SSMDE — Alignment Dial (how stable / how close to danger right now) (1.2)

The bounded, replayable signal that tells you whether the value is calm, drifting, or approaching risk.

What the alignment dial represents

align is a portable stability / stress dial in the range (-1, +1).

It does not replace the value.
It answers a different question:

“How much should we trust this value right now?”

Interpretation (these meanings are declared in the manifest, not guessed later):

+0.8 → stable, predictable, far from danger
0.0 → neutral / baseline behavior
-0.6 → unstable, drifting, or near tolerance limits

The exact meaning of positive vs negative is declared, not assumed.

Why the dial is bounded

Unbounded “confidence scores” break quickly — they explode under noise, aggregation, or model drift.

The alignment dial is mathematically forced to stay inside (-1, +1), so:

It can be safely merged across time
It can be safely merged across sensors / vendors
It is order-invariant (batch == streaming == distributed)

This is achieved through the four-step stability pipeline.

The alignment pipeline (core SSMDE math)

a_c   := clamp(a_raw, -1+eps_a, +1-eps_a)
u     := atanh(a_c)
U     += w * u
W     += w
a_out := tanh( U / max(W, eps_w) )

Where:

a_raw = your domain’s initial signal of confidence / stability / risk
eps_a = tiny safety margin (e.g., 1e-6), prevents hitting exactly ±1
w = weight (can be time, magnitude, certainty, or domain-specific rule)
U and W = accumulators storing fused evidence
eps_w = prevents division by zero

Then you publish:

align := a_out

What each step ensures

Step	Purpose	Why it matters
`clamp(a_raw)`	Stops illegal/outlier shocks	Safety & numerical sanity
`atanh(a_c)`	Moves to a space where signals can be combined additively	Enables fair evidence fusion
`U += w*u; W += w`	Builds memory across time/sensors/vendors	No single spike dominates
`tanh(U/W)`	Returns to a bounded human-readable dial	Always in `(-1,+1)`

Key thermodynamic-style properties

-1 < align < +1                       # always bounded
align(batch) == align(stream)         # order-invariant
align(A merged with B) is stable      # multi-sensor safe
phi((m,a_out)) = m                    # collapse parity preserved

Interpretation in practice

Operations / industrial:
align = -0.45 → the temperature is okay numerically but trending toward a thermal stress boundary.
Finance:
align = -0.20 → revenue is stable, but daily pattern jitter shows weakening reliability.
AI decision routing:
align = -0.75 → model score appears high but unstable, route case to human review.
Mechanical / fatigue:
align = +0.62 → system is within normal oscillation envelope.

Do / Don’t

# follow the canonical pipeline
a_c   := clamp(a_raw, -1+eps_a, +1-eps_a)
u     := atanh(a_c)
U     += w * u
W     += w
align := tanh( U / max(W, eps_w) )

Don’t

align := a_raw            # NO — unbounded, non-portable
align := normalize(...)   # NO — normalization does not preserve order-invariance
align := tanh(a_raw)      # NO — loses memory and fusion integrity

Validation checklist

[ ] align ∈ (-1, +1) always
[ ] collapse parity holds: phi((m,align)) = m
[ ] order-invariant: batch vs streaming gives identical align
[ ] weight rule w is declared in manifest
[ ] eps_a and eps_w are declared in manifest

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