The math, in full

Your hashrate is a pro-rata share of the whole fleet:

your_TH = (your_staked / total_staked) × fleet_TH

fleet_TH  = total token supply (1 token = 1 TH, always)
example   = (580 / 58,000) × 100,340 = 1,003.4 TH

While any supply sits unstaked, stakers mine with more than 1 TH per token. Earnings use the live hashprice we compute from primary data:

hashprice ($/TH/day) = last_144_blocks_rewards_BTC × BTC_USD ÷ network_TH
network_TH           = difficulty × 2³² ÷ 600 ÷ 10¹²

energy      = delivered_TH × $0.01368/day
            = your_TH × 0.228 kWh × $0.06     (9.5 J/TH)
net_per_day = your_TH × (hashprice × (1 − pool_fee) − $0.01368)

You pay for the hashrate you actually receive: energy bills hourly at 570 µUSD per delivered TH-hour, on the same your_TH that earns. At a 50% stake ratio each staked token delivers 2 TH and pays 2× energy per token; the per-TH cost never changes. The balance may run negative up to 240 hours of your current burn rate, ten days at any stake ratio, whatever the token trades at. Then delivery pauses with 72 hours to cure free; after that the position settles in one transaction: tokens worth the debt burn at the reference price and the rest of the stake force-unstakes back to your wallet. Segments recovers the bill by mining with the freed hashrate before it rejoins the fleet-wide split.

The SHASH/USDC pool is constant-product, and its depth is protocol-owned. A quarter of the transfer fee is added to it as Segments' own position, so the market always has depth nobody can pull:

pool invariant : x × y = k   (x = SHASH side, y = USDC side)
fee split      = 50% Segments · 25% burned · 25% protocol-owned depth
seed           = USDC worth 10% of every batch minted, never withdrawn

Selling n tokens gives up value in three separate places, and the sell desk shows all three rather than netting them into one number. This is the exact arithmetic behind it:

transfer fee : a = n × (1 − 0.025)      withheld in SHASH, never reaches the pool
swap fee     : b = a × (1 − 0.0025)     the venue's cut, taken from the input
proceeds     : usdOut = y × b / (x + b) from x × y = k
price impact : n·P − transferFee − swapFee − usdOut

effective price = usdOut / n
new pool mid    = (y − usdOut) / (x + b)

The three deductions plus the proceeds sum exactly to n × P, so any ledger built from them reconciles. Adding both sides at the current price never moves the price; adding one side does, which is why the protocol never dumps tokens one-sided.