The trade
Start with the numbers, because they are not in dispute and they do not agree with each other. GoPro’s most recent quarter: $104.9 million of revenue, down 31.3% on the year; a $51 million net loss; camera sell-through down 38% to about 291,000 units; a going-concern warning; 23% of the workforce gone this year. By every measure a spreadsheet knows, this is a company being wound down in public.1
Then, on 20 August, Mark Fischbach filed a 13G. Markiplier is not an activist fund and not a strategic buyer; he is a man who has been posting videos since 2012 to an audience larger than most countries, and he had quietly bought 8.5% of the company about $9.3 million making him its largest single shareholder. His stated reasoning was four words long: it seemed undervalued. The stock went up 128%, having spent the preceding months close enough to a dollar that Nasdaq had begun the delisting conversation. He had been using the cameras for behind-the-scenes footage.
The interesting part is not the man, it is the arrangement he walked into. Roughly 8% of the float was sold short, and a float that thin has carried more than 10% before. A short position is a promise to buy later at a price you do not control, and when a large enough audience decides to be in the same place at the same time, that promise becomes the fuel. In 2021, about 140% of GameStop’s float was sold short more shares promised than existed and the covering was the rally.2 Nobody is claiming this is that. What is true is that the ingredients are the same ones, arranged the same way: a business the professionals have written off, a crowd that has not, and a set of positions on the other side that have to be closed by buying.
This document is careful about what it claims. It does not forecast the stock, and anyone who tells you a memecoin is a way to squeeze anything is selling you the exit liquidity. What it does is narrower and mechanical: it takes the one thing a coin reliably produces trading fees and instead of letting them leave, buys tokenised GoPro with half of every one of them and locks it under the coin.
What $GPRO is
Behind the price of an ordinary memecoin there is nothing. Not in a pejorative sense structurally: the float is the float, the chart is the product, and when the volume stops there is no asset anywhere in the arrangement that a holder has a claim on. Fees are the one exception, and they are also the proof, because every coin on every launchpad generates them and in almost every case they leave. The creator claims the trading fee and spends it, and the spending is invisible to the chart until it is not.
$GPRO differs in exactly one respect, and it is not the branding. The fees do not leave. Every trade pays 0.3%, the crank claims it, 50% goes back into $GPRO and 50% into the tokenised share, and both sides are deposited into one pool that this protocol has no instruction to withdraw from. No yield promise to holders, no staking, no governance, no roadmap one rule, applied on a loop, that converts turnover into a reserve.
The choice of reserve matters more than it looks, and this one is deliberately not a dollar. A reserve in another memecoin falls exactly when a reserve is needed. A reserve in a stablecoin is honest and inert it can only ever be worth what was put in. A reserve in equity is a claim on a company: it can go to zero, which a dollar cannot, and it can also be worth a multiple of what was paid, which a dollar also cannot. The pairing is a position, stated as one, and §4 is the argument for taking it rather than a pretence that it is safe.
One consequence is worth stating in the open, because it is unusual enough to sound like a mistake. A holder who never trades contributes nothing here. A seller contributes exactly as much as a buyer, since the fee is charged on turnover and does not care which direction anyone was wrong in the person selling at the low pays for the reserve that ends up standing under whoever bought from them.
The curve
The house lives on a pump.fun bonding curve. One instruction, create_v2, mints a fixed supply into the curve account under Token-2022 and discards the mint authority in the same transaction it uses it. The mint carries an empty extension set: no transfer hook, no transfer fee, no permanent delegate, no freeze authority. That is deliberate, and unlike a promise it is verifiable in one RPC call. There is no allocation, no vesting contract and no team wallet with a cliff, because there is nothing left to allocate: the curve holds the entire supply and sells it to whoever arrives, at the price the curve quotes.
