PART 1 -- velocity under Mode A deflation (relative to price-stable baseline=1.00)

  semi-elasticity eta=0.5 (Lucas 2000 baseline; range 0.3-0.6)

    deflation pi  velocity index  velocity drop
          +0.0%           1.000          +0.0%
          -1.0%           0.995          -0.5%
          -1.9%           0.991          -0.9%
          -3.0%           0.985          -1.5%

  Reading: at Mode A's ~-1.9%, velocity sits ~1% below the price-stable baseline on
  the central elasticity. That is SMALL and matches Atkeson-Kehoe: mild productivity
  deflation does not, by itself, trigger a hoarding spiral. The case for demurrage is
  NOT the steady mild-deflation state; it is the CONDITIONAL tail where deflation
  expectations deepen or a confidence shock drops velocity further.

PART 2 -- demurrage delta that neutralises the hoarding reward

  Demurrage adds a carrying cost that offsets the -pi reward on idle cash.
  Setting delta = -pi zeroes the net carry and restores velocity to baseline.

    deflation pi  delta to neutralise  velocity restored to
          -1.0%               1.0%               1.000
          -1.9%               1.9%               1.000
          -3.0%               3.0%               1.000

  So the required demurrage is modest: ~1.9%/yr to exactly offset Mode A's deflation,
  far below Worgl's 12% or Chiemgauer's 8%. Revenue recycled equally per-capita makes
  it net-neutral on average (no money created/destroyed, price path preserved); only
  the relative incentive bites -- above-average hoarders pay, fast-spenders gain.
PART 3 -- leakage cap: how hard can delta be pushed before money flees?

  Demurrage is evaded by switching to untaxed liquid stores (Keynes). The usable
  rate is bounded by the liquidity value of staying in transactional money.
  - Floors are LOCKED (can't dump money there), removing the easiest escape, but
    assets/foreign/crypto remain. Worgl/Chiemgauer sustained 8-12% only because
    the scrip was the ONLY local means of payment + tax-receivable (high captive
    demand). A national CS would have more escape routes -> lower ceiling.
  - Practical safe band: delta up to ~the transactional liquidity premium
    (order a few %), comfortably above the ~1.9% needed to offset Mode A. The
    offset rate sits INSIDE the leakage-safe zone; pushing far beyond it (Worgl-
    scale) would drive flight, not circulation, at national scale.

PART 4 -- conditional design (the honest recommendation)

  Demurrage should ARM only when velocity falls below a threshold, not run by
  default (Atkeson-Kehoe: the benign state needs no intervention; intervening
  there would just impose a deadweight carrying cost).
  Trigger: arm if velocity index < 0.95 (>5% below baseline).
   pi=-1.9%: velocity 0.991 -> dormant (benign)
   pi=-4.0%: velocity 0.980 -> dormant (benign)
   pi=-6.0%: velocity 0.970 -> dormant (benign)

  RECOMMENDATION:
  - Mode A (and any mild-deflation config) carries demurrage as a DORMANT, conditional
    tool, armed only if velocity drops materially (e.g. >5% below baseline) signalling
    the benign deflation is tipping into hoarding.
  - When armed, delta ~ -pi (a couple %), revenue recycled equally per-capita, applied
    to the TRANSACTIONAL circuit ONLY (Floors exempt, as with reverse-KT).
  - This is the ONE failure mode KI cannot address (KI would issue money and destroy
    the intended deflation); demurrage decouples the price path from the hoarding
    incentive, which no other CS lever does.
  HONEST RESIDUALS:
  - The velocity-elasticity (eta) and the leakage ceiling are the two soft numbers;
    both are bounded by data (eta 0.3-0.6; Worgl/Chiemgauer show 8-12% is sustainable
    only with captive demand) but neither is sharp at national scale.
  - True Gesell demurrage (face-value decay) bites harder than a constant-face 'negative
    interest' version, which holders can still hoard through; design must specify which.
  - Demurrage's gain is velocity, NOT new purchasing power; it cannot substitute for
    KI in a genuine demand collapse where you need more money, not just faster money.
