SSMT – Making It Operational: Alignment Dials and Survival Bands (1.4–1.5)

From “how far from baseline” to “are we in danger, and how deep?”

So far we have T_K and e_T.
Now we add two powerful (and optional) dials:

  • a global stress / alignment dial you can safely pool across assets, and
  • a survival-proximity dial that answers “which side of the danger line are we on?”

These dials let operators act fast without touching raw °C/°F, and without guessing at brittle cutoffs like “32 F”.

1.4 Bounded alignment dial (a_T)

a_T turns the raw contrast e_T into a smooth, bounded dial in (-1, +1).

a_T := tanh(c_T * e_T)
a_T := clamp_a(a_T, eps_a)   # enforce |a_T| <= 1 - eps_a

Where:

  • c_T > 0 controls sharpness/sensitivity.
  • eps_a is a tiny positive clamp (for example 1e-6) to guarantee you never hit exactly ±1.

Why this matters:

  • a_T is safe to average.
  • a_T is safe to rank.
  • a_T cannot “blow up” and dominate pooled dashboards.
  • a_T stays interpretable as “how stressed are we against the declared baseline,” not “what random unit are we using here.”

This makes a_T perfect for:

  • fleet dashboards (“which site is running hottest vs nominal?”),
  • ML priors / ranking,
  • governance summaries (“these 3 rooms are at high thermal stress”).

You only emit a_T if you need that pooled view.
If you don’t need pooled stress scoring, you can skip a_T entirely and just publish e_T.

1.5 Phase proximity dial (a_phase)

Temperature is not only “high vs low.”
There are specific pivots that matter in real life: freeze, melt, warp, boil, gel, human survivability, structure softening, battery runaway, etc.

We express those pivots as a smooth survivability dial.

d_m := (T_K - T_m) / DeltaT_m
a_phase := tanh(c_m * d_m)
a_phase := clamp_a(a_phase, eps_a)

Where:

  • T_m is the critical pivot (for example 273.15 K for water freeze).
  • DeltaT_m > 0 is the softness width around that pivot (how wide is “near the edge?”).
  • c_m > 0 sets how bold or sensitive you want the dial to be.
  • eps_a again keeps the output in (-1, +1).

How to read a_phase:

  • Near 0: you are sitting right on the pivot.
  • Strongly negative (near -1): safely on the “cold side” of the pivot (for freeze, that means solid-leaning).
  • Strongly positive (near +1): safely on the “hot side” (for freeze, liquid-leaning).

In plain words:

  • It answers: “Which side are we on?”
  • It also answers: “How far into that side are we?”

This replaces brittle if T < 0°C then ALERT logic with a graded, debounced, human-readable dial.

Multi-pivot fused dial (a_phase_fused)

Many systems don’t have just one danger line.
Example: you care about both freezing and boiling, or both gel-point and warp-point of a polymer, or both “too cold for skin” and “too hot for skin.”

Instead of managing five different booleans, you can fuse them into one bounded survival dial:

a_phase_fused := tanh(
    sum_i( c_m_i * (T_K - T_m_i) / DeltaT_m_i )
)

Guidance:

  • Each pivot i has its own (T_m_i, DeltaT_m_i, c_m_i).
  • You can tag them ("freeze", "warp", "boil", "human_hot", etc.).
  • You typically emit either a_phase (single pivot) or a_phase_fused (multi-pivot). You don’t need both.

Why a_phase_fused is powerful:

  • One dial captures “thermal survivability posture” across multiple materials or biological limits.
  • You can hand that dial to decision logic without giving it private material constants.

Why these dials are operationally huge

Let’s say you are protecting:

  • a power battery stack,
  • a biomedical transport line,
  • a human EVA suit,
  • a bridge joint in extreme weather,
  • a habitat wall on Mars.

You don’t just care “is it 18°C or 22°C?”
You care “are we drifting into damage or danger and how fast?”

a_phase and a_phase_fused let you:

  • route attention,
  • trigger slow-down / warm-up / cooldown routines,
  • set escalation levels for human review,
  • or throttle risky operations.

All of that happens without arguing over °F vs °C and without sprinkling dozens of hard-coded constants through code.

Pocket example (freezing edge)

Assume:

  • T_m := 273.15 K (freeze pivot),
  • DeltaT_m := 2.0 K,
  • c_m := 1.0,
  • eps_a := 1e-6.

For a reading just below freezing:

T_K = 272.5 K
d_m = (272.5 - 273.15) / 2.0  ≈ -0.325
a_phase ≈ tanh(-0.325) ≈ -0.314

For a reading just above freezing:

T_K = 273.8 K
d_m = (273.8 - 273.15) / 2.0  ≈ +0.325
a_phase ≈ tanh(+0.325) ≈ +0.314

Notice:

  • Magnitudes are nearly symmetric (≈0.314 vs ≈0.314).
  • Signs flip cleanly at the pivot.
  • No brittle “0°C special case.”
    You get a smooth survival dial instead of a flickering alert.

This is exactly the kind of dial that cold-chain logistics, human safety systems, or structural monitoring wants.

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