Purpose. Net cash is positive, but on-time receipts are eroding (longer “past-due” tails). Add a bounded stability lane so leaders see schedule slippage early while m stays identical (phi((m,a)) = m).
Classical KPI (unchanged).m := net_cash_inflow
Lanes (schedule adherence + lateness depth; optional drift canonicals).
# Schedule adherence (primary)
q_on_time := receipts_on_or_before_due / max(receipts_total, 1)
a_sched := 2*q_on_time - 1
a_sched := clamp(a_sched, -1+eps_a, +1-eps_a)
# Lateness depth (how far past due on average)
late_days_avg := SUM_i max(0, days_past_due_i) / max(invoices_count, 1)
a_late := tanh( 1 - late_days_avg / b_days ) # b_days > 0 declared once
a_late := clamp(a_late, -1+eps_a, +1-eps_a)
# Optional ZEOZO-Core drift on a timing series x_t (e.g., q_on_time_t or late_days_avg_t)
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 adherence with one timing source (rapidity-safe)
# pick a_timesrc in {a_late, a_zeozo, a_gap, a_syasys}
alpha in [0,1]
a := tanh( alpha*atanh(a_sched) + (1 - alpha)*atanh(a_timesrc) )
# Clamp all lanes before any atanh. Export band from chosen lane (a_sched 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).
Definition of “on or before due” (policy), window_days for the computation, b_days (lateness bound), eps_a=1e-6, alpha (blend). If drift is enabled: lam=0.10, mu=0.04, c and Z_ref or k_gap; SYASYS: rho=0.90, kappa=0.50, R=8.0, muR=ln(2)/R.
What good vs weak looks like.
- Good: high
q_on_time, smalllate_days_avg, calmZ_twithA_t >= Z_t⇒ lanes near +1 (A++/A+). - Weak:
mstays positive butq_on_timeerodes and/orlate_days_avgrises;Z_tandDelta_tclimb →a_schedand chosen timing lane slide to A0/A-.
Acceptance signal.a_sched drops one band and stays there 3+ days ⇒ immediate runway-assumption review. If the timing lane (a_timesrc) also downgrades within the same week, escalate to cross-functional collections/credit review and tighten terms on affected segments.
Mini calculator kit (10 rows).
date,kpi,m,a,band
2025-10-01,Cash_inflow,250000,0.90,A++
2025-10-02,Cash_inflow,240000,0.88,A++
2025-10-03,Cash_inflow,255000,0.80,A+
2025-10-04,Cash_inflow,260000,0.73,A+
2025-10-05,Cash_inflow,245000,0.61,A+
2025-10-06,Cash_inflow,250000,0.52,A+
2025-10-07,Cash_inflow,255000,0.45,A0
2025-10-08,Cash_inflow,248000,0.41,A0
2025-10-09,Cash_inflow,252000,0.36,A0
2025-10-10,Cash_inflow,251000,0.29,A0
Owner playbook.
- Declare due-date policy and
b_daysonce; do not change mid-pilot. - Slice by segment/region/payment terms to find the slipping corridors.
- If using SYASYS, show a green “calm” badge only when
SyZ_tis sustained high; keep CI on stamps/manifest parity.
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: identical inputs+knobs reproduce exports bit-stable after formatting;
knobs_hashflips on any knob change.
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SSM-Audit – Q & A
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