-1,+1 (twL)

In 2022 we released two now pivotal pieces in Tapioca lore and DeFi itself-  R.I.P. Liquidity Mining  which described Tapioca’s evolution of the stagnant broken DeFi economic model (fka “flywheels”) into a value capture maximized, aligned, and sustainable call option incentive model, and the twAML (time weighted average magnitude lock) whitepaper . twAML was designed to be a dynamic consensus based liquidity locking system. twAML supported both Time Weighted TAP or twTAP, and Call Option TAP or oTAP. Within twTAP, twAML dictated the output of twTAP for your input of TAP + Time. For example, if you locked 100 TAP for 1 to 8 weeks- 0-100% twTAP would be outputted in return (0-100 twTAP). twTAP is the locked version of TAP which grants a share of 100% of protocol revenue paid in USDO, and voting power, thus the higher the output, larger your voting power, and the yield you would receive. Within oTAP, twAML dictated the discount level of your call options against the spot price of TAP, from 0-50%, based on how long you locked your minted USDO for, the larger the discount level, the higher your profit and thus yield would be.

The goal of twAML was to iterate Curve’s Vote Escrowing or “ve”, which uses fixed outputs: for example at any point in time if you lock 100 CRV for four years you will always receive 100 veCRV (100%) in return, locking the same 100 CRV but instead for 2 years would result in 50 veCRV (50%), etc. Because the time-to-output is fixed, the system cannot dynamically modulate itself to market forces in order to reward early participants, and wield free market efficiency to keep equilibrium and maximize the total amount of CRV locked. Imagine the demand for veCRV requiring four year locks during the peak of Mitche’s CRV liquidation cascade versus the peak of the Curve Wars- time is never a stable commodity. The goal of twAML simply put was to find the free market value of time in order to lock the most liquidity possible for as long as possible (in order of precedence). Time is obviously not fixed nor valueless, or there would be no treasury bill yield curve based on duration, and simply put, you would be happy to receive $1,000,000 for either 1 second or 10 years.

After releasing Death of Liquidity Mining, Tapioca’s fingerprints immediately spread across DeFi. Today, you can hardly find a new DeFi protocol without an oTKN. Tapioca DAO consistently produces the best concepts in DeFi, and twL is no different.

How twL was produced was also no different than the production of twAML- iteration. Finalizing twL and reaching this endstate simply took taking a hard self reflective look at the end goal of twAML (and twL by extension)- which is defined as finding the free market’s value of time in order to lock the most liquidity possible for as long as possible (in order of precedence). Most importantly- we had to analyze the twAML system and take inventory- what furthers reaching the end goal and what doesn’t. This hard look was first necessitated by the release of Tapioca in June 2024 and the subsequent need to pause the protocol from twAML economically breaking due to a parameter, Epoch_Duration, not being set. Even though this was a simple parameter issue, the decision was made that twAML had too high of a chance for failures by other means because it was too fluid (which it was purposefully and misguidedly designed to be) which meant that we needed to make the system more hardened, and once that state was reached we needed to revalidate it due to this refactor. We had many small iterations throughout that improved the system. However, by the end of this revalidation process, we realized two things simultaneously; twAML had many flaws in its approach in that it had complexities that were completely unnecessary and some wholly illogical, and simultaneously that we were on the precipice of designing, building, and executing what we always dreamed of twAML being- the most powerful and elegant liquidity locking system ever devised.

“The art of simplicity is a puzzle of complexity” - this quote has never been more poignant. From this entire journey with twAML, from death to rebirth as twL, I have learned an important lesson from DeFi; functionality design needs to be centered around creating the absolute simplest architecture which meets a rigid and well defined goal. With fellow Tapioca contributors EnigmaDarkLabs revalidating twAML and assisting on the iteration that followed, the process culminated in a final discussion which brought up this very point. Sometimes it’s hard for us to dismantle our previously held thought processes and decisions, but I quickly realized while twAML was extremely innovative, many of its components in this lens were illogical or unnecessary, and between both made it frankly far too confusing for anyone to truly understand and appreciate it. Sometimes our greatest successes are born from small failures, and twl is no exception, I wouldn’t change any part of the process as I honestly don’t believe we would have ideated this final design. Many ingenious inventions seem so simple in retrospect like Velcro, Band-Aids, etc, however someone had to dream them up first. More than anything, we came at this from a standpoint of, how can we build the “X*Y=K” for token locking (foundational formula for the Uniswap AMM).

