A bounded, replayable trust dial in (-1,+1) that any team can compute, verify, and fuse
4.1 The pair (m,a) and collapse parity
A signal is a pair:
x := (m,a)
phi((m,a)) = m
m= classical magnitude (temperature, cash, strain, …)a= alignment lane (stability / trust / proximity-to-stress)
Collapse parity ensures value stays exact:
phi((m,a)) = m
In SSMDE:
value := m
align := a_out # computed via steps below
4.2 Step 1 — Clamp for safety
a_c := clamp(a, -1+eps_a, +1-eps_a)
# eps_a is a tiny positive margin (declare in manifest)
Why: Prevents divergence at ±1, keeps the math finite, portable, and safe to merge.
4.3 Step 2 — Map to rapidity space
u := atanh(a_c)
atanh() spreads edge intensities onto the real line so they can be weighted and added:
a_c= human-readable dialu= math-friendly dial for fusion
4.4 Step 3 — Fuse over time, shards, or samples
Maintain two accumulators:
U += w * u
W += w
Weight choices (declare in manifest):
w := 1 # simple average
w := |m|^gamma # emphasize large magnitudes
w := quality_score # source trust
w := duration # time weighting
Property: Fusion is order-invariant. Batch, stream, or cross-site merges yield the same (U,W) when the same w rule is used.
4.5 Step 4 — Return to a bounded dial
a_out := tanh( U / max(W, eps_w) )
# eps_w is a tiny positive guard (declare in manifest)
Publish:
align := a_out
Results: align ∈ (-1,+1); comparable, graphable, alertable, and replayable.
4.6 Pseudocode (reference mini-implementation)
# Inputs over time:
# a_raw[t] : unbounded trust/stress reading at time t
# w[t] : nonnegative weight (manifest-declared)
init:
U := 0
W := 0
for each new reading t:
a_c := clamp(a_raw[t], -1+eps_a, +1-eps_a)
u := atanh(a_c)
U := U + w[t] * u
W := W + w[t]
# on report:
align := tanh( U / max(W, eps_w) )
Norms: Declare eps_a, eps_w, and the exact w rule in the manifest. Any change → new manifest_id.
4.7 Why this becomes unstoppable once two parties agree
- Merge vendors safely. Combine
(U,W)across feeds without exposing internals. - See drift early. Trend
align:+0.8 → +0.1 → -0.4tells operations to act. - Encode duty-of-care. Bands (e.g.,
"CRITICAL" if align <= -0.6 for 10 min") are action contracts, not colors. - Audit cleanly. Each record carries
value,align,band,manifest_id,stamp—history can’t be rewritten.
One-line takeaway (Section 4).align is a disciplined trust dial in (-1,+1)—built by clamping, transforming, fusing, and re-bounding—so teams exchange not just facts but stability, with outcomes that are consistent, auditable, and mergeable.
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