The story of a short

A trader posts P = 62.5 τ. We follow every τ and every α through opening, daily decay, and three possible closes.
Pool reserves
Trader's P (floor)
E (escrow τ, held by protocol)
N → R (buffer τ, held by protocol)
Q (α debt the trader owes)

Part 1 — Opening the short (3 steps)

Pool starts at 1,000 τ / 100,000 α (price = 0.01). Trader wants to short. Three things happen at open.
Pool Trader Protocol Buffer Debt
Step TAO (τ) Alpha (α) Price P (τ) E (τ) N → R (τ) Q (α)
Start 1,000.00100,0000.010000000
1 Borrow α−39.00−3,900+39.00+3,900
After step 1 961.00 96,100 0.010000 39.000 3,900
2 Sell α back−37.48+3,900−7.6%+37.48 (N)
After step 2 923.52 100,0000.009240 39.0037.483,900
3 Trader funds P+62.50
Open complete923.52 100,0000.0092462.5039.0037.48 (R₀)3,900
1Borrow α from the pool. The pool gives up ϕA = 3,900 α and ϕT = 39 τ at the same time — a proportional withdrawal, so the price doesn't move (still 0.01). The 39 τ goes into protocol-held E (escrow). The 3,900 α is borrowed and about to be sold.
2Sell the borrowed α back into the (now smaller) pool. This is what moves price. CPMM math: selling 3,900 α into 961 τ / 96,100 α gives 37.48 τ out. Pool TAO drops to 923.52. Pool α goes back to 100,000. Price drops from 0.01 to 0.00924 (−7.6%) — the short has now happened. The 37.48 τ proceeds are the notional N; at open they seed the buffer, so N = R₀ = 37.48 τ. From here on it's called R (buffer) and decays daily.
3Trader funds P. Trader sends 62.50 τ to the protocol as the non-decaying floor. Open is done. TAO reconciliation: pool 923.52 + E 39 + R 37.48 = 1,000 τ ✓ (matches starting pool). Trader's 62.50 τ is fresh capital on top.

Part 2 — Each day, E and R shrink, price drifts up

R and E both decay at the same rate d ≈ 0.45%/day. The decayed slivers flow back into the pool via the restoration zap. Pool TAO refills. Spot price drifts back upward — that's the trader's carry cost.
Pool Trader Protocol Buffer Debt
Day TAO (τ) Alpha (α) Price P (τ) E (τ) R (τ) Q (α)
Why this matters: Every day a slice of E + R flows back into the pool. Pool TAO refills → spot price drifts upward. The trader is racing the clock: they need price to fall faster than R decays, OR price has to drop enough below open that the buyback cost (price × 3,900) stays below R.
What stays the same: P (62.50 τ) — the floor never decays. Q (3,900 α) — the debt never changes. What changes: R and E shrink. Pool refills. Spot rises (absent external trades).

Part 3 — Three ways the short closes

Same short. Day 10 close. R remaining = 35.78 τ. E remaining = 37.21 τ. The ONLY thing that changes between these scenarios is the α price. Trader's job is the same in all three: buy 3,900 α from the pool, return it, collect P + R. Whether that's a win or a loss depends entirely on what price has done.

A. Big win — price kept dropping

Price at close: 0.005 τ/α  (−46% vs open of 0.00924, −50% vs start of 0.01)
Lots of fear, low demand for this α. The trader's bet paid off.
Price at close
0.005 τ/α
R remaining
35.78 τ
Cost to buy back 3,900 α
0.005 × 3,900 = 19.50 τ
Buyback cost (19.50 τ) < R (35.78 τ) → close for profit.
Trader pays: 62.50 (P) + 19.50 (buyback) = 82.00 τ out of pocket
Trader receives: P + R = 62.50 + 35.78 = 98.28 τ
Net: +16.28 τ profit (+26.0% on P)

B. Partial loss — price drifted back up

Price at close: 0.0095 τ/α  (+2.8% vs open of 0.00924, almost back to the starting 0.01)
Carry has mostly eaten the open price drop. R has decayed slightly. Buyback now costs more than R.
Price at close
0.0095 τ/α
R remaining
35.78 τ
Cost to buy back 3,900 α
0.0095 × 3,900 = 37.05 τ
Buyback cost (37.05 τ) > R (35.78 τ), but < P + R (98.28 τ) → close to limit the loss.
Trader pays: 62.50 (P) + 37.05 (buyback) = 99.55 τ out of pocket
Trader receives: P + R = 62.50 + 35.78 = 98.28 τ
Net: −1.27 τ loss (−2.0% on P)
Still rational to close — abandoning would have lost all 62.50 τ.

C. Total loss — trader walks away, position defaults

Price at close: 0.030 τ/α  (+225% vs open of 0.00924, +200% vs start of 0.01)
The trader's directional bet failed badly. Buying back α now costs more than P + R — closing would lose more than walking away, so the trader does nothing and lets the position default.
Price at close
0.030 τ/α
R remaining
35.78 τ
Cost to buy back 3,900 α
0.030 × 3,900 = 117.00 τ
Buyback cost (117.00 τ) ≥ P + R (98.28 τ) → closing costs more than walking away. Trader doesn't close.
Trader pays: 62.50 τ (P forfeited) — sent to protocol sink, not used to pay the α debt.
Trader receives: 0 τ (α debt extinguished, limited recourse; residual R+E if > 1 τ returned to pool).
Net: −62.50 τ (full P lost)
No forced close, no liquidation. The trader is never liquidated by price. They simply stop — they never send the buyback τ. The position ends one of two ways, both protocol-driven, neither needing a trader action:
Time-based default — R decays to the dust floor (R ≤ Rdust, ~1 τ). The protocol recycles P outside the pool, dust-bounds residual R+E back into the pool, and extinguishes Q under limited recourse.
Subnet deregistration — terminal settlement values the short at last-tradable close cost, recycles P, extinguishes residual Q.
There are no price-based liquidation levels, no liquidation price to target, no short squeeze, no cascade — a deliberate design property. Default triggers on the buffer running out, not on the mark.

The decision rule — every day, every close

Condition (buyback cost = price × 3,900)ActionTrader's net
buyback < R Close for profit R − buyback (positive)
R ≤ buyback < P + R Close to limit lossR − buyback (negative, but > −P)
buyback ≥ P + R Walk away (defaults)−P (full floor lost)
The whole short, in one sentence: the trader is paying carry (R decaying back to the pool) for the right to buy back Q α whenever they want. They win if α gets cheap faster than R decays. They lose if α gets expensive or stays flat too long.