SSM-Audit – Implementation Guide (2.1–2.3)

# Minimal columns to add (read-only pilot)
a            # stability lane in (-1,+1)
band         # A++ / A+ / A0 / A- / A--
knobs_hash   # fingerprint of declared settings

# Optional (recommended for audit dashboards)
build_id     # run tag
stamp        # one-line ASCII provenance (when enabled)
# If using ZEOZO/SYASYS: Z, A, Delta, Q, SyZ (dashboard-only)

# Coverage (AR tails)
a := 2*q - 1                  # q in [0,1] is within-window coverage

# Agreement (reconciliations)
d := |m_platform - m_bank|
a := tanh( 1 - d / b )        # b > 0 is the declared tolerance/bound

# Residual stability (forecast vs actual)
r := actual - forecast
a := tanh( k*( 1 - |r|/s ) )  # s > 0 (scale), k > 0 (sensitivity)

# Always clamp lanes before any atanh
a := clamp(a, -1+eps_a, +1-eps_a)

# Collapse parity (numbers never change)
phi((m,a)) = m

# Edge-normalize once (robust)
med := median(x)
rad := median(|x - med|); rad := max(rad, eps)
y_t := (x_t - med) / rad

# Bounded energy + log-compress
E_t := (1 - lam)*E_{t-1} + lam*(y_t^2)
Z_t := log(1 + E_t)

# Lane options
# Risk lane (Option A)
a_zeozo := tanh( c*( 1 - Z_t / Z_ref ) )    # Z_ref := median(Z_t over pilot)

# Alignment-track lane (Option B)
A_t := (1 - mu)*A_{t-1} + mu*Z_t
Delta_t := | Z_t - A_t |
a_gap := tanh( k_gap*( A_t - Z_t ) )        # positive when calm dominates

# Deterministic init and pinned knobs
E_0 := 0
A_0 := Z_0
# Declare lam, mu, c, k_gap, Z_ref in the manifest

Zentrube_t := log( Var(x_{0:t}) + 1 ) * exp( -lambda*t )
a := tanh( c*( 1 - Zentrube_t / E0 ) )
# lambda := ln(2)/T_half, choose E0 from a calm baseline

# Ratio lane for m := f/g
a_div := tanh( atanh(a_f) - atanh(a_g) )

# Product lane for m := f*g
a_mul := tanh( atanh(a1) + atanh(a2) )

# Blend two lanes A and B (alpha in [0,1])
a := tanh( alpha*atanh(a_A) + (1 - alpha)*atanh(a_B) )

# Always clamp before atanh; re-clamp on output
a := clamp(a, -1+eps_a, +1-eps_a)
# Numbers remain identical by construction
phi((m,a)) = m