

==============================================================================================
PART 1 — realized loss vs how much of the SHORT currency is withdrawn off-chain.
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  Desk short 10 EUR at the 10.0% cap: lockedEUR 100, circEUR 110. EUR rises 20.0%.
  PAPER position (mark-to-market) = 10 × 20.0% × rate = $2.20. But REALIZED only on
  withdrawals that exceed lockedEUR (100). Realized loss = min(withdrawn−100, 10)₊ × move:

     EUR withdrawn   as % of circEURfrom locked (free)     desk must BUY     REALIZED loss
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              27.5             25.0%              27.5               0.0             $0.00
              55.0             50.0%              55.0               0.0             $0.00
              82.5             75.0%              82.5               0.0             $0.00
              93.5             85.0%              93.5               0.0             $0.00
             100.0             90.9%             100.0               0.0             $0.00
             104.5             95.0%             100.0               4.5             $0.99
             110.0            100.0%             100.0              10.0             $2.20

  => The desk realizes NOTHING until ~90.9% of the short currency is withdrawn off-chain
     (= lockedEUR/circEUR = 100/110). Below that, every withdrawal is served from locked EURC at
     ZERO cost. The paper position ($2.20) is only realized on the over-issued slice, capped at Δ×move.


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PART 2 — two-way flow keeps the imbalance NEAR ZERO (it is a buffer, not a bet).
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  Net imbalance Δ over 139 weeks, ±10 EUR band:

           flow regime               max |Δ|   weeks pinned at cap              ending Δ
----------------------------------------------------------------------------------------------
 two-way (mean-revert)                  10.0                     8                  -3.8
 one-way (toxic trend)                  10.0                    37                   4.3

  => Two-way flow keeps Δ small and oscillating around 0 — users swapping each way "find a balanced
     state," and the desk rebalances via natural deposit/withdraw netting at ~no cost. Only a
     PERSISTENT one-way regime pins Δ at the cap — and even then the loss is only the PAPER
     position until >~90% of the short currency is actually withdrawn (Part 1).


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PART 3 — the honest guardrail: the over-issue can INCENTIVISE a run on the short currency.
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  The one way the "90% stays on-chain" assumption can break under stress: if the over-issue is
  visible and εEUR can be redeemed 1:1 first-come, rational holders RACE to withdraw EUR while
  the desk is short — a run concentrated exactly on the short currency in an adverse move. Two
  mechanisms defang it, and they are already in the design:
   • PRO-RATA redemption during a shortfall (ADR-0031 published range): no first-mover advantage
     => no race => the "90% stays" assumption holds even under stress; the desk realizes the loss
     gradually as it rebalances, bounded at Δ × move (band × move).
   • THE BAND itself caps Δ small, so even a full run on the short currency realizes only band×move.
  So the worst realized cost is NOT a slow bleed — it is a rare, BOUNDED event (≤ band×move),
  requiring persistent one-way flow AND a >~90% withdrawal of the short currency AND a sustained
  adverse move. In every other regime the desk's position is paper that self-corrects.



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VERDICT — correction accepted
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 1. "Slowly bleeds" was WRONG for the normal regime. The desk's FX position is a PAPER mark, not a
    realized cost. It is realized only when withdrawals of the short currency exceed its locked
    reserve — i.e. not until ~90.9% of that currency is withdrawn off-chain (Part 1). The band is a
    REBALANCING WORKING-CAPITAL BUFFER, not a directional bet.

 2. Two-way flow keeps the imbalance near zero (Part 2): users swapping each way find a balanced
    state; the desk nets deposits vs withdrawals and rebalances at ~no cost. Most value stays on
    BCH (the hub thesis), so the source-chain boundary — the only place FX is realized — sees only
    the small net.

 3. The residual is a BOUNDED TAIL (≤ band × move), not a drip: it needs persistent one-way flow +
    a >~90% withdrawal of the short currency + a sustained adverse move, and it is defanged by
    pro-rata redemption + the band (Part 3). A thin premium is optional insurance for THAT tail,
    not compensation for a continuous expected loss.

 CAVEAT: stylised flow (seeded), single real path, aggregate accounting (per-currency split shifts
 the exact ~90% threshold — it is lockedC/circC). Directional, not a forecast.

