SSM-AI – Appendix P — FAQ & Troubleshooting (P1–P5)

Quick answers and reproducible checks for teams deploying SSM-AI.

Purpose. Provide fast, copy-paste-ready explanations to the most common field questions.
All formulas are plain ASCII. Classical magnitudes remain intact (phi((m,a)) = m).
The alignment lane and chooser are observation-only; they do not alter model outputs.

P1) Quick FAQ (top 10)

Q1. Does SSM-AI change my numbers?
No. Collapse parity is absolute: phi((m,a)) = m. The alignment lane a and chooser RSI exist purely for interpretability, ranking, or gating.

Q2. Why use tanh/atanh instead of averaging a directly?
Order and shard invariance. The fuse works in rapidity space:
U += w*atanh(a) ; W += w ; a_out := tanh( U / max(W, eps_w) ).
Averaging raw a breaks both invariance and boundedness near ±1.

Q3. What does the calm gate actually scale?
Alignment only.
RSI_env := g_t * RSI (mode "mul") or RSI_env := tanh( g_t * atanh(RSI) ) (mode "u_scale").
The magnitude m never changes.

Q4. What do I band — a or RSI?
Band decisions on RSI (or RSI_env). a bands are for diagnostics only.

Q5. How should I pick uniform vs weighted fusion?
Use w := 1 for comparability across items, or w := |m|^gamma (γ=1 default) when stronger magnitudes deserve higher influence.

Q6. What if W = 0?
Neutral default: RSI := 0. Always safe because tanh(0)=0.

Q7. How do I tune c and Unit?
Target |c*e| ≈ 0.3–1.2. If a saturates (>0.9), reduce c or increase Unit.
If a stays near 0, increase c or lower Unit.

Q8. What happens near ±1?
Clamp before mapping: a_c := clamp(a, -1+eps_a, +1-eps_a) then atanh(a_c).
Typical eps_a = 1e-6 for f32, 1e-12 for f64.

Q9. How do I validate order invariance quickly?
Shuffle inputs 10×; verify same a_out or RSI (within dtype tolerance).
Fusion via (U,W) guarantees identical results independent of order.

Q10. What’s the minimal stamp I must emit?
A single ASCII line, for example:
SSMCLOCK1|iso_utc|svc=decode|U=...|W=...|RSI=...|g=...|band=...|manifest=knobs_hash.

P2) Troubleshooting (symptom → fix)

Symptom	Likely cause	Quick fix
RSI identical for all candidates	Lens gain too low	Raise `c` or lower `Unit`
Bands flip near thresholds	No hysteresis	Add ±0.02 hysteresis and smooth `g_t`
Order changes output	Using raw average	Always fuse via `(U,W)`
Overflow near ±1	Missing clamp	Apply `a_c := clamp(a, -1+eps_a, +1-eps_a)`
Gate over-damps high RSI	Mode too linear	Use `"u_scale"` instead of `"mul"`
Division errors	`"strict"` policy triggered	Fall back to classical path
Ledger replay mismatch	Averaged RSI instead of fused	Recompute `tanh(sumU / max(sumW, eps_w))`

P3) Minimal acceptance battery

Run this before every deployment:

# 1. Collapse parity
assert phi((m,a)) == m

# 2. Clamp round-trip
assert tanh(atanh(clamp(a))) == clamp(a)

# 3. Order invariance
shuffle(inputs)
assert fuse(U,W) unchanged

# 4. Gate purity
assert output_m == input_m

# 5. Determinism
same_knobs_hash ⇒ identical outputs/bands

Pass all tests before rollout.

P4) Quick numeric recipes

Single-lane RSI:
RSI := tanh( sum w*atanh(a) / max(sum w, eps_w) )

Two-channel lens → alignment:
a_in := tanh(-c*e_in) ; a_out := tanh(+c*e_out)

Chooser:
RSI := tanh( (Σ w*atanh(a_out) − Σ w*atanh(a_in)) / max(Σ w, eps_w) )

Band function (default):

def to_band(x):
    if x >= 0.90: return "A++"
    if x >= 0.60: return "A+"
    if x > -0.60: return "A0"
    if x > -0.90: return "A-"
    return "A--"

P5) Priors, bias, and gate discipline

Tiny priors only: u' := u + beta*b with b ∈ [-1,+1], beta small.
Never encode PII or demographics.
Transparent gates:
- Inputs normalized [0,1],
- rho ≤ 0.2 for smoothing,
- g_t published if used in decisions.
Bounded guarantee: All a, RSI, and RSI_env remain in (−1,+1).

Stamp example (one line, ASCII)

SSMCLOCK1|iso_utc|k=faq|U=0.700000|W=1.000000|RSI=0.604368|g=0.80|RSI_env=0.483494|band=A0|manifest=knobs_hash

One-line takeaway.
Clamp → atanh → fuse (U,W) → tanh → band.
Nothing else changes — your original magnitudes stay untouched (phi((m,a)) = m), and every result is deterministic, bounded, and auditable.

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