Dark pools, hidden liquidity, and the soldier economy

Contents

00Abstract

Dark pools are trading venues that execute orders without displaying them. They exist because showing a large order to the market moves the price against the order before it fills. Roughly 40% of US equity volume now executes away from public exchanges. The venues doing it sell invisibility.

s1337 adapts that structure on Robinhood Chain. 7331 fully on-chain soldiers mint alongside the $1337 token in a single 24-hour window. They then trade in a two-leg venue: the token leg is fixed at 333,333 $1337 and never moves, while the ETH leg floats as a percentage of a bounded mark imported from the collection's best standing offer — the same import a midpoint cross performs against the NBBO.

Two reward streams run off that venue, and they are not the same asset. A staking layer (the Garrison) emits 9,000,000 $1337 per day from a finite reserve. Separately, every ETH fee accrues inside an ownerless reward contract with no withdrawal path; once the balance crosses a threshold, any wallet can call supplyDrop(), which swaps the entire balance into $GME stock tokens in one pass and credits activated soldiers pro-rata by rank weight, releasing linearly. One ticker, hardcoded, no allocation decision for anyone to make. This paper describes the venue, both streams, and the math.

01What a dark pool is

A dark pool is a private trading venue — in US regulation, an Alternative Trading System (ATS) — that matches buy and sell orders without publishing its order book. Orders rest hidden. Fills print to the tape only after they happen. Nobody outside the venue sees size, side, or intent beforehand.

The lineage runs from ITG's POSIT (1987), which crossed institutional orders at scheduled times, through Liquidnet (2001), which built a network where over a thousand asset managers cross blocks directly with each other, to the broker-dealer pools of the 2000s — Credit Suisse Crossfinder, Goldman Sigma X, UBS ATS — and the independent venues of today. The SEC's Regulation ATS (1998) formalized the category; FINRA now publishes weekly ATS volume. As of 2025 there are over 50 registered ATS venues in US equities.

In 2025, total off-exchange execution ran at roughly 40–44% of consolidated US equity volume. ATS dark pools proper account for about 15–18% of that, the rest being wholesaler internalization. Dark execution set records in early 2026.

02How dark pools execute

Midpoint pricing

Dark pools borrow their prices from the lit exchanges, referencing the National Best Bid and Offer (NBBO). The canonical dark execution is the midpoint cross:

A buyer and a seller matched at P_mid each save half the spread versus crossing the lit book, and neither order ever appeared on a screen.

Matching styles

• Continuous crossing — orders match the moment a contra arrives (most broker-dealer pools).
• Periodic crosses — orders accumulate and match at scheduled or randomized times (the original POSIT model), which blunts timing games.
• Negotiated blocks — the venue alerts two naturals to each other and lets them negotiate size (Liquidnet).

Anti-gaming controls

Fills reveal information after the fact, so venues deploy minimum execution sizes, counterparty scoring and randomized matching against traders who ping pools to detect hidden blocks.

03The cost of being visible

Why does any of this exist? Because execution has a cost beyond commissions, and the cost is a function of visibility. Three standard results:

Market impact — the square-root law

Across venues, instruments and decades, the price concession paid by a metaorder of size Q is empirically well described by:

Impact grows with the square root of size: 4× the size costs 2× the concession per share. At institutional size this dwarfs commissions, which is what makes hiding the order worth paying for.

Kyle's lambda

Kyle (1985) models a market maker who can't tell informed flow from noise and therefore moves price linearly in net order flow q:

λ measures how much information the market reads out of each unit of flow. A dark pool lowers the λ your own trading faces by keeping the flow unobserved.

Implementation shortfall

Perold (1988) defines the true cost of execution as the difference between the paper portfolio (filled instantly at the decision price P₀) and the real one:

Almgren–Chriss (2000) then split impact into a temporary component (paid per slice, decays) and a permanent component (moves the price for everyone after you), and derive execution schedules that trade impact against timing risk. Dark pools attack the same cost earlier, at the point of disclosure.

04Taking the structure on-chain

A public blockchain is the most lit venue ever built: every order hits a public mempool before it executes, and MEV searchers are the same predatory flow dark pools were built against. An on-chain order book cannot be hidden. s1337 therefore splits the trade into two legs and treats them differently.

