The maths Primitive actually uses — and the maths it is still testing.
The central discipline is simple: do not let an elegant mathematical idea become a production fact merely because it is elegant. Canonical state, experimental charts and open hypotheses are kept visibly separate.
Production Primitive has one canonical ternary cube: E/P/A, 3³ = 27 states, Q00–Q26, with UNKNOWN outside the cube. Three extra Environment/Relation/Context charts and a seven-axis coupled coordinate are experimental shadow metadata only.
We use three switches, and each switch can be down, middle or up. Three choices on three switches gives 27 combinations. We are testing other sets of switches too, but we do not let those experiments steer the real system yet.
Ternary coordinates are compact local descriptions, not universal truth. A coordinate only means something when its chart, frame, reference and derivation are known. The long-term research direction is an atlas of versioned local charts connected by causal lineage.
1. The E/P/A cube
The production coordinate is:
Therefore:
| Axis | Meaning | Values |
|---|---|---|
| E | Epistemic / Evidence orientation | −1, 0, +1 |
| P | Potency / Capacity | −1, 0, +1 |
| A | Actionable / Agency | −1, 0, +1 |
The Q-address is deterministic: index = (E+1)×9 + (P+1)×3 + (A+1). The result is Q00 through Q26.
2. Probability, uncertainty and risk are overlays
Probability, uncertainty, consequence, risk, confidence and importance are continuous evaluation variables. They are deliberately not extra ternary axes. Otherwise “add two more ternary fields” would silently change the model from 27 states to 243 states.
3. Three shadow charts: Environment, Relation and Context
W-05 specifies three experimental three-axis charts — env@1, rel@1 and ctx@1 — registered alongside, not instead of, the accepted EPA chart. Their status is explicitly experimental and the packet requires hard isolation from production routing/orchestration/decision paths.
| Chart | Axes in W-05 |
|---|---|
| env@1 | Environment certainty, resource potency, agentic alignment |
| rel@1 | Relational trust, coupling strength, resonance divergence |
| ctx@1 | Context scope, context load, context volatility |
4. Three independent 27-state cubes would have 19,683 combinations
That number is the raw Cartesian product if all nine ternary axes were independent. The research programme instead explores shared causal structure so the combined representation does not need to behave like nine unrelated coordinates.
5. W-05's seven-axis causal coordinate has 2,187 signatures
The current experimental packet selects seven ternary dimensions: canonical e/p/a plus environment certainty e1, relational trust r1, coupling strength r2 and context scope c1.
It emits a seven-digit base-3 cell plus a SHA-256 frame reference. It is derived metadata for introspection/benching, not an authority signal and not a production routing input.
6. Zero means the local reference, not “the object”
In the working theory, a frame F declares observer/inquiry/time/scale/scope/lens/reference/validity. A local coordinate is relative to that frame. The same node may be zero in one frame and non-zero in another without contradiction.
7. A → B → C → A′
The behavioural origin model is not a circle returning to the exact same state. Consequence C changes the conditions for the next antecedent.
This is the useful core of the 1 → 2 → 1′ / transformed-return idea. It is a model for recurrence with state change, not evidence that every complex system follows the same law.
8. What is canonical, experimental and open
| Claim | Status |
|---|---|
| E/P/A ternary chart, Q00–Q26, zero ≠ UNKNOWN | Implemented / canonical runtime |
| Continuous overlays stay separate | Implemented contract |
| env@1 / rel@1 / ctx@1 | Experimental shadow charts |
| Seven-axis 3⁷ coupled signature | Experimental derived metadata |
| ±3 resolution shell / relevance horizon | Working theory / benchmark target |
| Seven dimensions and ±3 are one deep law | Open / contested hypothesis |
| Every collective has an identical fractal power structure | Refuted as a law; analogy only |