I7 — Portfolio stability index (optional roll-up)
Purpose. One-look view across lanes to spot broad “stability debt” while keeping classical values identical (phi((m,a)) = m). The index stays bounded in (-1,+1) and composes via rapidity to remain order-invariant and interpretable.
Index (bounded, rapidity-safe).
# Inputs: lanes a_i in (-1,+1), weights w_i >= 0
W := SUM_i w_i # use w_i := 1 for equal weighting
u := ( SUM_i w_i*atanh(a_i) ) / max(W, 1e-12)
a_sdi := tanh(u) # bounded portfolio lane in (-1,+1)
# Clamp inputs before any atanh:
a_i := clamp(a_i, -1+eps_a, +1-eps_a) with eps_a := 1e-6
Group-balanced option (avoid over-weighting one module).
# Within each module j
W_j := SUM_i w_{j,i}
u_j := ( SUM_i w_{j,i}*atanh(a_{j,i}) ) / max(W_j, 1e-12)
a_j := tanh(u_j)
# Across modules
V := SUM_j v_j
u_all := ( SUM_j v_j*atanh(a_j) ) / max(V, 1e-12)
a_sdi := tanh(u_all)
Optional smoothing (executive display only; not for CI math).
u_sdi_raw := ( SUM_i w_i*atanh(a_i) ) / max(W, 1e-12)
u_sdi_t := (1 - eta)*u_sdi_{t-1} + eta*u_sdi_raw # 0 < eta <= 1
a_sdi_t := tanh(u_sdi_t)
Interpretation.
High a_sdi => broad stability; low a_sdi => cross-functional fragility. Bands use the global thresholds (A++/A+/A0/A-/A--). Classical m values remain unchanged everywhere (phi((m,a)) = m within each underlying KPI).
Knobs to declare (manifest).
[SSM_AUDIT_SDI]
lane_set = ["Refunds_agreement","AR_collected_issued","Revenue_actual"] # example
weights = {Refunds_agreement=1.0, AR_collected_issued=1.0, Revenue_actual=1.0}
group_balanced = false
# Optional display smoothing (do not use in CI calculations)
eta_display = 0.20
eps_a = 1e-6
Mini calculator kit (10 rows; copy-ready).
date,kpi,m,a,band
2025-10-01,Stability_index,0.0,0.78,A+
2025-10-02,Stability_index,0.0,0.76,A+
2025-10-03,Stability_index,0.0,0.72,A+
2025-10-04,Stability_index,0.0,0.66,A+
2025-10-05,Stability_index,0.0,0.60,A+
2025-10-06,Stability_index,0.0,0.54,A+
2025-10-07,Stability_index,0.0,0.47,A0
2025-10-08,Stability_index,0.0,0.42,A0
2025-10-09,Stability_index,0.0,0.37,A0
2025-10-10,Stability_index,0.0,0.31,A0
4.5 — Legal, Licensing, and Repository Note (brief)
Scope and intent. Observation-only; this work does not replace controls, statutory reporting, or professional advice. Results preserve classical figures (phi((m,a)) = m). As-is, no warranty. No endorsement or affiliation implied.
Anonymization and derived-only. Real-style case studies are anonymized. No third-party data is embedded here; we publish derived values only (lanes, bands, charts, manifests, stamps).
Repository link for artifacts.
Full, stampable artifacts (scripts, stamped runs, sample CSVs, and any third-party license notes where applicable) are available via the repository link below.
License for this page.
© The Authors of Shunyaya Framework and Shunyaya Symbolic Mathematics. Released under CC BY-NC 4.0 (non-commercial, with attribution). Observation-only; not for operational, safety-critical, or legal decision-making.
Navigation
Previous: SSM-Audit – Illustrative Case: Cash healthy, schedule slipping (4.4 I6)
Next: SSM-Audit – BI and Operations (5.1–5.11)
Directory of Pages
SSM-Audit – Table of Contents
Frequently asked questions
SSM-Audit – Q & A
SHUNYAYA 