Two legs

The token leg is the cross. A soldier changes hands for a constant P = 333,333 $1337 regardless of size or direction: ΔP = 0 for all Q, so the fill carries no impact and no information. The ETH leg is the reference. It is charged as a percentage of M, a bounded mark derived from the collection's highest standing offer on OpenSea — the closest thing this venue has to an NBBO. Eq (1) prices a midpoint cross by importing a number from a lit book rather than discovering one; §5 imports in exactly the same direction, and the fixed token leg is what the imported number prices.

The fixed-ratio NFT/token vault is established design on Robinhood Chain. Clutch Markets' Anvil AMM v2 is the reference implementation and StonkBrokers the reference market; the random-versus-specific buy split and the tiered soft-staking ladder both originate there. s1337 runs its own contracts and diverges in three places: the burn is charged at the trade edges rather than the pool side (§5), the ETH leg floats against a lit reference price rather than sitting flat (§5), and the fee stream settles into a single RWA rather than a menu (§8).

That relocation is the honest cost of the design and is worth stating twice. A buyer who needs $1337 to buy a soldier must first acquire it on a public AMM, and a seller who wants ETH must sell it back the same way. The concession they pay there is visible, ordinary and scales with √Q. What the soldier pool removes is impact on the soldier, not impact in aggregate. §9 repeats this as a risk.

Invisibility of selection

Traditional pools sell invisibility of orders; the soldier pool sells invisibility of selection. The standard buy does not let the buyer name a soldier, so accumulating quietly gives away nothing about which pieces the buyer values. Choosing a specific target is the information leak, and §5 prices it accordingly.

Robinhood Chain has no Chainlink VRF on the production path, so the pool does not claim randomness it cannot provide. The standard buy fills FIFO: the soldier that has been in inventory longest leaves first. The rule is deterministic and verifiable from the inventory array, and the outcome of any given buy depends on the inventory state at execution — see §9.

Distribution: one window, two lanes

The collection is 7331 soldiers, distributed in a single 24-hour window that opens when the $1337 position goes live.

• Whitelist lane — a merkle snapshot of holders of six Robinhood Chain collections (StonkBrokers, Chain Mancers, Yardkeepers, Cash Cats, Zaibatsu Wagies and pyopyopyopyo) mints one soldier per wallet, free.
• Public lane — 0.01 ETH per soldier, up to 10 per transaction and no per-wallet cap, open to anyone. Both lanes open in the same block. Mint proceeds transfer to the team wallet as each mint lands and fund the launch itself: the Uniswap position, the pool's token side and the Garrison reserve. They sit outside the rewards stream described in §8, which is fed by trading and activation fees.

Wallets holding several of the six collections still get a single free claim. The per-transaction cap on the paid lane is a throughput limit: it stops one transaction clearing the book in a single block, while leaving buyers free to send as many as they want.

When the window expires, the remainder N_rest = 7331 − N_minted is swept into the dark pool by a permissionless sweepToPool() call and becomes NFT-side liquidity at the fixed price. Demand during the window therefore sets the pool's depth.

05The soldier pool

Contract: DarkPool1337. One fixed token price, three operations, a floating ETH leg, and a burn on every trade.

The burn, β = 10%

Every trade in either direction destroys 10% of the base price:

The burn is charged at the edges of the trade: buyers pay it on top of P, sellers have it withheld from their proceeds. Taking it from the pool's own side would drain β·P per round trip and let a trader cycle the reserve dry for the cost of gas. Charged this way, the reserve after any buy-then-sell cycle is where it started:

Liquidity holds constant while supply falls. The price stays fixed in nominal $1337, and the $1337 it is denominated in gets scarcer with every trade.

Buy — blind fill

Of that, P = 333,333 enters the pool and 33,333.3 is burned. The buyer does not name the soldier — no selection information leaves the wallet — and inventory is drawn FIFO: longest-held out first.

Snipe — targeted fill

Choosing a specific soldier reveals preference, so it carries a premium φ = 20% on top of the burn:

Split three ways: 333,333 to the pool, 66,666.6 to the Garrison reward reserve, and 33,333.3 burned. The emission schedule pays the premium back out to activated holders, so snipers subsidize soldiers.

