a time. The pile steepens until it reaches a critical slope; from then on, a single grain can set off an avalanche of any size, and avalanche sizes follow a power law, with no typical size. Large events need no large cause. Bak and Kan Chen, whom the design notes cite, described the idea for a general audience in 1991.

The design draws a lesson from it: in a critical system you cannot prevent avalanches by hunting for triggers, because the triggers are ordinary grains. You manage the slope and the connectivity, which decide how far a disturbance travels before it dies out.

The couplings

Where the slope is steep

• Leaving the placeholder. Every distance to a threshold is still computed mostly from an assumed price. PIXA has traded on one market since 2026-10-15, and on 2026-11-03 the witnesses' market readings ranged from 31.731 to 70.792 PIXA per PXS against a median of 51.000. Once most scheduled witnesses read the market, the median moves to their middle feed within about two days, and the collateral ratio by the same factor (Oracle and Price Feed).
• The treasury's PXS. 95.11% of all PXS sat outside the ratios on 2026-11-03. Paid out to proposals and held, all of it would bring the collateral ratio to about 7.6 at that day's median, within a factor of two of the print stop at 4.
• The allocations. About 66.8% of all PIXA, on 2026-11-03, is stake that the two allocation accounts have still to distribute (Genesis and Distribution). How it reaches the market will shape PIXA's market value, and through it every ratio above.
• Correlated failure. Until mid-October, one feed program, one placeholder and a small set of voters made the parts of the system fail together rather than independently. By 2026-11-03 the feeds came from several programs and countries, and 23 accounts voted for witnesses, but every market reading still reads one order book.

The design's claim, assessed

The design notes say the supra is "engineered not to be un-shockable, but to be non-cascading". Part by part:

Inherited → changed

Sources

• C. S. Holling, "Resilience and Stability of Ecological Systems", Annual Review of Ecology and Systematics 4 (1973), 1–23.
• B. Walker, C. S. Holling, S. R. Carpenter and A. Kinzig, "Resilience, Adaptability and Transformability in Social–ecological Systems", Ecology and Society 9(2): 5 (2004).
• P. Bak, C. Tang and K. Wiesenfeld, "Self-organized criticality: An explanation of the 1/f noise", Physical Review Letters 59 (1987), 381–384.
• P. Bak and K. Chen, "Self-Organized Criticality", Scientific American 264(1) (January 1991), 46–53.
• PXS design notes (Pixagram, June 2026), §3.2, §5.3, §5.4 and §8.1.
• Live values, read at block 917,250 on 2026-10-06: condenser_api.get_dynamic_global_properties, condenser_api.get_feed_history, condenser_api.get_accounts.