Emission balance
Elasticity is zero, and that is the correct value
Versions up to v2.2b set production elasticity to 1: drop = base × (P/P0)¹, justified as "output grows slower than the gate, so the system stays deflationary". That reasoning no longer applies and the term has been removed.
The reason is that drops are denominated in USD and minted as $YIELD at a fixed rate of 0.4695 per dollar (v3.3 — one $YIELD carries $2.13 of face value; it used to carry $0.01, and the change is a redenomination, not a pay cut). Indexing a USD amount to the price of $SHARD would move the reward for killing a bat based on what a coin did — a double count, and one that makes the game unreadable: players would earn more $YIELD for the same action purely because somebody else traded. Elasticity is now 0.
v2.2b: drop = $0.035 × (P/P0)¹ ← the same kill pays more because a coin moved
v3.3: drop = $0.01 ~ $0.06 ← the same kill always pays the same
= 0.0047 ~ 0.0282 $YIELD
Price linkage still exists where it belongs — on the cost side. Gates and tickets are priced in USD and settled in $SHARD at the live price, so a rising $SHARD reduces the quantity required. The player feels the coin's performance through what things cost them, not through what the game hands them.
Grinding no longer reaches the gate
This is the sharpest difference from v2.2b and it should be stated plainly, because the old paper implied the opposite.
In v2.2b, drops paid ETH, ETH bought $SHARD, and therefore time could be converted into gate access: 137 hours at launch, 69 hours at ×2. That chain had two links that do not survive contact with a real launch — ETH is not ours to mint (section 04), and $YIELD is not a tradable asset.
v2.2b: play ──► ETH ──► $SHARD ──► gate (broken: first link does not exist)
v3.2: play ──► $YIELD ──► territory, upgrades (and nothing else)
│
└──► redemption ──► buys $SHARD on the market
$YIELD cannot be sold, swapped, or transferred. It buys territory, upgrades and redemption — and redemption is a market purchase funded by fees the game has actually earned. A player with a great $YIELD balance and no $SHARD still does not pass the gate. The gate costs $30 in $SHARD and the only ways to obtain $SHARD are to buy it or to be paid it by the reward pool.
That is a deliberate change in the social contract, not an oversight. The trial tier is the whole game minus the economy, and it is permanently free. The full economy asks for a real commitment, and v3.2 stops pretending otherwise.
The emission ledger
| Activity | Per hour of active play | $YIELD | Type |
|---|---|---|---|
| Kills (~99/h at mean $0.035) | $3.50 | 1.64 | Mint |
| Territory upkeep, per level | −$0.50 / day | −0.23 | Burn |
| Territory upgrade | −$20 − $22 × level | −(9.39 + 10.33×lv) | Burn |
| Raid clear, T1 | +$25.00 one-off | +11.74 | Mint |
| Redemption | balance × R | all of it | Burn |
Territory is a sink, not an income stream. An earlier revision paid a passive trickle of $0.02 per level per minute on a wall-clock timer. At level 10 that is $288 per day against $5 per day of upkeep — a 57× money printer that paid players for leaving a tab open, punished actually playing, and minted $YIELD with no fee behind it. The trickle is gone. Territory now only costs $YIELD and grants efficiency in return: +25% energy cap and +25% material drops at level 10. There is no wall-clock faucet anywhere in the game.
A T1 raid clear mints roughly seven hours' worth of killing. That is the intended scale: raids are the fast path, grinding is the slow one, and territory converts a windfall into a recurring obligation that outlives it.
The only control variable that matters
Because emission is not pegged to anything, the question "is the economy balanced?" reduces to a single inequality about R:
R holds ⟺ fees accrue at least as fast as $YIELD is minted net of burns
R falls ⟺ players are out-earning the trading that funds them
Every lever we have is on the right-hand side. We cannot set R — it is whatever the reserve divided by the float happens to be. What we can do is keep the sinks in the table above large enough relative to emission that net issuance stays subordinate to fee accrual. That is a tuning problem measured against live data, not a number this paper can promise.