Sell

The pool releases P less an optional spread s (0 at launch, hard-capped at 20%); the seller receives that amount less the burn:

Sizing the pool

The token side sets how many soldiers can be sold in before it empties. For a token reserve R:

That is 16.4% of the collection, not the whole of it. Depth is two-way — each buy returns P to the token side and each sell takes it out — and by (7) the burn never touches the reserve, so a matched round trip leaves N_bid exactly where it started. Net flow is a different matter. Eq (7)'s neutrality is a statement about round trips, not about direction: sustained one-directional selling drains the reserve at P per soldier with no offset, and when it reaches zero the fixed price stops being quotable on the bid. Roughly 1,203 consecutive sells with no intervening buy is all it takes. This is the venue's most likely failure mode.

The NFT side has the opposite problem: it may never clear. Each buy permanently removes 366,666.3 $1337 from float — 33,333.3 burned outright, 333,333 locked into the pool's bid side, recoverable only if someone sells a soldier back. Against a total supply of 1,337,000,000 the absolute ceiling is 1,337,000,000 / 366,666.3 ≈ 3,646 soldiers, and that assumes every token in existence is available to buy with. Realistic float — the 534,800,000 Uniswap and operations tranche plus Garrison emission net of activation burns — supports closer to 1,500–2,500.

The consequence runs both ways. The pool's standing offer caps a soldier at 366,666.3 $1337 indefinitely, so no soldier prices above that number in tokens while inventory remains: the collection appreciates in ETH terms only, never in token terms. That same cap is what makes M a clean derivative of the $1337 price rather than an independent quantity.

The mark

The ETH leg is charged against M, an ETH mark for one soldier. M derives from the highest standing collection-wide offer for s1337 on OpenSea. That is off-chain data. It reaches the contract as a posted value, and a posted value is a trust assumption — stated here in the body, not only in §9.

The poster is bounded so that trust is small. Let o_t be the 24-hour time-weighted average of the observed best offer and M_t−1 the mark in force. Each update resolves as

Because the pool's own offer caps a soldier at 366,666.3 $1337 for as long as inventory lasts, the mark is not an independent price so much as the ETH translation of a token price the venue already fixes — see "Sizing the pool" above.

If no fresh value lands inside the staleness window the contract keeps using the last good mark. It does not halt and it does not fall to zero — a stale mark is a worse price, a zero mark is a free venue. At launch M is initialised to the public mint price of 0.01 ETH and stays there until the offer history is long enough to mean anything.

Fees

The ETH leg is a percentage of the mark, not a flat number:

Garrison activation pays the swap rate, 0.10 · M. At M = 0.5 ETH a blind buy costs 366,666.3 $1337 + 0.05 ETH and a snipe costs 433,332.9 $1337 + 0.075 ETH. The ETH cost of trading a soldier therefore rises with the collection and falls with it. That is the design: a flat fee decays into irrelevance as the asset appreciates, while a proportional one keeps the reward stream (§8) scaled to what a soldier is actually worth.

Fees accrue in the reward contract described in §8. The pool's NFT and token inventory has no withdrawal function. The sell spread s is 0 at launch and hard-capped at 20%, which until it is disarmed is a live lever on every seller's proceeds; the setter is renounced once the mark stabilises — [TBD: renunciation date/block].

06Garrison emission math

Contract: Garrison. Soft staking — soldiers stay in the holder's wallet. Activating soldier i at rank r burns the rank cost c_r and registers weight w_r:

The ladder is priced off the pool: 10%, 25%, 50%, 100% and 250% of one soldier, a 25× span across five tiers. Activation burns leave supply permanently. Upgrading from rank a to rank b burns c_b − c_a. Ranks, costs and the emission rate are immutable in the contract, which has no owner.

The drip

The Garrison emits at a fixed rate E = 9,000,000 $1337/day while at least one soldier is active and the reserve is positive. It uses a standard accumulator: with total active weight W(t), the per-weight index A advances as

and the claimable balance of soldier i with weight w_i activated when the index stood at A_i is

Equivalently: each soldier's share of any day's 9M is w_i/W. Upgrades settle pending at the old weight into carried and re-index at the new weight, so no drip is lost.

Voiding and discharge

Selling or transferring an activated soldier voids its activation and forfeits its pending back into the reserve. The NFT contract calls the Garrison on transfer, so the common path is automatic. For any case where a soldier's registered weight outlives its activation, discharge(tokenId) is permissionless: anyone may call it against a soldier whose activating wallet no longer holds it, clearing its weight from W(t) and returning its pending to the reserve. Without that anyone can leave stale weight in the denominator, diluting every honest holder until someone happens to touch it.

