$SHARD — supply & the Pons V2 curve

$SHARD has a fixed supply of 1,000,000,000. The entire supply is minted into the Pons V2 curve contract at launch. There is no mint function afterwards — not for us, not for anyone. Whatever gets burned stays burned.

That has a consequence the earlier versions of this paper got wrong: we did not get to choose the curve. The shape of the price path, the way supply is divided, and the condition for graduation are all properties of the Pons V2 launch factory. Our only free parameter is the creator tax.

How the supply is divided

Pons V2 splits the 1B three ways, and the split is fixed by the factory, not by us:

            1,000,000,000 $SHARD minted once, at launch
                              │
            ┌─────────────────┼──────────────────────┐
            │ 5/7             │ 10/49                │ 4/49
            │ 714,285,714     │ 204,081,633          │ 81,632,653
            ▼                 ▼                      ▼
       sold on the      seeds the Uniswap      locked permanently
       bonding curve    v4 pool at             (never circulates,
       (the float)      graduation             never sellable)

Graduation

The curve phase ends when the contract has accumulated 4.2 ETH. At that moment three things happen atomically: the 10/49 seed and the accumulated ETH are swept into a Uniswap v4 pool, the pool's liquidity is locked forever, and the permanent 4/49 is locked away. From then on the price is set by the open market.

The fee stack

Every trade on the curve pays 3%, split between two parties who are not us:

  a $100 buy  ──►  $3.00 total friction
                         ├─ 1%  ($1.00) ──► Pons (the protocol)
                         └─ 2%  ($2.00) ──► creator tax ──► us
                                                  │
                                  ┌───────────────┴───────────────┐
                                  ▼ 80%                           ▼ 20%
                            fee reserve                      reward pool
                            (backs $YIELD)            (50% leaderboard / 30%
                                                       referral / 20% events)

Only the 2% is ours, and only the 80% of that 2% that reaches the fee reserve backs $YIELD. The 1% protocol fee is never ours to promise against.

The one price no design can change

An earlier version of this paper set $0.00002 as the price and solved the entire curve backwards from it. That treated one illustrative number as a physical constant. It is not. Two quantities genuinely are fixed by the launch factory, and dividing them produces the only price in this system that no design decision can move:

curve allocation  = 1e9 × 5/7   =  714,285,714 $SHARD   (Pons factory)
    reserve at graduation = 4.2 ETH =  $10,500 @ $2,500/ETH (Pons factory)

       average clearing price  =  $10,500 / 714,285,714
                               =  $0.0000147        ← IMMUTABLE

Every rising curve must sell some coins below that average and some above it. So the launch price is always below $0.0000147 and the graduation price is always above it — which is the short proof that $0.00002 was never available as a launch price, only as a graduation price.

Curve shape is a knob, not a constant

What is ours to choose is how that fixed average is distributed between the first buyer and the last. One parameter does it: k = P_graduate / P_launch. Modelling the curve as exponential, P(s) = P0 · e^(u·s/S) with k = e^u, the integral over the whole allocation gives:

avg = P0 · (k − 1) / ln k        ⇒        P_grad = avg · k·ln k / (k − 1)
                                                P0     = P_grad / k

That single knob sets the entire price range the game has to live inside:

Note the ceiling this imposes: on a linear curve, avg = (P0 + P_grad)/2, so letting P0 → 0 still caps the graduation price at 2 × $0.0000147 = $0.0000294. Any graduation price above $0.0000294 — including the $0.00005 figure sometimes quoted for this project — is only reachable on a convex curve, and needs k ≥ 27. That is a real constraint, not a preference.

We ship k = 12: a launch at $0.00000332, graduation at $0.00003985. Higher k buys a more dramatic early-entry advantage and a louder FOMO narrative, but it also builds a larger overhang of holders sitting on large multiples at the moment liquidity unlocks, and it widens the spread of coin quantities the gate has to quote. k = 12 keeps a real early-entry advantage without handing the first cohort the 27× overhang that $0.00005 would have required.

P(s) = P0 × e^(u · s / S)

      solving   ∫₀ˢ P(s) ds  =  $10,500   (graduate exactly when the curve sells out)
      at k = 12: u  = 2.4849
                 P0 = $0.000003321
                 P(S) = $0.000039849
                 full path = ×12.000

None of this is the ×19.22 curve this paper once invented. The shape is now derived from the two factory constants plus one stated parameter, and every figure above can be recomputed from k alone.

After graduation the price floats — and that is the hard case

Once the pool is live and locked, nothing supports the price. There is no floor, no buyback guarantee, and no redemption right. It can print $0.00001 or $0.00005 or worse, and it can stay there. The curve maths above stops being relevant the moment graduation happens; from then on the game is reading a market, not an integral.

This is the regime the whole economy is actually built for, and it is why every mechanic is denominated in USD rather than in coin count. Section 07 covers what that takes: a TWAP rather than a spot reading, a clamp that refuses to price at all rather than price off a manipulated quote, and a grace period so a red candle does not revoke a player's access mid-session.