Floor Raising

A floor raise increases the guaranteed minimum price f without adding capital to the reserve and without moving the spot price. It works by trading area between segments of the price curve. The ramp advances into territory that was priced on the main schedule, and because the ramp runs below the main through that stretch, the area it gives back pays for a taller floor.

Precondition

Supply must sit strictly above x2, the ramp-main boundary. Equivalently, the spot price must lie on the main schedule.

If supply is inside the ramp or the floor region, x2 has nowhere to advance and no area deficit exists to redistribute. An area-preserving raise is unavailable in those states.

What is held invariant

Three things do not change across a raise.

Reserve. The area under the curve from zero to current supply is identical before and after. No capital enters and none leaves.

Spot price. The price at current supply does not move. Only the floor moves.

Main schedule. M(x) is untouched. Both slopes keep their values. The raise operates on the floor and the ramp alone.

What changes

The floor f rises. The ramp adjusts so that, at its steeper slope, it still connects the new floor to the unchanged main schedule. Both x1 and x2 advance, so the ramp widens and the floor region grows behind current supply.

The new ramp is whatever position satisfies area preservation:

integral from 0 to x of y_new(s) ds  =  integral from 0 to x of y_old(s) ds

The main schedule is held fixed throughout, so the raise resolves against the floor and the ramp alone.

Why the reserve survives it

The ramp constraint states that R(x) < M(x) throughout the transition zone. When x2 advances, a strip of curve that was priced on the gentle main slope is replaced by the steep ramp, which sits lower there. That substitution decreases the area under the curve. At the same time, raising the floor increases the area of the floor rectangle. The two changes are equal and opposite, and the reserve comes out unchanged.

Another way to read it: the ramp declines to use some of the area the main schedule would have occupied, and the unused difference is the budget. Every raise spends part of that budget.

The ceiling

A raise is bounded by how far supply sits beyond the ramp-main boundary. The ramp can only advance into territory that supply has already passed; push the boundary past current supply and the spot price would move, which breaks the invariant. The further out a market has traded, the more headroom a single raise has, and a market sitting just past the boundary has almost none.

Example

Take a market whose floor is 0.10 and whose spot price is 0.19, with supply well past the ramp-main boundary so a raise is available.

Raising the floor to 0.12 widens the ramp, advances the boundary, and keeps it below current supply. The floor ends up 20 percent higher. The spot price is still 0.19 and the reserve is the same size. What moved is the split: guaranteed value per token went from 0.10 to 0.12, and the discovery pocket shrank by the matching amount.

Interaction with contraction

Contraction and raising are complementary operations rather than mirror images. A sell into the ramp or floor lowers the main schedule and pulls x2 backward. That lowers the bar for the next raise, because any subsequent buy that carries supply past the retreated x2 re-enables the mechanism, possibly at a lower price level than before.

The cycle runs like this. Supply sits above x2 and a raise is available. A large sell pushes supply down; the main schedule drops and x2 follows it back. New buys lift supply past x2 again. A raise becomes available, increases f, and slides x2 forward along the now-lower main schedule. In the extreme case where supply returns to zero, the very next buy puts supply beyond x2 immediately.

Sell pressure therefore does not disable the floor mechanism. It relocates the threshold that governs when a raise can occur.

Related

• The Assured Value Machine for the curve, the segments, and the reserve identity.
• Cash advance, whose capacity is a direct function of f.