From one clean signal (e_T) to safer alerts, calmer dashboards, and easier ML.
3.1 Unified coupling to g_t (env-gate)
Goal: turn “temperature situation” into one bounded gate g_t in (0,1) that can modulate anything downstream — chemical risk, actuator throttle, rate limits, etc.
We start from SSMT outputs you already know:
a_T— bounded alignment dial from temperature contrasta_T := tanh(c_T * e_T)then clamp to keep |a_T| < 1a_phase— near-pivot phase dial that says “which side of the critical temperature are we on, and how deep?”Q_phase— soft memory that stops flicker around that pivot (stable vs risky side)
Step 1 — Build a bounded stress lane S_t in [0,1].
You declare how you want to blend the pieces:
S_t := clip( w1*abs(a_T) + w2*Q_phase + w3*abs(a_phase) , 0 , 1 )
• w1, w2, w3 >= 0, and w1 + w2 + w3 <= 1.
• Simpler alternative: just pick one dial, e.g. S_t := abs(a_T) or S_t := Q_phase.
• You write this recipe once in the manifest under a gate block (Section 3.1 semantics).
Why S_t matters:
It’s now a single “environmental stress signal” that stays bounded, meaning it’s safe to multiply into anything else — a chemical reactivity index, a risk score, a throughput target.
Step 2 — Measure stress volatility over a short window.
Let Z_t := log(1 + Var_{t-L+1:t}(S_t))
• L >= 2 samples.
• High variance → unstable environment → higher risk.
Step 3 — Compare raw volatility with an “antagonist” calm term.A_t := 1 / (1 + Z_t)Delta_t := abs(Z_t - A_t)
Intuition:
- If volatility is high (
Z_thigh),A_tshrinks. Delta_thighlights the imbalance between “how shaky it is” vs “how calm it should be.”
Step 4 — Accumulate calm vs stress memory.
We run a soft memory that builds caution when stress keeps recurring:
Q_t := rho_g * Q_{t-1} + (1 - rho_g) * clip(A_t - Z_t, 0, 1)
• 0 < rho_g < 1, e.g. rho_g = 0.9.
• Initialize Q_0 := clip(A_0 - Z_0, 0, 1).
Interpretation:
- If the system has been mostly calm,
Q_tstays low. - If stress is persistent,
Q_tgrows. Q_tis in [0,1] and gives “are we steadily in a risky thermal regime?”
Step 5 — Final gate g_t.
Combine instantaneous volatility and accumulated memory:
g_t := ( 1 / (1 + Z_t + kappa*Delta_t) ) * ( 1 - exp(-mu*Q_t) )
• kappa >= 0, mu >= 0. Typical: kappa = 1.0, mu = 3.0.
• Output: 0 < g_t < 1 as long as mu > 0.
How to use g_t:
- Chemistry / reaction control
RSI_env := g_t * RSI
You’re saying: “Even if chemistry wants to go fast, environmental stress might slow it.” - Phase-aware safety gating
phi_phase := clip((a_phase + 1)/2, 0, 1)gives a [0,1] mask of “we are on the hot/liquid side”
Then:RSI_env := g_t * RSI * phi_phase
Now reactions are automatically suppressed if the material is on the wrong side (too cold / solid side). - Throttling actuators, fans, pumps
throttle_factor := g_t
High stress → lowg_t→ automatic slow-down. - Alerting
“Thermal Stress Alert if g_t <= theta_g for 2 minutes,” wheretheta_gis declared in the manifest.
Important:
This is fully deterministic. You choose the recipe once (weights w1/w2/w3, window L, rho_g, kappa, mu, theta_g). You publish it in the manifest. Then anyone can replay the same decision offline. No magic.
3.2 First-order benefits (what you get day one)
When you adopt Shunyaya Symbolic Mathematical Temperature (SSMT), you immediately gain:
• Zero unit drama
One Kelvin step, then e_T means the same thing across Celsius/Fahrenheit devices. No more “is this °C or °F?” incidents.
• Clear direction and magnitudee_T = 0 means “at baseline T_ref.”
Positive means “hotter than baseline.”
Negative means “colder than baseline.”
This is human-readable and ML-friendly at the same time.
• Phase-aware safety
Instead of brittle if/else at 0 °C (32 °F), you emit a smooth dial a_phase in (-1,+1) that says which side of the survival pivot you’re on and how deep into risk you are.
Soft hysteresis (Q_phase) stops alert chatter when hovering near that pivot.
• Stable ML featurese_T is zero-centered and unitless.a_T, a_phase, and Q_phase are bounded in (-1,+1) or [0,1].
Bounded + centered = models behave better, retraining gets simpler, outliers stop blowing up your scale.
• Portable thresholds
You can finally say policies like:
- “Heat Advisory if
e_T >= +0.8for 3 hours.” - “Freeze Risk if
a_phase <= -0.6for 20 minutes.”
These rules can be copy-pasted from one site or fleet to another without rewriting thresholds in °C vs °F.
• Auditability and compliance
Every alert rule becomes replayable from raw Kelvin + manifest.
You can show regulators or insurers:
“Here is the manifest. Here is the rule. Here is the data. The device followed the rule exactly.”
• Cost relief
You stop maintaining duplicated °C/°F logic per vendor, per region, per line of business. You ship one stream (e_T, maybe a_phase) and your downstream stack just consumes it.
This is why SSMT scales from a single cold-chain fridge to a planetary habitat system.
3.3 Why zero-centric with lenses (the math intuition)
SSMT always expresses temperature as a contrast around a published reference T_ref.
That contrast is called e_T.
All approved lenses produce e_T with these guarantees:
- It’s monotone in Kelvin (
T_K). e_T = 0exactly atT_ref.- Sign is meaningful (hotter/colder than baseline).
- You pick ONE lens per deployment and freeze it.
Core lenses:
• Log lens (default for wide ranges, cross-fleet)e_T := ln(T_K / T_ref)
– Scale-invariant.
– Good across huge spans (city → desert → orbit).
– Interprets “how many multiplicative steps from baseline.”
• Linear lens (tight industrial bands)e_T := (T_K - T_ref) / DeltaT
– Intuitive in controlled environments (HVAC, process control).
– Reads like “how many DeltaT-widths away from nominal.”
• Beta lens (cold-emphasis / cryo)e_T := (T_ref / T_K) - 1
– Focuses on cold-side risk.
– Very good when “too cold” is the danger, e.g. maintaining just-above-gel states.
• kBT lens (thermo / chemistry coupling)e_T := (R*T_K)/E_unit - (R*T_ref)/E_unit
– Connects temperature to an energy scale per mole.
– Lets you say “thermal drive” in the same numeric space as reaction kinetics.
• Hybrid lens (mixed regimes)
Piecewise: near baseline use linear, far from baseline use log.
Keeps small variations readable and big excursions bounded.
• Quantum-safe log (near absolute zero)
Uses an offset (alpha > 0) so ln() stays well-behaved even when T_K is tiny, but still guarantees e_T = 0 at T_ref.
Why this matters:
If you publish “Lens = log, T_ref = 298.15 K,” everybody — your data team, your vendor, an auditor 2 years later — knows exactly how to convert Kelvin to your e_T.
No retraining surprises. No secret scaling. No “our platform uses a proprietary comfort index.”
It’s honest math, declared up front.
Navigation
Previous: SSMT – Device Passport, Auto Lens Policy, and Audit Stability (2.10–2.11)
Next: SSMT – Bounded Dials, Hysteresis Memory, and Gentle Safety Near the Edge (3.4–3.6)
Directory of Pages
SSMT – Table of Contents
SHUNYAYA 