For those who aren’t familiar, the twAML formula had a few primary components. To make this as simple as possible, the first was the Cumulative which was based on the collective of each users locks Magnitude which in of itself was based on user’s lock duration. Because user’s could DDoS twAML with $1.00 locks, there was a minimum capital threshold enforced for a users lock (and associated magnitude) to effect the cumulative. The cumulative was then “smoothed” based on the number of participants to find a real market rate for time; less participants- cumulative moves faster, more partipants- cumulative moves slower. The cumulative was then capped at how much it could grow per epoch so that the lock duration requirement couldn’t grow to 10 years in a single week. Unlocks would then remove the users magnitude and allow the cumulative to decay. The problem is, what does any of this have to do with the goal? We have a puzzle of complexity, but certainly no simplistic art.

To the question of “What parts of the mechanism exist to further the goal, and which do not?” I almost jokingly responded “Consensus in DeFi is almost universally based on liquidity, right? We should just grow or decay the time duration for the output of twTAP discount of oTAP based on if there’s more or less liquidity locked, that’s it- that reaches the goal of locking as much TAP USDO as possible for the longest time possible, and is precisely what time weighted liquidity was billed to be as a dynamic consensus based liquidity locking system”. Ben had an idea previously of employing a set number of “buckets”, fixed output buckets users could lock into, think like Curve- 25%, 50%, 75%, 100% outputs for twTAP, 20%, 30%, 40%, 50% discounts for oTAP, but then, the time requirement for all of the buckets would grow or decay based on if more or less capital was locked into the entire system. Ben then said “Wait, what if each bucket moved independently based on the capital locked into it specifically, like if there was a lot of demand to max lock into the 100% bucket, the 100% bucket would grow and grow until it was too long, and people would naturally be incentivized to “arbitrage” and lock into the other, smaller buckets”. This may sound contradictory, don’t we want to lock capital for as long as possible? Yes, however, when people see a “good deal” they rush to receive it, and that’s precisely what behavior we want- the most TAP USDO locked as possible, for as long as possible, in that order of precedence.

Infographic on twL

As this was laid out, everyone stated almost in unison, “This is brilliant”. “It’s as simple as -1,+1, but even better than twAML at the same time”. Thus -1,+1 was born. Four buckets, more capital locked in a bucket? +1. Less in the bucket? -1, +1, -1. Then, a Ceiling would be enforced of 52/52/52/52 for twTAP 16/16/16/16 for oTAP (One Year Four Month Max, respectively), and a Floor of 1/2/3/4. The first epoch will start at 1/2/3/4 (the floor), and Epoch 2 will compare to 0/0/0/0 locked in the buckets in “Epoch 0”. Thus, Epoch 2 will grow all 4 buckets, and on and on we go with comparing the TAP USDO locked in the current epoch to the prior epoch using -1, +1. No magnitude, no cumulative, no unlocks, no voodoo magic formula that may work or may not- capital controls time, as simple as it is powerful.

twL is just as simple as ve, with much more powerful market based dynamics and control, anyone could comprehend the mechanism, with zero validation needed as it’s so rigid. Literal perfection. The game theory involved is also extremely powerful, there is an early advantage phase to participants as they can receive large outputs for a small amount of time as Tapioca is in its infancy, then an arbitrage phase where participants can find “good deals” each epoch on capturing the largest outputs with the smallest time commitment, to then culminate in an equilibrium phase where the buckets time requirements are in perfect unison with the free market to adequately price time and blackhole USDO TAP.

As you can see above with a simple simulation, these buckets grow and decay against the -1,+1 moniker and find equilibrium. The only discernible edge case is growth occurring from a small amount of liquidity being locked into a singular bucket for two consecutive epochs, however because the growth is only +1 and decay -1, this edge case is benign. There are a number of governance controls available as well to control the buckets if need be, such as resetting the buckets, changing the floor and ceiling, adding or removing buckets, etc.

Because the system is so simplistic, you can very easily model it with AI tools! You can see above in this simplistic example, the buckets simply grow or decay by +1 or -1 per epoch as stated, and after 25 epochs in this randomized scenario, the ending results (in twTAP terms) are: 1 Epoch Lock for 25% Output, 4 Epoch Lock for 50% Output, 11 Epoch Lock for 75% Output, and 12 Epoch Lock for 100% Output.

I truly feel we have devised something extremely special with twL. The brilliance is in it’s simplicity, and this is a system we can not only all trust and comprehend, but has obvious power in reaching the true value of time and capturing the maximal amount of locked liquidity. With oTAP, we very palpably impacted the entire space of DeFi with it’s broad employment in new DeFi protocols, and twL I wholeheartedly believe will have a similar long term impact. With the last three months of hard work and ingenuity, Tapioca V1.1 has all the tools necessary for a successful mainnet release. Without all of you Tapiocans and your unwavering passionate support, none of this would be possible

MAKE DEFI GREAT AGAIN!

el jefe, twmatt