# Fil+ indefinite and collaterals

## Short summary
One proposal that is being discussed is to grant FIL+ status to verified data for an indefinite time. Currently FIL+ status is restraint by the sector lifetime.

We argue that if FIL+ status is to be made eternal as being discussed [here](https://github.com/filecoin-project/FIPs/discussions/313), and independent of the sector, there should be a corresponding FIL+ collateral that is also independent of the sectors. This will help counteract the large change in incentive dynamics that FIL+ indefinite introduces.

## Background on FIL+ and collateral

The amount of FIL+ deals on a sector play a significan role in the computation of that sector's collateral. Having a sector filled with verified data will give a 10X factor to the block rewards, but the sector must also be sealed with 10X of collateral.

Let's consider a sector with storage capacity of $\mathcal{X}$, which contains an amount $x_+$ of verified data. We will assume there is a deal to store this data for the whole lifetime of the sector.

The sector then receives a quality multiplier,
$$q=\frac{(m-1)x_++\mathcal{X}}{\mathcal{X}},$$
where $m=10$ (but we keep the notation general, as the particular number is not important here).

The collateral is pledge when sealing this sector, and consists of a storage pledge ($SP$) plus a consensus pledge ($CP$). Both of these quantities are directly proportional to $q$. The pledge is made at time $t_0$, using network information available at that time.

The storage pledge involves making a prediction on how the amount of block reward the sector is expected to receive in the following 20 days.
$$SP=q\mathcal{X}\int_{t_0}^{t_0+20d}\frac{R(P)}{QP}dt$$
where $P$ is the total network raw power, $Q$ is the average network quality multiplier, and $R(P)$ is the total new block rewards minted, which are solely a function of $P$. This integration, 20 days into the future involves making a prediciton of the quantities in the integrand.

The consensus pledge is given by
$$CP=q\mathcal{X}\frac{fS}{{\rm MAX}(QP,B)}$$
where $S$ is the total circulating supply, $f=0.3$, and $B$ is the baseline power function. This part of the pledge depends only on quantities that are known at $t_0$ and doesn't involve prediction.

## Decreasing collateral, terminating and resealing.

Given the expectation that network power, $P$ should generally grow over time, and that block rewards will decrease while circulating supply has a maximum possible cap so cannot grow indefinitely, We expect that both $SP$ and $CP$ will generally decrease over time in th long term.

If the sector is sealed for an amount of time $T$, then there exits the opportunity, when a sector commitment expires, to terminate the sector, recover the locked collateral, and reseal a new sector with a lower collateral.

This has the benefit to the storage provider of giving them more liquidity, being able to use their funds that were locked, at the cost of paying extra resealing fees.

We define $V[x]$ as the monetary *value* the Storage Provider places on releasing $x$ amount of their own funds from being locked. This function is subjective, and depends on the storage provider.

A storage provider will then terminate and reseal their sector when $V[CP(t_0)+SP(t_0)-CP(t_0+T)-SP(t_0+T)]$ is higher than the associated resealing costs.

Termination and resealing in turn can be less desirable to the network, as this generally means an increase in the total circulating supply, as well as an incentive to seal the sector for the lowest possible lifetime, $T$.

At the moment, a FIL+ deal lives only in the sector it is sealed. When that sector reaches the end of its lifetime. The storage provider would terminate and reseal a new sector, but they would not have that FIL+ piece of data available. **This means currently there exists an incentive to seal for the longest lifetime possible, if the sector contains FIL+ deals.**

## The incentive change of FIL+ indefinite

With making FIL+ indefinite terms that live outside of deal lifetimes, there is a change in incentive where Old FIL+ data will be incentivized to be stored for indefinitely long times, even when the client no longer has any interest in it being stored. This is especially the case if the collateral structure remains sector based.

A storage provider will seal their FIL+ data into a sector, earning $q*m$ times the block reward but also paying $q*m$ times the collateral. At the end of the sector lifetime, the storage provider can terminate their sector, recovering all the collateral, and resealing with a lower collateral.

Where there previously existed value for the storage provider in doing the terminate and reseal process, this extra liquidity is now multiplied by $q*m$, increasing the incentive to seal for the shortest times possible.

There is also a new incentive to just keep indefitely old data stored forever, even when the client isnt interested in this anymore. Old FIL+ data is as valuable as new FIL+ data.

With total block rewards given decaying exponentially over time, Filecoin already rewards early investors disproportionally. This adds another layer to this. Forever FIL+ will be disproportionately more beneficial to the earliest adopters. Later on in the future there will be a pool of more and more old FIL+ still being stored, diluting the FIL+ reward.

## Proposal: FIL+ collateral

Following the overall goal of decoupling FIL+ data from sectors, we propose that the solution to counter the above incentive changes is to also decouple the fraction of the collateral that corresponds to the FIL+ data.

Sector collaterals would be independent of FIL+ data being stored or not, and would be set as the collateral of an empty sector:
$$SP=\mathcal{X}\int_{t_0}^{t_0+20d}\frac{R(P)}{QP}dt,$$
$$CP=\mathcal{X}\frac{fS}{{\rm MAX}(QP,B)}$$

FIL+ status will now a property of the piece of data, rather than a property of the deal where it is contained. We propose that a FIL+ pledge collateral (FP) must be posted at the moment of granting that FIL+ status to the data. The amount of FIL+ collateral would be
$$ FP=(m-1)x_+\left[\int_{t_0}^{t_0+20d}\frac{R(P)}{QP}dt+
\frac{fS}{{\rm MAX}(QP,B)}\right]$$

Such that $SP+CP+FP$ add up to our current definitions of the initial pledge. However the FIL+ dependent part is treated separately.

The collateral, $FP$ is **locked as long as the piece of data retains FIL+ status. It cannot be reduced by terminating and re-sealing the sector where the data was stored. The only way to release the collateral is to terminate the FIL+ status of the data.**

## FIL+ collateral and restoring incentive balance

The idea of having a separate FIL+ collateral that cannot be reduced by terminating the sector effectively counteracts the two large changes in incentives introduced by the FIL+ indefinite proposal.

First, there would no longer be a $q*m$ times increased incentive to seal the shortest sectors possible. The amount of liquidity that can be retrieved by terminating and resealing a sector is constraint to the sector collateral, which does not benefit from the quality multiplier. This restores this incentive to its status quo.

Second, the incentive to store old FIL+ data unconditionally is also countered. Suppose a storage provider seals a sector with FIL+ data at time $t_0$, paying a FIL+ collateral $FP(t_0)$. The sector expires at time $t_0+T$. At this time, if there is enough supply of new FIL+ data, the storage provider would be incentivized to terminate the FIL+ status of the original data, retrieve the collateral, and store a new piece of FIL+ data which for which they need to pay a lower collateral $FP(t_0)$.

If a client is interested in having their FIL+ data stored forever, then they would actually need to pay the future differences in collateral required to keep their data profitable. That is, for instance at time $t_0+T$, the client would need to pay a difference $V[FP(t_0)-FP(t_0+T)]$, to keep the storage provider from dropping their old data and obtaining new more profitable data. This restores the status quo, where FIL+ status should not be a mechanism for the client to have their data stored forever.