From “what’s the temperature?” to “are we safe, stable, and compliant?” — in one portable lane.
Purpose.
Shunyaya Symbolic Mathematical Temperature (SSMT) turns raw °C/°F/K into a symbolic language (e_T, a_phase, Q_phase, excursion budgets) that can travel across vendors, cities, industries, and even planetary environments. This page shows how the core dials behave in the real world — and how they let you write policy, compliance thresholds, and safety rules that are honest, replayable, and portable.
Key idea.
We do not ask you to replace your sensors, rewrite your physics, or re-tune every location. We ask you to express temperature in one symbolic channel that any team can read, audit, and prove. The point is not “fancy math.” The point is: no more confusion, no more flicker, no more “was that °C or °F,” and no more silent drift in safety rules.
4.1 Unit invariance (same state, different units)
Problem.
Different devices report in °C, °F, or Kelvin. People argue. Alerts misfire. Investigations waste hours on “it wasn’t actually hot, it was just Fahrenheit.”
SSMT approach.
SSMT converts all sources to Kelvin once, and then encodes a unitless contrast e_T using a declared lens. After that conversion, everyone — operations, AI, auditors, safety, even insurance — can speak in one number.
Config. lens = log, T_ref = 298.15 K (25 C)
Physical state. 35 C = 95 F = 308.15 K
Compute.
e_T = ln(308.15 / 298.15) = 0.03298996
Meaning.e_T is the same portable signal for the same physical reality, no matter whether the sensor was talking °C, °F, or K. A policy can literally say:
“Trigger investigation if e_T >= 0.8 for >= 15 minutes.”
and that rule applies in Chicago, Chennai, or orbit — without rewriting thresholds into local units.
This is the first move toward a single “temperature truth layer.”
4.2 Near-freezing dial (water)
Problem.
Classic logic says: “If T <= 0 °C then FREEZE ALERT.” That explodes in practice:
- Surfaces hover around 0 °C and spam alerts.
- You can’t tell “slightly below freezing but still survivable” vs “deep in brittle danger.”
SSMT approach.
Instead of a brittle yes/no, we publish a smooth dial a_phase in (-1,+1) that says:
- Which side of the critical pivot you’re on (below or above the survival point),
- How deep you are into danger/safe territory.
Config.T_m = 273.15 K, DeltaT_m = 2.0, c_m = 1.2, eps_a = 1e-6
T = 271.15 K -> d_m = -1.0 -> a_phase = tanh(-1.2) = -0.83365461
T = 273.15 K -> d_m = 0.0 -> a_phase = 0.0
T = 275.15 K -> d_m = +1.0 -> a_phase = tanh(+1.2) = +0.83365461
Meaning.
a_phase ≈ -0.83means “we’re clearly on the cold/solid/brittle side.”a_phase = 0means “sitting right on the pivot.”a_phase ≈ +0.83means “we’re safely on the warm/liquid side.”
Instead of “ALERT NOW!!!” you get a graded survival dial that’s machine-readable, fleet-comparable, and emotionally honest. This is how you defend decisions to regulators and insurers without hand-waving.
4.3 Soft hysteresis around the pivot (reduced flicker)
Problem.
When you hover near a critical point (freeze point, gel point, warp point, human safety band), naive alerts flap:
- SAFE / DANGER / SAFE / DANGER every few seconds.
- Humans start ignoring alarms.
- Dashboards become noise.
SSMT approach.
We keep a soft memory called Q_phase. Instead of reacting instantly to micro-jitter, we accumulate evidence.
Config. rho = 0.90, k_side = 2.0
Update each step:
p_side := 0.5 * (1 + tanh(k_side * (T_K - T_m)))
Q_phase := rho * Q_prev + (1 - rho) * clip(p_side, 0, 1)
Meaning.
p_sideasks, “Which side of the pivot are we on right now?”Q_phasesays, “Have we been living on the risky side long enough that we should care?”
In plain language: you only escalate when the danger is sustained, not when the sensor jitters.
This kills alert flicker around survival boundaries like “critical freeze,” “gel point for diesel,” or “heat stress on exposed skin,” and gives you something you can log, prove, and replay.
4.4 Cold-chain excursion (symbolic, unitless)
Problem.
Cold-chain compliance today is a mess of wording like “8 °C for more than 9 minutes unless packaging X unless transit class Y…” It’s hard to audit, easy to argue.
SSMT approach.
We express excursion stress as a symbolic budget you can measure and sign.
Config.lens = linear, T_ref = 277.15 K (4 C), DeltaT = 2.0, c_T = 0.7
T = 281.15 K (8 C) -> e_T = +2.00 -> a_T = tanh(1.4) = +0.88535165
T = 275.15 K (2 C) -> e_T = -1.00 -> a_T = tanh(-0.7) = -0.60436778
We then define a symbolic “cooling degree-day” style budget:
S-CDD := sum_t max(e_T(t) - 0.5, 0)
Policy: "Reject if S-CDD > 1.5"
Meaning.
S-CDDis a clean numeric summary of “how badly we overheated, and for how long,” in symbol space.- You can paste “Reject if S-CDD > 1.5” directly into a supplier contract or temperature custody chain, and both sides can replay it later without fighting over unit conversions.
This is not cosmetic. This is the beginning of auditable thermal contracts.
Why this matters.
Across just these four subsections, you already have:
e_T: a single portable thermal contrast signal that survives °C/°F politics.a_phase: a survival dial that knows which side of danger you’re on.Q_phase: soft memory that prevents alert spam.S-CDD: a symbolic excursion budget you can write into policy and enforce across vendors.
This is the core of temperature governance. Once you express temperature this way, you can take it into hospitals, vaccine freezers, rail safety, telecom tower enclosures, reentry shields, mission habitats — and everyone is finally looking at the same language.
Navigation
Previous: SSMT – Validation, Human/Machine Boundaries, and Practical Limits (3.7–3.11)
Next: SSMT – Cross-Site Comparability, Rail Stress, Fuel Survival, and Spaceflight Cryo (4.5–4.8)
Directory of Pages
SSMT – Table of Contents
SHUNYAYA 