

==============================================================================================
PART 1 — STOCK vs FLOW: a component death leaves the reserve >> the withdrawal flow.
==============================================================================================
  Supply S of uniform USD. A component of weight w DIES → reserve drops to (1−w)·S. Withdrawals
  are honored at 1=1 while cumulative withdrawals ≤ reserve. So the peg only breaks if the exit
  flow exceeds (1−w) of supply — i.e. a near-total RUN. Normal flow is a small fraction:

        dead component w           reserve afterpeg holds for withdrawals up to          breaks only if
----------------------------------------------------------------------------------------------
                    5.0%         95.0% of claims    95.0% of supply exit              >95.0% run
                   10.0%         90.0% of claims    90.0% of supply exit              >90.0% run
                   15.0%         85.0% of claims    85.0% of supply exit              >85.0% run
                   20.0%         80.0% of claims    80.0% of supply exit              >80.0% run

  => A single death (w ≤ per-issuer cap ≤ ~10–20%) leaves the reserve at 80–95% of claims — which
     DWARFS any normal withdrawal flow (~5–20%). So internal face value stays 1=1, withdrawals stay
     honored, and the death only bites the WITHDRAWAL path to that dead chain. YOUR CLAIM CONFIRMED.


==============================================================================================
PART 2 — the buffer requirement COLLAPSES: back the FLOW, not the STOCK.
==============================================================================================
  Supply $100M. Two ways to define "hold 1=1":

  (A) REDEMPTION-proof (report-10): make total backing = 100% even after a death →
      buffer = cap × supply = 10% × $100M = $10M. Survives a TOTAL run. Expensive.
  (B) MONEYNESS (this sim): keep reserve > the actual withdrawal FLOW + confidence margin.
      normal flow 10.0% → even a 2× spike (20.0%) is < the 90% reserve → buffer needed for the peg: 0.0% ($0M).
      normal flow 20.0% → even a 2× spike (40.0%) is < the 90% reserve → buffer needed for the peg: 0.0% ($0M).

  => Because circulation dwarfs redemption, you almost never need the report-10 cap-sized buffer.
     A small confidence/smoothing buffer suffices; the cap-buffer is only the doomsday-run backstop.
     This is FRACTIONAL RESERVE done transparently — solvent-for-the-flow, not 100%-instantly-liquid.


==============================================================================================
PART 3 — the ONE dependency: CONFIDENCE. It is a two-equilibrium system.
==============================================================================================

  GOOD equilibrium (confidence intact): withdrawals are a trickle, internal value = 1=1, the reduced
   reserve easily covers exits, the dead component is invisible to everyone who just USES the money.
  BAD equilibrium (confidence breaks): everyone tries to exit at once; withdrawals > reserve; the peg
   snaps to redemption value; a self-fulfilling run.

  The whole game is staying in the GOOD equilibrium. The defenses (all already in our design):
   • TRANSPARENCY — the reserve + composition are ON-CHAIN, provable. Confidence rests on fact, not
     faith (the edge over Tether: reconcilable Σminted==Σlocked per issuer, publicly).
   • DIVERSIFICATION + CAPS — no single death is big enough to rationally trigger a run (Part 1).
   • A SMALL BUFFER — absorbs the loss so the reserve stays visibly credible.
   • PRO-RATA-DURING-STRESS (ADR-0031) — the killer defense: if a run ever starts, redemption becomes
     pro-rata (everyone gets the same share), which REMOVES the first-mover advantage → removes the
     REASON to run. It converts a disorderly run into an orderly, tiny, shared haircut. Self-defusing.



==============================================================================================
PART 4 — this is not exotic: it is how money ALREADY works.
==============================================================================================

  • FIAT — a dollar holds value by ACCEPTANCE (legal tender, network effect), not by gold redemption.
  • EURODOLLARS — dollars circulating OUTSIDE the US banking system, treated as dollars, rarely
    repatriated. Uniform-USD is the "eurodollar of Bitcoin Cash": an internally-circulating dollar.
  • USDT — fractionally/opaquely backed, yet holds its peg from deep adoption + marginal arbitrage;
    most holders never redeem with Tether directly. Uniform-USD is a MORE TRANSPARENT, MORE
    DIVERSIFIED version of the exact same money — reconcilable on-chain, no single-issuer dependence.

  So the design is not a bet on a novel mechanism — it is the PROVEN mechanism of circulating money,
  rebuilt with on-chain transparency and a diversified reserve. The user's instinct is monetary, and right.



==============================================================================================
VERDICT — internal 1=1 holds by MONEYNESS; the peg costs confidence, not 100% backing.
==============================================================================================

 CONFIRMED — at adoption, uniform-USD's INTERNAL value (trades/payments/exchange on BCH) is 1=1 by
 acceptance + circulation, and withdrawal is a minority flow. A component dying elsewhere hits the
 WITHDRAWAL PATH to that chain, but the direct effect on internal value is absorbed by the basket
 reserve — because the reserve (even minus a capped death) dwarfs the exit flow (Part 1). This makes
 the backing requirement FAR cheaper than a 100%-redemption model (Part 2): back the flow, not the stock.

 THE TRUTH-TELLER CAVEAT — this is fractional reserve, a CONFIDENCE equilibrium. It is stable until a
 run, and a run is the only thing that breaks it. So the redemption peg must stay CREDIBLE even though
 it is rarely used: on-chain transparency, diversification + caps, a small buffer, and — the decisive
 backstop — PRO-RATA redemption under stress (ADR-0031), which removes the first-mover incentive and
 makes a run self-defusing. Keep those, and internal 1=1 holds through any single issuer's death.

 ONE LINE: uniform-USD is the eurodollar of Bitcoin Cash — its value is its acceptance, its reserve
 serves the exit flow not the whole stock, and its peg is defended by transparency + pro-rata, not by
 a promise that every dollar is instantly redeemable at a bank.

