Scope (public, reproducible, dataset-neutral). We annotate country-level financial indicators with a bounded stability lane beside the classical value. Classical magnitudes remain identical by construction (phi((m,a)) = m). This page shows a single method applied across three distinct regimes—Nigeria (NG), Brazil (BR), and South Africa (ZA)—to demonstrate generality without embedding third-party data.
Method card (one rule for all countries).
# Track (EMA; fixed once per study)
A_t := (1 - mu)*A_{t-1} + mu*x_t # default mu = 0.30
# Robust scale (one pass over residuals)
r_t := x_t - A_t
s := 1.4826 * median(|r_t|)
# Bounded stability lane (clamp before/after any atanh/tanh)
a := tanh( k * ( 1 - |r_t| / s ) ) # default k = 1.2
a := clamp(a, -1+eps_a, +1-eps_a) # eps_a = 1e-6
# Bands (executive-friendly) with gentle hysteresis
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
promote if delta_a >= +0.05; demote if delta_a <= -0.05
Country snapshots (high-level, no source tables embedded).
- Nigeria (NG). Early windows show churn vs. the EMA track (lane dips including < 0), followed by a durable positive lane in the later window. Portfolio SDI across two indicators trends net positive—a concise “calm now, turbulence earlier” story—while reported values remain untouched.
- Brazil (BR). Lanes generally positive with brief mid-window softness; the portfolio lane stabilizes in the A+ region. The annotation highlights short stretches of residual widening that would be easy to miss from level charts alone.
- South Africa (ZA). After an early turbulent phase, lanes turn durably positive; the Z-score lane sits high while NPL lane hovers near the A0/A+ boundary. Portfolio SDI summarizes to a steady A+ profile.
Why a trio instead of one country.
- Generalization, not a one-off. Same knobs (
mu,k,eps_a) behave sensibly across three distinct macro contexts. - Cherry-pick defense. Showing NG, BR, ZA avoids “lucky example” optics while keeping the blog slim.
- Executive read. Bands + SDI communicate calm vs. churn at a glance; classical figures remain identical (
phi((m,a)) = m).
Replication note (calculator-fast, off-blog).
Full scripts, stamped runs, and licensing notes live in the repository link provided at the end of this section on the site. Keep the blog dataset-neutral; keep concrete artifacts in the repo.
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SSM-Audit – Table of Contents
Frequently asked questions
SSM-Audit – Q & A
Explore Further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Audit
Disclaimer
Research/observation only. Not for operational, safety-critical, or legal decision-making.
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