

==============================================================================================
PART 1 — the withdrawal haircut: bounded, ~0 normally, a few % in a stress tail.
==============================================================================================
Desk short Δ EUR (over-issued): circEUR = lockedEUR + Δ. On a EUR withdrawal the desk pays
pro-rata what it can source = lockedEUR + (excess USD / rNow). Haircut = 1 − available/claims.

  haircut = [Δ/(lockedEUR+Δ)] × [1 − r0/rNow]   (≈ over-issue-fraction × FX move)

      over-issue Δ            Δ/circ          EUR move  haircut per εEUR   on a $1000 exit
----------------------------------------------------------------------------------------------
             2 EUR             1.96%             2.00%             0.04%             $0.38
             5 EUR             4.76%             5.00%             0.23%             $2.27
            10 EUR             9.09%             5.00%             0.43%             $4.33
            10 EUR             9.09%            10.00%             0.83%             $8.26
            10 EUR             9.09%            20.00%             1.52%            $15.15
            20 EUR            16.67%            20.00%             2.78%            $27.78

  => Normal regime (small Δ, small move): haircut ~0. Worst realistic tail (10% over-issue, 20%
     EUR spike): ~1.5% on the EXITER. Bounded by the band: max haircut ≈ [band/(1+band)] × maxMove.
  => DESK SOLVENCY: it only ever pays out what it holds, pro-rata => ZERO FX risk, ALWAYS solvent,
     needs NO capital and NO band-for-solvency. (The band survives only as a HAIRCUT CAP for users.)


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PART 2 — aggregate cost is tiny, because ~90% stays on-chain (only exiters pay).
==============================================================================================
  Reserve $1000000.00, 10% over-issued, a 20% EUR spike, 10.00% of holders withdraw during it.
  Total FX shortfall to socialize: $20000.00. Haircut per exiter: 1.82%.
  Actual value transferred (exiters × haircut): $1818.18 = 0.18% of the reserve.

  => Because most value stays on BCH, only the small exiting slice pays, and only in the tail.
     The realized cost to users in aggregate is a fraction of a basis point of the reserve.


==============================================================================================
PART 3 — WHO bears the risk? three models, same "desk-zero-risk" goal, different incidence.
==============================================================================================

  model                    bears the FX drift        peg           desk risk   complexity
  ----------------------   -----------------------   -----------   ---------   --------------------------
  B / desk-insurer         the DESK                  hard 1:1      band+cap    hold inventory + premium
  B / swapper-margin       the SWAPPER (drift-mgn)   hard 1:1      ~zero       per-swap position + liquidation
  C / withdrawer-mutual>   the EXITERS (pro-rata)    SOFT in tail  ZERO        simplest: one global ratio, no
                                                                               per-user tracking, no liquidation

  All three can reach desk-zero-risk. They differ in INCIDENCE and PEG:
   • swapper-margin = "polluter pays": the user who CREATED the position bears its drift. Fairest by
     attribution; keeps a HARD 1:1 peg for everyone else; costs per-swap accounting + a liquidation path.
   • withdrawer-mutualized (THIS) = "exiter pays": the drift is socialized across whoever leaves during
     a shortfall. SIMPLEST (no per-swap tracking, no liquidation — just pay pro-rata what you hold), and
     the desk is trivially always solvent. Cost: the 1:1 peg becomes SOFT in the tail (εEUR = min(1 EUR,
     pro-rata share)); innocent exiters subsidize others' swaps; εEUR may trade < 1 EUR on the DEX during
     a shortfall (the market prices the expected haircut — which is honest, not a bug).



==============================================================================================
PART 4 — honest critique + where it fits.
==============================================================================================

 WORKS: yes — desk FX risk is genuinely ZERO and solvency is by construction (never pays more than it
   holds). This is the cleanest, most capital-light credit desk: no inventory, no premium, no per-user
   margin, no liquidation engine. It is ADR-0031 pro-rata redemption promoted to the default rule.

 THE REAL COST — it is a SOFT peg, not a risk eliminator. The FX risk did not vanish; it moved onto the
   token holders, realized as a haircut by whoever exits during a shortfall. So εEUR is no longer a hard
   1:1 IOU (ADR-0047 Σminted==Σlocked); it is a mutualized claim on a possibly-short reserve. Honest ONLY
   if the shortfall is on-chain-transparent and the haircut is a published function (ADR-0031 range).
   This partially re-enters what ADR-0050 guarded — an oracle-priced liability that can be short — except
   the shortfall is bounded (band) and socialized transparently rather than silently eating the desk.

 RUN-SAFETY: safe IFF the haircut is ORDER-INDEPENDENT (pro-rata equal for all exiters at the current
   shortfall ratio). Then there is no first-mover advantage => no race. A haircut that GREW with drain
   order would trigger a run — so the covenant must compute it from the *current global* ratio, not
   from remaining reserve. (This is exactly why ADR-0031 pro-rata is run-proof.)

 INCIDENCE FAIRNESS: the drift is created by the unmatched SWAPPERS but paid by the EXITERS — a
   mis-attribution the swapper-margin model avoids. For a PAYMENTS/spending product where users hold and
   spend on BCH (rarely exit), this is acceptable and nearly costless (Part 2). For a product where users
   expect a hard exit peg, prefer swapper-margin (attributed) or Version A (debit, no shortfall ever).

 RECOMMENDATION — offer BOTH credit settlements, disclosed:
   • Version A (debit) stays the default hard-peg product (no shortfall possible).
   • Version C (withdrawer-mutualized) is the SIMPLEST desk-zero-risk credit desk — best where value
     lives on BCH and exits are rare; label the soft-peg-in-tail honestly; keep the band as a haircut cap.
   • Version B/swapper-margin is the hard-peg desk-zero-risk option when attribution + a firm exit peg
     matter, at the cost of per-swap accounting + liquidation.
 CAVEAT: haircut formula assumes the desk converts its excess USD at rNow to cover EUR exits; single real
   path; stylised. Directional, not a forecast.