Reserve and runway

The reserve starts at R₀ = 401,100,000 $1337 (30% of supply). Runway at full emission:

Snipe premiums are the only inflow to the reserve. Activation burns are burned in full and contribute nothing to it, and there is no other funding path beyond a voluntary fund(). The premium is not a meaningful extension: each snipe adds 66,666.6 / 9,000,000 ≈ 0.0074 days, so it takes about 135 snipes to buy a single day of emission. Emission also pauses whenever nothing is activated, which stretches wall-clock runway past the nominal figure without adding a token to the reserve.

State it plainly: the $1337 drip is finite. At full rate the reserve is empty in about a month and a half, and no realistic volume changes that by more than days. It is a launch subsidy, not a yield. Steady-state yield is the $GME stream in §8, which is funded by fees rather than by a fixed reserve and does not run out.

Claims

Claiming is free and open at any time to the wallet that activated the soldier and still holds it. The cost sits at entry instead: activating charges 0.10 · M in ETH alongside the rank burn, and that ETH goes to the reward contract in §8.

07$1337 launch parameters

Fixed supply, no mint function, no owner:

$1337 trades against ETH in a one-sided Uniswap v3 position on Robinhood Chain, seeded with tokens only and live from the moment the mint window opens. The position sits in the range [p₀, p_max], where p₀ is the opening price in ETH. For a token-side deposit of Δx its liquidity is

Buyers walking the price up through the range convert the token side into ETH along the curve, so the pool capitalizes itself through trading rather than from a matched ETH deposit at launch.

Allocation

08Fees, the drop, and $GME

Every ETH fee the protocol charges — blind buys, snipes, sells and Garrison activations — accrues inside a reward contract. It is locked there: no withdrawal path and no owner. Nobody, including the team, can move that balance anywhere except through the mechanism below.

Supply Drop

When the accrued balance crosses a threshold of [TBD] ETH, supplyDrop() becomes callable. Any wallet can call it and pay the gas. The call swaps the entire accrued balance into $GME stock tokens on Robinhood Chain in one pass and credits every activated soldier pro-rata by rank weight. The caller keeps a tip of [TBD] of the pot — it exists for one reason, which is to make certain somebody always pulls the trigger.

There is no operator, no manual conversion and no off-chain step anywhere in this. The trigger is permissionless, the swap target is hardcoded, and the accounting is the same accumulator the drip uses. A drop of size G credits soldier i:

Nothing lands in full at the instant of the crank. A drop joins an undistributed pot that pays out at a constant rate over a rolling 30-day window, and credit accrues to whatever weight is activated as it is released:

Each new drop adds to the pot and resets r, so the rate reflects the current pot rather than a per-drop schedule; with no further drops the tail decays to zero in 30 days. Release pauses whenever nothing is activated, so no drop is ever paid into a vacuum.

The reason for the ramp is simple: paying in full at the crank makes the optimal play activate at the highest rank one block before a drop, claim, and discharge — one burn for a share of fees earned over weeks by everyone else. Spreading the release means a soldier only earns for the time it is actually activated. Claiming released $GME is free, has no lock of its own, and goes to the activating wallet. A holder who transfers or discharges mid-window forfeits what has not been released to them yet.

One ticker: $GME

Fees in ETH. Pay in GameStop.

The protocol converts into exactly one asset. Not a menu, not an election, not a basket, not a governance parameter — one ticker, hardcoded at deployment. The argument for that is narrow and worth making honestly: a single fixed target means there is no allocation decision for anyone to make, no governance surface to capture, no discretion for a team to exercise, and no way to quietly change what holders are paid in. The concentration is the trust minimisation.

The flipside is exactly as large. Holders take undiversified exposure to a single volatile equity, with no ability to opt out of the target and no diversification anywhere in the design, and they carry all of it. A bad quarter at GameStop is a bad quarter for the reward stream.

One mechanical detail worth knowing: Robinhood stock tokens implement ERC-8056. Corporate actions on the underlying — splits, cash dividends — update an on-chain uiMultiplier(), the shares represented per token, instead of rebasing balances. A raw balance never moves on a corporate action; a single token can come to represent more than one share. Chainlink's USD feeds already quote the multiplier-inclusive price, so a naive balance read understates the position after any such event.

