Poseidon Tokenomics

Poseidon AMM | Technical Infographic

Constant-Product AMM Mechanics

A production-grade teaching tool implementing the xy = k invariant with exact integer arithmetic. Featuring staking-driven fees, hourly rate limits, and absolute conservation of mass.

Invariant
xy = k
Constant Product
Precision
BigInt
10⁻⁶ Exact Arithmetic
Max Fee
100%
Driven by Staking
Safety
Conserved
Input = Output

Core AMM Mechanics

The pool holds pool_usdc (X) and pool_tokens (Y). Ignoring fees, the product remains constant. The ceiling is applied using exact BigInt division: ⌈a/b⌉ = (a + b - 1) / b. No float rounding.

The Bonding Curve

base_cost(q) = ⌈ pool_usdc × q / (pool_tokens − q) ⌉

Price Impact Surface

Slippage ≈ Trade Size / Pool Depth

Fee Hierarchy & The "Knee"

Fees are driven by the staking ratio. Sell fees are paid in tokens and remain in the pool, raising the spot price. Exact integer arithmetic creates a natural "Free Bucket" for small trades.

Fee Rates vs. Staked Percentage

Sell Fee BP
⌊ staked / supply × 10,000 ⌋
Mint Fee BP
⌊ sell_fee_bp / 5 ⌋
Buy Fee BP
⌊ mint_fee_bp / 2 ⌋

The Knee Escape Mechanism

fee_tokens = ⌊ taxable × sell_fee_bp / 10,000 ⌋

Integer Floor Dynamics

Because fees use floor(), sub-10000 products naturally drop to exactly 0. This is not a bug; it is the natural consequence of integer arithmetic protecting small players.

  • ➤ Free Bucket = ⌊ kneeMult × 10,000 / sell_fee_bp ⌋
  • ➤ Cumulative hourly sells below threshold pay 0 fee.
  • ➤ Dev parameter kneeMult widens the tax-free zone.

Transaction Reference

Detailed state changes for every protocol action. All math is exact.

💰

BUY

Swap USDC for Tokens. Unlimited quantity, fractional OK. Buy fee routes to developer wallet.

w.usdc -= total
w.tokens += q
pool_usdc += base
pool_tokens -= q
dev_usdc += buy_fee
🔄

SELL

Swap tokens for USDC. Subject to hourly cap (pool_tokens) and free bucket. Fees stay in pool.

w.tokens -= q
w.usdc += uout
pool_tokens += net + fee
pool_usdc -= uout
⛏

MINT

Create new tokens. Expands supply. Hourly cap = pool_tokens + staked per wallet.

w.usdc -= base + fee
w.tokens += q (new)
pool_usdc += base + pool_add
total_supply += q
🔒

STAKE

Lock tokens to earn fee yield indirectly via spot appreciation. Raises fees for everyone.

w.tokens -= q
w.staked += q
S.stk += q
Fees recalculate
🔥

BURN

Permanent token destruction for USDC. Payout is exactly 100% of spot price per 1T. One-way commit, round-robin execution.

At Commit (Immediate)
w.tokens -= n
total_supply -= n
At Execution (Per Tx)
pool_usdc -= payout
w.usdc += payout

Round-Robin Burn Queue

Every gas-bearing transaction triggers one burn from the queue, subject to a time delay of N = 1 + ⌊sell_fee_bp / 100⌋ seconds.

Trigger
Any Tx
(Buy, Sell, Mint)
↓
Delay Gate Passes
BURN QUEUE
1
Alice
Pending: 3T
→
Bob
Pending: 2T
→
Shark
Pending: 4T
Execution Order: Alice → Bob → Shark → Alice → Bob ...
Payout
100% Spot
⌊ U×C/T ⌋

Absolute Conservation

The invariant you can always check. No tokens or USDC are created from nothing.

💰

⚖ USDC Conservation

pool_usdc + dev_usdc + Σ(wallet.usdc) = ext_usdc

ext_usdc changes only on: +H yield: ext_usdc += (new - old)
Inject: ext_usdc += amount
Drain: ext_usdc -= amount

🔒

⚖ TOKEN Conservation

pool_tokens + staked + Σ(wallet.tokens) = total_supply

total_supply changes only on: Mint: total_supply += q
Burn commit: total_supply -= n

Developer Controls & Presets

Preset USDC Tokens Spot Use Case
Nano$1,0001,000$1.00Test extreme price impact
Default$100,000100,000$1.00Standard teaching session
Deep$1M1M$1.00Institutional depth, low slippage
Overweight$500K2M$0.25Below-spot price test
Ultra-thin$100K100$1,000Extreme price per token

Complete Formula Reference

Metric Expression Precision
base_cost(q)⌈ pool_usdc × q / (pool_tokens − q) ⌉BigInt exact
sell_fee_bp⌊ S.stk × 10,000 / total_supply ⌋Integer
mint_fee_bp⌊ sell_fee_bp / 5 ⌋Integer
free_bucket⌊ kneeMult × 10,000 / sell_fee_bp ⌋ tokens/hrInteger
fee_tokens (sell)⌊ taxable × sell_fee_bp / 10,000 ⌋BigInt exact
burn_payout⌊ pool_usdc × CENT / pool_tokens ⌋ per 1TInteger
⚓

POSEIDON AMM — TECHNICAL WHITEPAPER V4

All formulas exact integer arithmetic. Conservation guaranteed.

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