The following lays out a suggestion for a mining and minting model that aligns the interests of different players in the ecosystem of a new POWbased cryptocurrency. It is inspired by Primecoin’s mechanism.
Tl;dr
 Inflation never increases; inflation decreases as new hashrate joins
 Lower bound on final inflation (to guarantee sufficient perpetual security budget)
 Inflation decreaserate capped (to keep the mechanism in check and soften the effect of new hashrate)
 Total supply (per x years) is upper bounded but not fixed; early hodlers guaranteed that their holding can only improve; decreased supply → greater relative holding
 Hodlers incentivized to contribute to mining so as to secure the network AND decrease inflation rate
 Several benefits of this mechanism for decentralization of mining as well as decentralization of hodling (existence of early supply to meet early demand)
Main question: What should be the issuance schedule?
This is important in several contexts, of course, but also in the biz model context – what’s the correct model for incentivizing and sustaining a base layer protocol organization?
Premine, or other forms of inprotocol compensation for the founding team and its investors (such as founder rewards), are schemes that have been criticized for many reasons. I suggest below an alternative to this model which is inspired by Primecoin’s inflation mechanism. Note that when the parameters below are improperly set to the extreme (e.g., \delta=1000 instead of \delta\approx 0.75) then this mechanism reduces to a premine only with more drawbacks.
HAPI Mine
The following idea, which I call “HAPI mine”, aims at solving several problems simultaneously:
 How to disincentivize large mining entities? (decentralization of mining)
 How to ensure sufficient allocation to early investors? (sustainable & incentivized early development)
 How to ensure low inflation for early adopters/HODLers? (attractiveness for early adopters)
 How to ensure there is enough supply of the currency at inception so as to meet the demand? (sufficient supply to meet early adopters’ demand)
 How to tradeoff SoV/noinflation property against the need to distribute the coin? How to ensure a decreasing inflation rate as adoption grows? (peg inflation to adoption)
I propose HAshPegged Inflation (HAPI mine), which is a simpler variant of Primecoin’s monetary mechanism, namely: decrease issuance as hashrate grows. Specifically, I propose the following scheme:
 Minimal hashrate needed for basiclevel security: H_0 (think: H_0 \approx 3000 GPUs)
 Initial block reward: R_0 (a unitless parameter)
 Parameter for decreaserate of issuance: \delta (think: \delta = 0.75)
 Epoch length of hashrate measurement: M months (think M = 6)
 Total hashrate measured in epoch t: H_t
 Cap on decreaserate over one epoch: C
 Lower bound on minting: R_{\min}
The block reward R_t in epoch t is set as follows:
 At epoch 0 the block reward is R_0
 At epoch t, the block reward is defined by:
 if H_{t1}<H_0: R_t := R_{t1}
 if H_{t1} \geq H_0: R_t := \max(R_{t1}\cdot\max(\min(\frac{H_{t1}}{H_t},1))^\delta, \frac{1}{C}), R_\min)
It addresses the above problems as follows:
 By increasing one’s own hashrate one decreases the marginal profits on one’s existing mining machines. This effect exists in Bitcoin as well, but is enhanced by HAPI. It can be shown that a mining entity is disincentivized to increase their hashrate earlier (i.e., in smaller hashrates) than it would be in a Bitcoinlike minting setup.
 Early team can mine the coins early enough, and once the project gains traction and more miners join, the printing decreases, thereby ensuring that the early team and investors are not diluted too much by later miners joining.
 Once the project gains traction and more miners join, the printing decreases, hence by definition the inflation decreases. Compare that to a set up where printing does not decrease in which case early adopters suffer an arbitrary large inflation rate.
 Once the project gains traction and more miners join, the allocation of the initial miners in relative terms increases (as it becomes a larger share of the entire existing supply), and this effectively translates to them holding a large (relative) supply which in turn serves as a forcing factor for selling (hence: distributing) the coins. Compare this to a situation where the early miners own a linear share of the total supply, in which case they prefer to hoard.
 One can argue that, to a sufficient extent, growth of hashrate is a fine proxy for growth of adoption. Of course, the relationship between the two is not guaranteed, is not 1:1 (1000x growth of hashrate does not imply 1000x growth in adoption), and can be delayed in time. Still, roughly, hashrate and adoption correlate positively.
Final notes:

What happens when hashrate decreases? Do we increase minting?
The coin issuance model described above never increases the minting. It works well with optical proof of work (OPoW), which requires high capital expenses (CapEx) but low operational expenses (OpEx); this is outside the scope of this post. Low OpEx means there will be no large hashrate drop (even if machines are not highperforming). Of course, this is not without limit, and below a certain threshold OPoW miners will shut their machines as well, but even then the algorithm does not increase minting (and hence below that threshold the system would suffer a similar drop in security as a Bitcoin like mechanism) 
Can issuance decrease too much so as not to attract new miners?
Theoretically, yes, and that’s why we should choose a small decrease rate (\delta), cap the decrease per epoch (C), and choose large enough epochs (M); it is better to err on the less aggressive side, that is, to be less responsive to hashrate increases. 
One effect of this mechanism is that coin holders are more incentivized to join the mining as nonholders, as by mining they directly decrease the total supply. This seems like a positive effect. However, one can wonder whether this causes nonlinearities: Consider a case where Alice holds a stake of s_A% in the currency and Bob holds a stake of s_B% < s_A%. Is Alice disproportionately more incentivized to join mining than Bob, since she holds a larger stake? The answer is twofold: First, regardless of who adds hashrate to the system, if this has an effect of an increase in the price of the currency (because of reduced inflation), both Alice and Bob’s initial stake increase proportionally, and Alice continues to have the same factor more value than Bob. On the other side, the larger the supply of coins, the less the mining reward affects the price of the currency (as it’s a small fraction of the total supply). Thus, if Alice is considering buying x new hashrate, her utility function U(x) would have the same maxima regardless of the volume of coins she already owns. Indeed, initially when the total supply is small, we get some wacky scenarios.
Thank you to Alex Tran, Lulu Kiffer, and Ori Newman for help with this post.