These drops are protocol rewards paid by an ownerless contract on a permissionless trigger. They are not dividends, not a distribution of anyone's profits, and carry no claim on GameStop Corp. or on any issuer.

Two streams, two characters

The protocol pays in two assets from two sources. They are independent and neither inherits the other's durability:

Both share the same weighting rule. Over T days with average distributable value F̄ per day and average total active weight W̄:

Live trading operations, if they are stood up, would report into the same contract on the same terms; nothing in this paper depends on them.

Read it twice, once per stream: with F̄ = E = 9,000,000 $1337/day it describes the drip (eq 14–15) until the reserve empties; with F̄ equal to average daily fee flow it describes the $GME stream, which does not empty. Doubling time held doubles the take. A 1337 General (w = 333) earns 3.33× a Recruit over the same period. Because the ETH leg is proportional to M, F̄ on the second stream scales with the collection rather than decaying against it.

09Risk disclosures

• Smart contract risk. Contracts can contain bugs. These are open source and small; read them.
• Mark / oracle risk. The ETH leg depends on a value posted from off-chain observation of OpenSea offers. The bounds in (12) cap what a bad or compromised poster can do per update — 24-hour averaging, ±20% movement, immutable floor and ceiling — and a stale feed falls back to the last good mark rather than halting or zeroing. They do not cover a poster who moves the mark to a bound and holds it there across many updates, a sustained wash-offer campaign on OpenSea that the average genuinely reflects, or OpenSea ceasing to carry the collection. In the last case the mark freezes at its last value.
• Single-asset RWA risk. All fee value converts to $GME. That is GameStop equity risk in full, plus liquidity risk on the Robinhood Chain $GME pool at the moment a drop executes — a large drop into a thin pool converts at a worse price. The target is hardcoded and cannot be changed, by anyone, for any reason.
• Jurisdictional. Stock-token features on Robinhood Chain are restricted for US persons. That restriction applies to the $GME stream and it lives on the stock-token rails, not in s1337's view of anybody. Holders who cannot hold the stock token cannot receive that stream.
• Relocated impact. Fixing the token leg does not remove price impact, it pushes it into the $1337/ETH Uniswap position, where it is fully visible and behaves per eq (2).
• One-directional flow drains the bid. The token reserve bids for ~1,203 soldiers, 16.4% of the collection. A fixed price is not a guaranteed fill: when the reserve empties there is no bid at any price.
• Finite emission. The $1337 reserve runs to zero — about 44.6 days at full rate — and snipe premiums extend it by roughly 0.0074 days each.
• FIFO selection is deterministic. Blind buys are not random; they fill oldest-first, and the outcome of any buy depends on the inventory state at execution.
• Release schedule. $GME pays out over a rolling 30-day window and only to weight that is activated at the time of release. A holder who transfers or discharges mid-window forfeits everything not yet released to them.
• $1337 carries no claim on equity, no redemption right and no guaranteed value. Supply Drops are protocol rewards paid by an ownerless contract, not dividends, and carry no claim on GameStop Corp. or any issuer.
• The mint window is 24 hours and does not reopen. Public-lane mints are paid and non-refundable, and a soldier bought at 0.01 ETH may be worth less afterwards.
• Nothing in this paper is investment advice.

10References

1. Kyle, A. S. (1985). Continuous Auctions and Insider Trading. Econometrica 53(6).
2. Perold, A. F. (1988). The Implementation Shortfall: Paper versus Reality. Journal of Portfolio Management 14(3).
3. Almgren, R. & Chriss, N. (2000). Optimal Execution of Portfolio Transactions. Journal of Risk 3(2).
4. US Securities and Exchange Commission. Regulation ATS, 17 CFR §§ 242.300–304 (1998).
5. FINRA. ATS Transparency Data — weekly ATS and OTC volume reporting.
6. Bartlett, R. P. & McCrary, J. (2017). Dark Trading at the Midpoint: Does SEC Enforcement Policy Encourage Crossing Networks to Undercut Exchange Liquidity? American Law and Economics Review 19(2).
7. Ethereum Improvement Proposals. ERC-8056 — tokenized equity with an on-chain share multiplier for corporate actions.
8. Design antecedent: Clutch Markets, Anvil AMM v2 — fixed-ratio NFT/token vault on Robinhood Chain, and the StonkBrokers market built on it.