Scope (anonymized). A multi-year storyline where headline revenue stayed large while foundations weakened. We keep classical values identical (phi((m,a)) = m) and surface early warnings via a bounded lane a and a composite index. No third-party data is embedded here; full, stampable artifacts are available via the repository link below.
What we show (executive view).
- Band slide from
A+ → A- → A--well before the final break. - Strength lens
S(m,a) := m*aflips sign while revenuemis still high. - Deterministic math and order-invariant rollups so the same lane appears whether you run batch or stream.
Invariants (non-negotiable).
collapse: phi((m,a)) = m # value is sacred
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
KPIs and lanes (declared once, choose 2–3).
# Revenue (level) — residual vs early baseline
residual: res := Revenue - (beta0 + beta1*Time)
scale: s := 1.4826 * MAD(res)
lane: a_rev := tanh( k_rev * ( 1 - |res|/s ) )
# Liquidity
lane: a_liq := tanh( k_liq * ( Current_Ratio - 1.0 ) )
# Leverage
lane: a_lev := tanh( 1 - |Debt_Equity_Ratio| / b_de )
# Optional diagnostic — Cash coverage (for narrative only)
q_cov := CFO / max(eps_cash, |min(0, CFI)|)
a_cash := tanh( k_cash * q_cov )
Choose modest defaults (documented once): k_rev≈1.2, k_liq≈2.0, b_de≈2.0, k_cash≈0.5, eps_cash≈1.0.
Composite stability index (one-look).
a_index := tanh( ( atanh(a_rev) + atanh(a_liq) + atanh(a_lev) ) / 3 )
Strength lens (for ranking and sign flips).
S(m,a) := m * a
What the timeline shows (anonymized narrative).
- Early (calm): Revenue residuals are tight;
a_revhigh; leverage/liq lanes positive →a_indexinA+. - First downgrade: Residuals widen and leverage tolerance compresses →
a_indexslips toA-while revenue remains large. - Sustained distress:
a_rev → ~-1and leverage lane turns negative;a_indexsits inA--.
StrengthS(m,a)turns negative despite sizablem, signaling misaligned growth. - Late: Liquidity finally softens; the composite remains in
A--until after restructuring.
Actions this would have triggered (examples).
- At first band drop (
A+→A-): tighten credit terms, curb concession creep, gate capex; weekly reconciliation cadence. - At sustained
A--: formal turnaround track; independent policy audit; asset/liability program with stamped, replayable logs.
Calculator-fast replication (no data embedded).
# Step 0 — Fix knobs once
eps_a=1e-6; eps_w=1e-12; k_rev=1.2; k_liq=2.0; b_de=2.0
# Step 1 — Fit early baseline for revenue
fit Revenue ≈ beta0 + beta1*Time on an early calm window
# Step 2 — Lanes (clamp before any atanh)
res := Revenue - (beta0 + beta1*Time)
s := 1.4826 * MAD(res)
a_rev := clamp( tanh( k_rev * ( 1 - |res|/s ) ) )
a_liq := clamp( tanh( k_liq * ( Current_Ratio - 1.0 ) ) )
a_lev := clamp( tanh( 1 - |Debt_Equity_Ratio| / b_de ) )
# Step 3 — Composite and strength
a_index := tanh( (atanh(a_rev) + atanh(a_liq) + atanh(a_lev)) / 3 )
S_rev := Revenue * a_rev
# Step 4 — Bands + hysteresis gates
band := band_from(a_index) with promote>=+0.05, demote<=-0.05
# Step 5 — Order-invariance (rollups)
# If aggregating months/quarters: use the U/W fuse on lanes (weights per policy).
Artifacts you can obtain from the repository link (no dataset here).
- Minimal scripts to compute
a_rev,a_liq,a_lev,a_index,S(m,a). - A manifest with knobs and
knobs_hash. - Optional stamped CSVs (
time,kpi,m,a,band,knobs_hash,build_id,stamp) for replay.
Navigation
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Next: SSM-Audit – Case Study B: Growth Steady, Foundations Eroding (4.1B)
Directory of Pages
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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