Bound Pair Sum = 11
Definition
For every Bound on the 4×4 grid, its inner-outer pair partner has a number such that the two bound numbers sum to exactly 11. The 40 Bounds are organized into 20 inner/outer pairs per suit; each pair’s two members occupy the same archetype but face opposite horizons (Inner / Outer). The 11-sum structures this pairing geometrically.
The pairs are structured: 1+10, 2+9, 3+8, 4+7, 5+6 — five pairs per suit × four suits = 20 pairs = 40 bounds.
Why It’s Load-Bearing
Bound-pair-sum=11 is the polarity-anchor invariant for bounds:
- Inner Horizon and Outer Horizon are forced to be load-bearing because they distinguish the two members of each 11-pair
- The bound-number-keyword derivation (March 3-7, 2026) was validated against this invariant — every bound number’s keyword interpretation must hold for both Inner and Outer members
- Without this invariant, bounds could be assigned arbitrarily within their suit; with it, each archetype’s two bounds are structurally specified
Confidence Tier
COMPUTATIONALLY_VALIDATED. All 20 bound pairs verified to sum to 11. The bound-number-keyword derivation completed March 2026 with all 40 bounds passing this check.
Examples
| Bound | Pair Partner | Sum |
|---|---|---|
| Activation (Ace of Wands, 1) | Attainment (10 of Wands) | 11 |
| Reverie (4 of Cups) | Allure (7 of Cups) | 11 |
| Reflection (2 of Swords) | Multiplicity (9 of Swords) | 11 |
| Endurance (5 of Coins) | Support (6 of Coins) | 11 |
Cross-References
- Operation_Bound_Pairing — the operation that uses this invariant
- Principle_Inner_Horizon — Inner side of pair (Tier 2)
- Principle_Outer_Horizon — Outer side of pair (Tier 2)
- Treatise_Bound_Number_Keywords — derivation of all 40 bound names
Canon Narratives
- corpus: Bound_Number_Keywords_Derivation — full bound derivation
- corpus: Elemental_Pairing_Invariants — pairing structure