Scope (anonymized). Multi-currency, inflationary environment with respectable gross margins on paper. We keep classical values identical (phi((m,a)) = m) and surface margin fragility via bounded lanes on margin stability, price realization, and collections schedule. No third-party data is embedded here; full, stampable artifacts are available via the repository link below.
What we show (executive view).
- Margins look fine, stability slides: composite lane drifts
A+ → A0 → A-while reported gross marginmremains “healthy.” - Pass-through lag is visible: lane on price realization vs. reference weakens first; collections schedule follows.
- Deterministic & portfolio-ready: fixed knobs, batch == stream, and a one-look composite for boards.
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
Pre-normalization lens (reading aids; lanes stay bounded as usual).
# Declare once (manifest)
ccy_base, fx_source, index_source
# Reading transforms (do not alter the lane math; phi((m,a)) = m holds)
m_fx_norm := m_native * fx_rate(native->base)
m_real := m_nominal * ( I_0 / I_t )
# Optional FX data-quality lane
a_fxq := tanh( 1 - |fx_mid - fx_used| / b_fx )
KPIs and lanes (declared once).
# KPI 1 — Gross margin stability vs mix-adjusted baseline
# Fit a calm-window baseline: GM ≈ beta0 + beta1*Mix_Index
res := GM - (beta0 + beta1*Mix_Index)
s := 1.4826 * MAD(res)
a_gm := tanh( k_gm * ( 1 - |res|/s ) )
# KPI 2 — Price realization vs reference (with optional FX-quality blend)
real := realized_price_base / list_price_base
a_real := tanh( 1 - |real - real_ref| / b_real )
# Optional rapidity blend with FX-quality
a_realfx := tanh( ( w_r*atanh(a_real) + w_f*atanh(a_fxq) ) / max(w_r+w_f, 1e-12) )
# KPI 3 — Collections schedule (cash predictability)
q_on_time := receipts_on_or_before_due / receipts_total
a_sched := 2*q_on_time - 1
Choose modest defaults (document once): k_gm≈1.1, b_real≈0.03, b_fx≈0.01, w_r≈0.7, w_f≈0.3, eps_a=1e-6, eps_w=1e-12.
Composite stability index (one-look).
a_index := tanh( ( atanh(a_gm) + atanh(a_realfx) + atanh(a_sched) ) / 3 )
Strength lens (for ranking margin drift).
S(m,a) := m_gm * a_gm
What the timeline shows (anonymized narrative).
- Early: Reported GM stable and high; lanes positive (
A+). - Mid: Price pass-through lags →
a_real(ora_realfx) softens;a_gmanda_schedtrend towardA0. - Late: Composite
a_indexlands inA-while GM still looks respectable; strengthS(m,a)weakens steadily, signaling elevated risk of visible GM compression and DSO drift.
Actions this would have triggered (examples).
- Early slide (
A+→A0): tighten pass-through cadence; hedge review; regional pricing experiments. - Sustained
A0/A-: AR tightening in affected corridors; mix re-weighting; CFO oversight on FX and near-term cash predictability.
Calculator-fast replication (no data embedded).
# Step 0 — Fix knobs once
eps_a=1e-6; eps_w=1e-12
k_gm=1.1; b_real=0.03; b_fx=0.01; w_r=0.7; w_f=0.3
# Step 1 — Fit calm baseline for GM
fit GM ≈ beta0 + beta1*Mix_Index # pick a calm window; document it
# Step 2 — Lanes (clamp before any atanh)
res := GM - (beta0 + beta1*Mix_Index)
s := 1.4826 * MAD(res)
a_gm := clamp( tanh( k_gm * ( 1 - |res|/s ) ) )
real := realized_price_base / list_price_base
a_real := clamp( tanh( 1 - |real - real_ref| / b_real ) )
# optional FX-quality lane, then rapidity blend
a_fxq := clamp( tanh( 1 - |fx_mid - fx_used| / b_fx ) )
a_realfx := clamp( tanh( ( w_r*atanh(a_real) + w_f*atanh(a_fxq) ) / max(w_r+w_f, 1e-12) ) )
q_on_time := receipts_on_or_before_due / receipts_total
a_sched := clamp( 2*q_on_time - 1 )
# Step 3 — Composite and strength
a_index := tanh( (atanh(a_gm) + atanh(a_realfx) + atanh(a_sched)) / 3 )
S_gm := GM * a_gm
# Step 4 — Bands + hysteresis
band := band_from(a_index) with promote>=+0.05, demote<=-0.05
# Step 5 — Order-invariance for rollups (if any)
# use U/W fuse on lanes with declared weights
Artifacts you can obtain from the repository link (no dataset here).
- Minimal scripts for
a_gm,a_real/a_realfx,a_sched,a_index,S(m,a). - A manifest with knobs and
knobs_hash. - Optional stamped CSVs for replayable evidence.
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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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