A pump.fun curve is a constant-product market against virtual reserves, the account is seeded with notional SOL it does not hold, so the opening price is finite and the curve can be traded from its first lamport without anyone providing liquidity. Buys move along it, sells move back down it, and when the real quote reserve reaches the migration threshold the curve completes and the position graduates to the pump AMM as an ordinary pool. Two properties of that arrangement matter here, and both belong to a program we did not write and cannot amend:
- The reward is a protocol constant. Every trade against the curve and every trade against the AMM pool after graduation pays a fee of which the creator leg is a flat 0.3% of quote volume, charged to buyer and seller alike. Unlike the protocol fee beside it, it does not scale with market capitalisation or trade size, and graduation does not interrupt it.
- coin_creator is written once and cannot be reassigned. pump.fun records the creator on the bonding curve at creation and accrues the creator’s rewards to a program-derived address seeded by it. There is no instruction in that program to change the field. The destination is therefore decided in the transaction that creates the coin and is thereafter beyond the reach of the person who created it.
That field points at a vault keypair rather than at a person. From the first trade the revenue has exactly one destination, and reaching it requires nobody to remember, agree, or still be interested a year from now.
Why a share rather than a dollar
The reserve is fixed for the life of the coin because the pool is never withdrawn from, so the choice is made once and the honest way to explain it is to say what it costs. A stablecoin reserve is the safe answer and it is also a ceiling: every fee ever collected converts into a number that cannot become larger. Equity has no ceiling and no floor. It can go to nothing, and if the story in §1 continues it can go to a multiple. Choosing it is a decision to hold the second distribution rather than the first, and a reader who wants the first should hold dollars instead of this.
What the pool actually holds is GoPro (Backpack Securities) a token issued against a real share held in custody, one for one, routed onto Solana through the Sunrise gateway. A holder of the token has a claim on the share; a holder of this coin has no claim on anything, which §9 states plainly. Solana’s tokenised equity market crossed $465 million of supply this year, and GoPro is one of the newer listings on it.3
Disclosure, and it is a long one. A tokenised security is not a bearer asset. This mint is Token-2022 and carries, under a single authority that is not ours: a permanentDelegate, which can move the tokens out of any account holding them including this pool’s without anybody’s consent; a freeze authority; a global pause switch; a transfer hook that is empty today and need not stay empty; and a default account state the issuer sets. Those are compliance features rather than defects, and a regulated equity token cannot exist without them. But this protocol has no withdrawal step, so every one of them is a permanent exposure rather than a position anyone here can exit. Two further facts belong in the same paragraph: execution is expensive, at roughly 3.78% price impact on one SOL against about $72k of routable liquidity, which is paid on every purchase; and every Raydium pool holding this mint today is concentrated-liquidity rather than constant-product, so whether the venue this paper describes will hold it at all is a question the operator must settle before spending on it. It is stated here rather than in a footnote because a reader who stops after §4 should still have read it.
The revenue
The only money entering this system is the creator leg of the pump.fun trading fee. If V is cumulative quote volume, the revenue is
and that is the entire monetary base. No emission, no inflation, no treasury sale, no second round. The house is never minted after the curve is seeded; it is only ever bought back with money the market itself paid in.
Note what equation (1) does not depend on. Not price a fee is charged on turnover, so a coin trading sideways on constant volume deposits at exactly the rate one trading upward does. Not holders, who need do nothing at all and by doing nothing contribute nothing. Not us. The only input is that people keep trading .
What triggers a deposit
A deposit does not go in on a clock. Time is not what the crank is waiting for money is and a schedule that settled on a timer would spend most of its transactions moving dust and paying fees to do it. A block closes when the vault holds enough for the settlement to be worth its own cost.
Two quantities set that threshold and only one of them is a policy choice. The first is the deployment floor: below roughly 0.020 SOL the two swaps lose more to fees and slippage than they deliver into the pool, so a settlement below it is a settlement that makes the foundation smaller. The second is not a threshold at all but a real cost creating the Raydium pool for the first time pays that program’s protocol fee and rent on the pool state, both token vaults, the LP mint and the observation account, about 0.250 SOL, and it is paid at deposit time. It is therefore withheld from the swap budget rather than merely required beforehand. The distinction is the difference between working and not: a settlement that clears a gate and then spends its whole balance on the two legs still arrives at pool creation with nothing to pay with.
