Purpose. Same AR ratio looks fine, but within-window coverage is weakening and a long tail is building past policy. Add a bounded stability lane so leaders see the tail risk early while m stays identical (phi((m,a)) = m).
Classical KPI (unchanged).m := collected_total / issued_total for the period.
Lanes (coverage + tail pressure; optional drift canonicals).
# Coverage in policy window (primary lane)
# window_days is your standard policy (e.g., 30)
q_cov := collected_within_window / max(issued_total, eps_m)
a_cov := 2*q_cov - 1
a_cov := clamp(a_cov, -1+eps_a, +1-eps_a)
# Tail pressure (how much sits past the window)
p_tail := past_due_gt_window / max(issued_total, eps_m)
a_tail := 1 - 2*p_tail
a_tail := clamp(a_tail, -1+eps_a, +1-eps_a)
# Optional ZEOZO-Core on tail series (preferred over legacy volatility)
# x_t := daily p_tail
med := median(x); rad := median(|x - med|); rad := max(rad, 1e-6)
y_t := (x_t - med) / rad
E_t := (1 - lam)*E_{t-1} + lam*(y_t^2) # lam ~ 0.10
Z_t := log(1 + E_t)
A_t := (1 - mu)*A_{t-1} + mu*Z_t # mu ~ 0.04
Delta_t := | Z_t - A_t |
# Lane from ZEOZO (choose ONE if using drift)
a_zeozo := tanh( c*( 1 - Z_t / Z_ref ) ) # Z_ref := median(Z_t over pilot)
a_gap := tanh( k_gap*( A_t - Z_t ) )
# Optional SYASYS-Core calm-gated alignment (exec-friendly)
Q_t := rho*Q_{t-1} + (1 - rho)*clip( A_t - Z_t , 0 , 1 ) # rho ~ 0.90
muR := ln(2)/R, with R ~ 8.0, kappa ~ 0.50
SyZ_t := ( 1 / ( 1 + Z_t + kappa*Delta_t ) ) * ( 1 - exp( - muR*Q_t ) )
a_syasys := 2*SyZ_t - 1
# Blend coverage with one tail source (rapidity-safe)
# pick a_tailsrc in {a_tail, a_zeozo, a_gap, a_syasys}
alpha in [0,1]
a := tanh( alpha*atanh(a_cov) + (1 - alpha)*atanh(a_tailsrc) )
# Clamp any lane before atanh. Export band from your chosen lane (a_cov or blended a).
Bands (executive defaults).A++: a>=0.75, A+: 0.50<=a<0.75, A0: 0.25<=a<0.50, A-: 0.10<=a<0.25, else A--.
Hysteresis: promote if delta_a >= +0.05; demote if delta_a <= -0.05.
Knobs to declare (manifest).window_days, alpha (if blending), eps_a=1e-6, eps_m for safediv, and if using drift: lam=0.10, mu=0.04, c and Z_ref or k_gap; optional SYASYS rho=0.90, kappa=0.50, R=8.0, muR=ln(2)/R.
What good vs weak looks like.
- Good: high
q_cov, lowp_tail, calmZ_twithA_t >= Z_t⇒ lanes near+1(A++/A+). - Weak: headline
msteady butp_tailrises;Z_tandDelta_tclimb ⇒a_covand/or blendedaslide to A0 while meetings still celebrate the same ratio.
Acceptance signal.
Band drop sustained 5 business days in a_cov or the chosen tail lane ⇒ tighten credit on affected segments. If the second lane also downgrades within the same week, escalate to cross-functional review.
Mini calculator kit (10 rows).
date,kpi,m,a,band
2025-10-01,AR_collected_issued,0.9600,0.84,A++
2025-10-02,AR_collected_issued,0.9600,0.82,A++
2025-10-03,AR_collected_issued,0.9600,0.79,A+
2025-10-04,AR_collected_issued,0.9600,0.72,A+
2025-10-05,AR_collected_issued,0.9600,0.66,A+
2025-10-06,AR_collected_issued,0.9600,0.58,A+
2025-10-07,AR_collected_issued,0.9600,0.49,A0
2025-10-08,AR_collected_issued,0.9600,0.44,A0
2025-10-09,AR_collected_issued,0.9600,0.37,A0
2025-10-10,AR_collected_issued,0.9600,0.30,A0
Owner playbook.
- Slice weekly by segment, region, and age bucket to reveal where the tail forms.
- Keep
window_daysfixed during the pilot; do not move the goalposts. - If adopting drift, prefer
a_gapfor a simple calm-vs-drift read; usea_syasyswhen leadership wants a gated “green” only after sustained calm.
Conformance hooks.
- Order-invariant rollups:
a_out := tanh( (SUM w*atanh(a)) / max(SUM w, eps_w) )witheps_w := 1e-12. - Collapse parity:
phi((m,a)) = mthrough all ETL hops. - Determinism: same inputs and knobs reproduce identical exports (bit-stable after formatting);
knobs_hashflips on any knob change.
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