Patent-pending — U.S. Provisional 63/921,717

The Master Equation calculator.

Drag the eight axis sliders. Watch the CH score recompute live. Every term in the math breakdown updates with the inputs, so you can verify the result yourself. 41 in-browser validation tests below — click Run tests to confirm the math.

CH = (S × Sp)^C × (T + E)^p × (ER × RS)^C/3 Three-wing canonical form

Drag the axes.

Each axis is independently scored 0–100. Drag a slider to see how it moves the CH score and the math breakdown.

Which axis matters most right now

Click an axis to see how much the CH score drops if that axis were zero (with all others held steady). Longer bar = bigger penalty if you neglected it.

CH score · live orb

—

050100

Computed variables

S—
= (PO + NM) / 2

Sp—
= SC

C—
= mean of all 8 axes

T—
= TA

E—
= ES

p—
= PV

Three wings

Left: (S × Sp)^C —

Right: (T + E)^p —

Resilience: (ER × RS)^C/3 —

raw —

log₁₀(raw) —

norm to [0,100] —

Validate the math yourself.

41 assertions covering: bounds (all-zero, all-max, all-mid), monotonicity (raising any axis raises CH, lowering any axis lowers CH), non-linearity (zeroing any axis from balanced harms CH significantly), range (every preset lands in [0,100]), determinism (same input → same output), and NaN safety.

Click Run validation tests to execute all 41 in-browser. The tests run instantly against this page's loaded calculator — no server round-trip.

Preset	PO	NM	ER	SC	RS	ES	TA	PV	CH

For the curious

How the math works.

The three wings

The CH composite is the product of three multiplicative "wings", each anchored to a different aspect of a healthy life:

Left wing — (S × Sp)^C: Somatic foundation (Physical + Nutritional) times the coherence amplifier (Social/Communal), raised to the Conceptual Mastery™ exponent (mean of all 8 axes). Says: your body and your community context multiply, and consistency amplifies both.
Right wing — (T + E)^p: Temporal/technological addend plus the environmental addend, raised to the provisional/vocational exponent. Says: your adaptation to time and place is additive, and purpose shapes how steeply that compounds.
Resilience wing — (ER × RS)^C/3: Emotional/Relational times Religious/Spiritual, raised to a third of the Conceptual Mastery™ exponent. Says: relationships and spiritual practice are a separate multiplicative term — they're independent of body and environment, and damped to one-third of C so they don't dominate.

Why multiplicative?

Legacy health composites (PROMIS Global, SF-36, HOS) average a handful of items. Averaging lets a high score on one axis mask a collapse on another — a heart-attack survivor with great labs and 0 social support still scores "ok". The CH formula is multiplicative because real health isn't: a deficit in any axis non-linearly reduces the whole.

The consistency exponent

C (Conceptual Mastery™) is the mean of all eight axes. It's the exponent on both the left and resilience wings because: when you're consistently strong across the board, C ≈ 1 and the wings reflect their honest multiplicative result. When you're inconsistent and chaotic, C → 0 and the wings approach 1 — but the raw values they sit on are also small, so the overall CH stays low. Consistency rewards the consistent and protects the inconsistent from infinite penalty.

Log rescaling

The raw multiplicative result spans many orders of magnitude (from near zero to ~10⁴⁰). We rescale via log₁₀ bracketed to [0, 39.68], then map to [0, 100]. The brackets were chosen so all-axes-at-0 displays as 0 and all-axes-at-100 displays as 100, with a meaningful gradient between.

Reference implementation

The function shown here is the same one running in production at /api/v1/healthcoin/ch-score and on every patient's daily orb. Source: master-equation/calculator.js in the open-source protocol layer. Test suite: master-equation/calculator.js#runTests() — 41 assertions. Patent: U.S. Provisional 63/921,717 (filed 2025).

Want to verify the math yourself? Three options:

Run the tests live: click the Run validation tests button at the top of this page — all 41 assertions execute in your browser against the loaded calculator code.
Console it: open your browser's developer console on this page, type CHMasterEquation.runTests(), press Enter, read the results object.
Read the open-source code: the raw JavaScript source (~300 lines, no minification, fully commented) is at calculator.js — view source →. Heads-up: that link opens the plain-text source file in your browser, not another calculator page — it's the actual code that runs on this page, served for line-by-line audit.
Cross-platform parity: the byte-equivalent Python port calculator.py ships with 50 golden vectors. Both JS and Python must pass every vector to ≤ 0.05 on every commit. Anyone can clone the repo and run python3 master-equation/tests/test-golden-vectors.py — 50/50 must pass.
Run the reference Independent Validator: python3 master-equation/validators/run_validator.py --api default verifies all 50 vectors locally, hits our live /api/v1/master-equation/compute for each one, and pins the audited calculator_sha256 against the live /spec endpoint. Passing runs may be submitted as a signed audit report — see validator program → and the bug bounty.

Sub-signals & action map: every patient action that moves the equation is declared in sub-signals.yaml (75 measurable signals across 8 axes) and action-axis-map.yaml (every action → which signal(s) it updates, with fraud controls and HCR mining lane). No CH movement happens outside this contract.