Anchoring a price that will not hold still
$SHARD has two price regimes and they need completely different treatment. Treating them the same is the mistake this section exists to prevent.
On the curve, the price is not manipulable and needs no oracle. It is a pure function of how many coins the contract has sold. Nobody can move it inside a single block without paying for every coin they buy to move it. Reading it is arithmetic, not trust.
After graduation, the price is whatever a Uniswap v4 pool says it is — $0.00001 today, $0.00005 tomorrow, and possibly $0.000002 next month. Spot price in that regime is flash-loanable: an attacker rents a block's worth of liquidity, prints a price that never existed in any real trade, and uses it. Left unguarded, that attacker walks through a $30 gate for pennies, or makes every rival's raid ticket momentarily ruinous.
So the game never reads spot. Four rules do the work:
| Rule | What it does | What it prevents |
|---|---|---|
| USD denomination | Every gate, ticket and drop is defined in dollars; the coin count is usd ÷ price, recomputed at the moment of the action. | A price move changing what the game costs. The player's cost is stable; only the coin count floats. |
| TWAP, not spot | Gate and ticket decisions read a 10-minute time-weighted mean. | A one-block spike setting the price the game charges. A flash loan buys one sample, not ten minutes. |
| Divergence clamp | If spot is more than 50% away from the TWAP, the action is refused, not repriced. | Pricing off a quote we cannot corroborate. Refusing is safe; guessing is not. |
| Gate grace period | Once cleared, the $30 gate stays cleared for 7 days regardless of price. | A red candle silently revoking access mid-session — the fastest way to convert a holder into a seller. |
The window is 10 minutes rather than the 30 minutes most DeFi writing recommends, and the reason is specific: the window must be sized against the sampling rate. At one sample per five seconds, a 30-minute mean lags a genuine trend far enough that honest moves trip the clamp — roughly 1.8 standard deviations, so the game would pause pricing about 7% of the time for no reason. A 10-minute mean puts normal drift at ~3.2σ while still catching a flash-loan spike, which arrives as a 100%+ jump inside one block. On-chain this should not be sampled at all: read the pool's own observe() accumulator over the same span.
Elasticity: the one setting that decides whether the sink survives success
USD denomination alone has a failure mode that is easy to miss. If a ticket is a flat $3, then the number of coins burned is $3 ÷ P — so a 10× pump cuts the quantity burned to a tenth. The deflation story silently decays to nothing at exactly the moment the coin is succeeding. That is the flaw in a purely inelastic design.
The fix is to let the dollar cost rise with the price, by an exponent E:
ticket_usd = base × (P / P_grad)^E
ticket_shard = ticket_usd ÷ P = base × P^(E−1) / P_grad^E
E = 0 → shard ∝ 1/P flat dollars. A 10x pump cuts burn to 1/10. Sink decays.
E = 1 → shard = const BURNED QUANTITY IS PINNED. Burn per raid is a fixed
number of coins no matter where the market goes.
E = 3 → shard ∝ P² a 10x pump demands 100x the coins. Raids stop cold.
E = 1 is the setting we ship. It is the knife-edge between a sink that decays with success and a sink that chokes on success, and it is the only value that is simultaneously fair to the player and predictable for the economy. Fair, because a player whose coins just doubled is asked for twice the dollars for the same number of coins — their real burden is unchanged. Predictable, because the deflation rate becomes a fixed number of coins per raid rather than a function of market sentiment.
E = 3 deserves a note, because it was the original instinct: "price +1% ⇒ requirement +3%". The intent behind it is right — costs should follow price up, so that early holders cannot coast on appreciation alone. But taken literally it makes the coin quantity scale with P², which is a burn stall: the game stops being playable precisely when the price is doing well. E = 1 preserves the intent without the quadratic blow-up. The gate uses the same setting.
None of this fixes the price. Nothing here can. What it does is make the game's economics indifferent to the price: whatever $SHARD prints, the cost of play stays $30, the burn per raid stays constant, and a manipulated quote gets refused instead of honoured.