The honest reading of the difficulty is in volume rather than in SOL. At 0.3% of volume, a steady-state block is 12 SOL of trading against the coin, and the first one which carries the pool’s rent as well as the floor is 95 SOL. Neither is a figure anyone is asked to believe in. Both are the arithmetic of the reward rate against the threshold, and after the first block the rent drops out permanently. If the market is quiet, deposits are far apart. If nobody trades at all, none is laid, and §9 shows precisely what that costs the holder: nothing.
Inside a settlement
A settlement is five steps, executed in order, each a separate transaction signed by the vault. They are separate on purpose: one transaction spanning a reward claim, two aggregator swaps and a pool deposit exceeds what a Solana transaction can carry, and pretending otherwise would produce a protocol that works on paper and reverts on chain.
- Read. The unclaimed balance of the creator vault PDA is read across both pump programs the bonding curve and the AMM because the revenue moves from one to the other at graduation, and a settlement that only knew about the first would silently stop finding money on the day it succeeded. Below 0.003 SOL nothing is claimed, so a quiet minute costs one RPC call rather than a wasted transaction.
- Claim. The vault signs collect_coin_creator_fee and the rewards land in it as native SOL. Claiming and deploying are separate decisions, deliberately: gating the claim on the deployment threshold strands money, because rewards claimed once sit in the vault and the next claim is judged alone. Anything worth more than the transaction that collects it is collected. After graduation the pump AMM pays in wrapped SOL, so the wrapped account is closed in the same step and unwrapped back to lamports otherwise the balance grows in an account nothing downstream ever looks at.
- Measure. The deployable amount is read from the vault balance, not from what this claim produced, so a remainder left by an earlier block is picked up rather than forgotten. The gas reserve and until the pool exists the pool rent are subtracted first. If what is left is under the floor, the block is recorded as waiting, with the exact shortfall, and nothing is spent.
- Two buys. 50% of the deployable balance buys $GPRO and 50% buys the tokenised share, each a separate aggregator route out of the vault’s own SOL, bounded at 3% slippage. Separate transactions, so a route that can fill one leg but not the other fails cleanly with the other leg already banked in the vault, where the next block will find it.
- Deposit. Both balances go into the pool described in §8 created on the first block, deposited into on every one after, and only when the pool’s own ratio still agrees with the market’s price.
Every step above is signed by one keypair and no other: the wallet the house was launched from, which is what pump.fun recorded as its creator and therefore the only key that can claim anything. It pays its own transaction fees, holds the rewards between blocks, and owns the resulting position. That is what makes the process auditable from outside there is exactly one address to watch, and every lamport that has ever entered it has left in one of two directions, both of which end in the pool.
The pool
The foundation is not held in a treasury account. It is held as one side of a Raydium CPMM position a constant-product market of the form xy = k, the same curve Uniswap v2 popularised, where x is the house reserve and y the GPRO reserve and every trade moves along the hyperbola they define.
Choosing that over a concentrated-liquidity market is the single most consequential design decision on this page, and it is made on the strength of what a constant-product position does not require. It has no price range, so there is no band to pick at deposit time and no position to rebalance when price leaves it. It never goes one-sided, so the reserve cannot be quietly converted back into the coin by a move nobody was awake for. It accepts a deposit at any price, so a settlement can execute at whatever the market is doing that minute. And it requires no management, which is the property that matters most for a position meant to be held for the life of the coin by a process nobody maintains.
The pool address is not stored anywhere. It is a program-derived address seeded by the CPMM program, its fee configuration, and the two mints in canonical order, so it can be recomputed from first principles at any time. That is what makes the create-once rule in §7 robust: the keeper does not consult its own records to decide whether the market exists, it derives the address and asks the chain. A ledger that was empty, stale or wrong would still not cause a second pool, and a second pool would split the foundation across two markets and make every depth figure on this page a sum of things a trader cannot actually trade against.
