Scope (neutral acknowledgment). We reproduce a well-known public audit-style benchmark without embedding third-party data here. Classical magnitudes stay identical (phi((m,a)) = m). The stability lane annotates when “big” values are misaligned with simple agreement and risk-pressure checks. Full, stampable artifacts (scripts, manifests, CI notes) are available via the repository link below.
Executive readout (what leaders see).
- Same numbers, clearer signal. Magnitudes remain unchanged; lanes add
A++/A+/A0/A-/A--. - Early tail surfacing. The sign of
S(m,a) := m*ahighlights “large-but-misaligned” entries early. - Deterministic & auditable. Fixed knobs, clamp discipline, order-invariant fusion, and a one-screen method card.
Invariants (non-negotiable).
collapse: phi((m,a)) = m
clamp: a := clamp(a, -1+eps_a, +1-eps_a) with eps_a = 1e-6
fuse: a_out := tanh( (SUM w*atanh(a)) / max(SUM w, eps_w) ) with eps_w = 1e-12
bands: A++: a>=0.75; A+: a>=0.50; A0: a>=0.25; A-: a>=0.10; else A--
hysteresis: promote if delta_a >= +0.05; demote if delta_a <= -0.05
Method card (calculator-fast, dataset-neutral).
# Inputs (table columns; names are illustrative, not prescriptive)
m := metric_value # classical number you already report
t := scale_variable # e.g., a simple total/driver column
R[] := bounded risk factors in [0,1] # e.g., inherent/control/detection-like scores
# Knobs (declare once; stable for all runs)
eps_a=1e-6; eps_w=1e-12
k1=1.2; k2=1.0
# 1) Residual agreement lane (bounded)
# Fit a simple line once (baseline window documented in the manifest):
# m ≈ beta0 + beta1 * t
res := m - (beta0 + beta1*t)
s := 1.4826 * MAD(res) # robust scale
a_res := tanh( k1 * ( 1 - |res| / s ) ) # then clamp before any atanh use
a_res := clamp(a_res, -1+eps_a, +1-eps_a)
# 2) Risk-pressure lane (bounded, monotone)
risk_scaled := mean(R[]) # already in [0,1]; clamp if needed
a_risk := tanh( k2 * ( 1 - risk_scaled ) )
a_risk := clamp(a_risk, -1+eps_a, +1-eps_a)
# 3) Combine in rapidity (order-invariant)
a := tanh( ( atanh(a_res) + atanh(a_risk) ) / 2 )
a := clamp(a, -1+eps_a, +1-eps_a)
# 4) Ranking lens (symbolic strength)
S := m * a # sign-flip flags large-but-misaligned
# 5) Bands (with hysteresis gates)
band := band_from(a) # A++/A+/A0/A-/A--
What it surfaces (narrative).
- Rows with big m but low/negative a move left under
S(m,a)(earlier triage). - Rows with moderate m and strong a remain confidently right (calm).
- Because the rules are bounded and declared, each label is explainable and replayable.
Reproduction checklist (PASS/WARN/FAIL).
[ ] Clamp safety: -1 < a < +1 after clamp
[ ] Collapse parity: phi((m,a)) == m everywhere
[ ] Band parity: band == band_from(a) (declared thresholds)
[ ] Determinism: rerun with same inputs/knobs reproduces a and band
[ ] Order test (if rolling up): U/W fuse yields same a_out for batch/stream/shuffle
[ ] Knobs fingerprint: knobs_hash flips on any knob change
CI note (daily).
eps_num := 1e-12
- Recompute bands from a; assert equality
- (Optional) Produce S := m*a and a sorted table for reviewer triage
- Emit a 1-page summary: band counts, top-|S| rows (by absolute strength)
Artifacts you can obtain from the repository link (no dataset here).
- Minimal scripts for
a_res,a_risk, rapidity fuse,S(m,a). - A manifest with knobs and
knobs_hash. - Optional stamped CSVs and a CI report template.
Navigation
Previous: SSM-Audit – Case Study C: FX & Inflation Hide Margin Erosion (4.1C)
Next: SSM-Audit – Public Case: Country Indicators — NG, BR, ZA (4.3)
Directory of Pages
SSM-Audit – Table of Contents
Explore Further
https://github.com/OMPSHUNYAYA/Symbolic-Mathematical-Audit
Disclaimer
Research/observation only. Not for operational, safety-critical, or legal decision-making.
Frequently asked questions
SSM-Audit – Q & A
SHUNYAYA 