Purpose. Month-end ties can mask daily friction that later bites cash. Publish a bounded stability lane beside your existing refund/chargeback KPI so executives see drift early while m stays identical (phi((m,a)) = m).
Classical KPI (unchanged).m := refunds_total / shipments_total (or keep your current published rate/value).
Lane (agreement quality).
# Inputs (declare once per pilot)
d := | m_platform - m_bank | # daily divergence (same units as m)
b := acceptable bound on d (e.g., 0.005 for 0.5% rate difference)
eps_a := 1e-6
# Stability lane (bounded, clamp-safe)
a_agree := tanh( 1 - d / b )
a_agree := clamp(a_agree, -1+eps_a, +1-eps_a)
# Bands (executive-friendly)
A++: a>=0.75, A+: 0.50<=a<0.75, A0: 0.25<=a<0.50, A-: 0.10<=a<0.25, A--: a<0.10
# Hysteresis (reduce flicker)
promote if delta_a >= +0.05 ; demote if delta_a <= -0.05
Knobs to declare.b (e.g., 0.005), eps_a = 1e-6. Keep these fixed during the pilot; any change regenerates knobs_hash.
What “good” vs “weak” looks like.
- Good: small, stable
d⇒a_agreein A++/A+. - Weak: creeping
d⇒a_agreeslides to A0/A- whilemlooks “fine.”
Acceptance signal.a_agree in A0 (or worse) for 3 of 5 days ⇒ open reconciliation RCA before month-end close.
Mini calculator kit (10 rows).
date,kpi,m,a,band
2025-10-01,Refunds_agreement,0.0200,0.69,A+
2025-10-02,Refunds_agreement,0.0198,0.66,A+
2025-10-03,Refunds_agreement,0.0201,0.58,A+
2025-10-04,Refunds_agreement,0.0200,0.49,A0
2025-10-05,Refunds_agreement,0.0203,0.43,A0
2025-10-06,Refunds_agreement,0.0202,0.40,A0
2025-10-07,Refunds_agreement,0.0201,0.37,A0
2025-10-08,Refunds_agreement,0.0200,0.35,A0
2025-10-09,Refunds_agreement,0.0204,0.29,A0
2025-10-10,Refunds_agreement,0.0203,0.24,A-
Owner playbook.
- Normalize both platform and bank views to the same basis (same currency, window, and inclusion rules).
- Align time keys (UTC date) and define tie-breaking for late postings.
- Declare the denominator once (e.g., shipments_total for rates) and keep it stable during the pilot.
Optional enhancements (still bounded & order-safe).
# Timing-drift lane on the divergence series d_t (ZEOZO-Core)
med := median(d); rad := median(|d - med|); rad := max(rad, 1e-12)
y_t := (d_t - med)/rad
E_t := (1 - lam)*E_{t-1} + lam*(y_t^2)
Z_t := log(1 + E_t)
a_drift := tanh( c*( 1 - Z_t / Z_ref ) ) # pick lam=0.10, c≈1.0, Z_ref := median(Z_t over pilot)
# Composite reconciliation lane (rapidity-safe blend)
a_recon := tanh( ( w1*atanh(a_agree) + w2*atanh(a_drift) ) / max(w1+w2, 1e-12) )
# Clamp inputs before any atanh; w1,w2 >= 0. Report band on a_recon if you prefer a single badge.
Conformance hooks.
- Order-invariance: fuse any rollup with
a_out := tanh( (SUM w*atanh(a)) / max(SUM w, eps_w) ). - Determinism: fixed knobs ⇒ identical reruns (bit-stable after formatting).
- Collapse parity:
phi((m,a)) = mholds through every export/ETL hop.
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SSM-Audit – Q & A
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