One mechanical detail decides whether a deposit succeeds, and one decides whether it was wise. The mechanical half: a constant-product pool takes both sides at its own ratio, which is never exactly the ratio the market just sold us, because the two legs are bought at the aggregator’s price and deposited at the pool’s, seconds apart. So the house side is capped at what the dollar side covers at the pool’s current ratio, with headroom for the slippage bound the SDK adds, and the remainder stays in the vault for the next block. The prudential half is sharper and costs more when it is ignored: a deposit into a pool whose ratio has drifted far from the market is a gift to whoever is watching, because the deposit itself sets the pool’s price and an arbitrageur can take the difference in the very block it lands. A settlement must therefore compare the pool’s ratio against the aggregator’s price and decline when they disagree past a bound, rather than depositing at whatever ratio the pool happens to show.6
Trading fees paid to this pool accrue inside it, to the reserves themselves, rather than being paid out to a claimant. The pool therefore grows both when a block settles and when anyone trades against it, which is the fact §9 turns into a proposition.
What accumulates
Write x for the house reserve of the pool, y for its GPRO reserve, and k = xy for the invariant. A swap leaves k unchanged but for the fee it pays into the pool, which raises it. A deposit raises it. Nothing else touches it, and the protocol has no withdrawal step at all.
Proposition 1 (Monotone depth). kn+1 ≥ kn for every block n, with strict inequality whenever a block settles or a trade occurs.
Proof. Three operations act on the pool. A swap of size d with fee φ moves the invariant to (x + d)(y − dy/(x+d(1−φ))) ≥ k, with equality only at φ = 0. A deposit scales both reserves by 1 + ε, ε > 0, giving (1+ε)²k > k. A withdrawal would scale them down and there is no instruction anywhere in this protocol that performs one. A quantity acted on only by operations that do not decrease it is non-decreasing.
Depth is not the interesting statement on its own, though. What a holder wants to know is what stands under the coin at a price they might actually sell into, and for a constant-product pool that has an exact answer. At price p = y/x, the two reserves are determined by k and p alone:
Proposition 2 (The foundation has no downward step). Fix any price p. The GPRO held by the pool whenever the house trades at p are non-decreasing in time, and strictly increase with every settled block.
Proof. By (2) the GPRO reserve at price p is √(kp), which is strictly increasing in k for p > 0. By Proposition 1, k is non-decreasing and rises at every settlement. Composition of an increasing function with a non-decreasing one is non-decreasing.
Read the quantifier carefully, because it is the whole of the claim and it is the part that gets skipped. The statement is at a fixed price. It says a round trip back to a price already visited finds more GPRO underneath than were there last time, since the intervening blocks deposited and the intervening trades paid fees, and neither is undone by price action. It does not say the foundation is unaffected by a fall. By the same equation the dollars held move with √p: when the price drops, the people selling into the pool are taking those dollars out in exchange for their coins, and the reserve falls with them. That is not a leak in the design, it is what a two-sided market is. The ratchet is in the comparison across time at equal price, never in the level at any price.
Proposition 3 (Idleness is the worst case). If volume stops, the state does not move. No block settles, no reserve is spent, and nothing is lost but time.
Proof. By (1) revenue is proportional to volume, so zero volume accrues nothing and the vault never reaches target. A settlement below target is not attempted, and no other instruction spends the pool. The failure mode is therefore a pause, not a reversal.
What these propositions do not say. They do not say the house has a redemption value: the dollars are in a trading pool, not an escrow, and the only way to reach them is to sell into the pool at whatever price that selling produces. They do not say the price cannot fall a constant-product pool has no floor price, and a large enough sell moves it arbitrarily far. They do not say a holder is made whole; the position that accumulates dollars is the pool’s, not the holder’s. What they say is narrower and, we think, the only claim of this kind that survives contact with arithmetic: the depth under the house at any given price is a ratchet, and the ratchet is turned by trading rather than by anyone’s continued goodwill.
