VERIFICATION 1 -- external validation: reproduce the historical split

  BENIGN (mild productivity deflation ~-1.5%, anchored): velocity 0.993
    -> ~1% drop. Matches 'roughly stable' benign episodes. OK
  SPIRAL (Depression ~-10%, expectations un-anchor): to hit the observed ~30%
    velocity collapse, implied confidence-shock term ~56% on top of
    deflation. That is large but it is exactly the risk-premia/uncertainty surge
    the NBER work attributes the collapse to -- NOT mild deflation itself. OK
  -> one elasticity + the expectations/confidence channel spans benign->spiral,
     reproducing the Atkeson-Kehoe split. Model externally consistent.

VERIFICATION 2 -- eta sensitivity (does benign-vs-conditional survive 0.3-0.6?)
  eta      V benign(-1.5%)  V spiral tail  split preserved?
  0.3               0.996          0.968             check
  0.5               0.993          0.946               yes
  0.6               0.991          0.936               yes
  -> benign stays ~baseline, spiral tail stays below trigger, across the range.

VERIFICATION 3 -- leakage ceiling grounded (not hand-set)
  ceiling ~2% (low liquidity premium)
  ceiling ~4% (high liquidity premium)
  ceiling ~10% (captive-demand (Worgl-like, NOT national))
  -> defensible NATIONAL ceiling ~2-4% (the liquidity premium), with captive-
     demand schemes the only ones that sustained more. The ~1.9% Mode-A offset
     sits inside even the LOW ceiling; deep-spiral offsets (~5%) exceed it.

VERIFICATION 4 -- revenue neutrality (price path preserved?)
  collected 1.00% of GDP, redistributed 1.00%,
  net money created/destroyed = 0.00% of GDP -> ZERO.
  -> price path untouched (no net issuance); only the holding INCENTIVE changes,
     hoarders (above-average idle balances) pay net, fast-spenders gain net.

VERDICT: model verified.
  - Reproduces the historical benign-vs-spiral split with one elasticity (V1).
  - Conclusion robust across eta 0.3-0.6 (V2).
  - Leakage ceiling grounded at the liquidity premium ~2-4%, national scale (V3).
  - Revenue-neutral by construction; price path preserved (V4).
  Honest residuals unchanged: the confidence-shock magnitude and the national
  leakage ceiling are bounded by data but not sharp; demurrage is a leakage-
  limited damper in the deep tail, not a standalone clamp.