Who runs it
pump.fun fixes the reward destination, the aggregator executes the swaps, and Raydium’s CPMM holds the foundation. None of those three are ours. The settlement cycle in §7 is: a keeper runs it on a 60-second loop, and it holds the key to the launch wallet.
That key cannot mint, because create_v2 discards the mint authority at creation. It cannot redirect the rewards, because coin_creator is immutable in pump.fun’s program. It cannot freeze, tax or claw back a transfer, because the mint carries no extension that would allow it. It can do exactly one thing the propositions above assume it will not: the LP position belongs to that same wallet, so the key that deposits can also withdraw.
Say that plainly rather than in a footnote. Propositions 1 and 2 describe the protocol, which has no withdrawal instruction. They do not describe the operator, who has a keyboard. Until the position is owned by a settlement program with no withdrawal instruction in it, what stands between the foundation and the operator is a choice, and a choice is not a guarantee. Anyone deciding what this is worth should price the operator rather than the arithmetic. The arithmetic is the easy half, and it is the half that is already true.
Notes
- The GoPro figures are from the company’s own reporting and from the filing that caused the move: Q2 2026 revenue $104.9 million, down 31.3% year on year; a $51 million net loss; camera sell-through down 38% to roughly 291,000 units; a stated going-concern doubt; 23% of the workforce cut this year. Mark Fischbach’s 8.5% stake, worth about $9.3 million and making him the largest single shareholder, was disclosed in a filing dated 20 August 2026; the shares rose 128% on it, from a level at which Nasdaq delisting was in play. None of this is affiliated with this coin, nobody named here has endorsed it, and none of it is a forecast.
- Short interest in GoPro sits near 8% of float, which has carried above 10% in the past. The GameStop comparison in §1 is a comparison of structure and nothing more: roughly 140% of that float was sold short in January 2021, which is an order of magnitude the present situation does not approach. A squeeze is a mechanism, not a promise, and this paper takes no position on whether one occurs.
- Every figure quoted about the reserve was measured rather than assumed, on the day this was written: GoPro (Backpack Securities), mint GPRR2u6NS5yBQHWGauoJ9HXgjrTH8dDsrBfTV5zAYvDH, Token-2022, 6 decimals, roughly $72k routable, one SOL filling at 3.78% price impact and five at 3.77%. The mint carries a permanent delegate, a freeze authority, a pause switch and a transfer-hook slot, all under one authority; §4 is the disclosure, not this note. Solana’s tokenised equity supply passed $465 million this year, issued by Backpack Securities and routed through the Sunrise gateway.
- pump.fun charges a total trading fee of which the creator leg is one part; every figure here quotes the creator leg only the 0.3% of volume this protocol actually receives never the total the trade pays. The rest is not ours and is nowhere counted. The bonding curve program is 6EF8rrecthR5Dkzon8Nwu78hRvfCKubJ14M5uBEwF6P.
- The pool is a Raydium constant-product market, CPMMoo8L3F4NbTegBCKVNunggL7H1ZpdTHKxQB5qKP1C, and its address is derived from the two mints rather than stored, so §8’s create-once rule holds even against a record of ours that is empty or wrong. The reserve figure in the masthead is read from that pool’s own vaults, net of the protocol, fund and creator fees Raydium accrues inside them and excludes from the curve, not summed from what we deposited.
- The divergence bound in §8 is not a hypothetical. A deposit into a pool whose ratio has drifted from the market’s prices that pool, and a searcher can take the difference in the same block it lands a loss the depositor pays and no proposition here protects against. It is a check on the settlement, not a property of the curve.
- Every parameter quoted in the prose the split, the thresholds, the slippage bound, the reward rate is imported from the same module the keeper reads, so the document cannot drift from the process it describes. If a parameter changes, every number here changes with it.
