K=3 Braid Hypothesis: spatial consensus and temporal persistence are the SAME operation. Three observers agreeing NOW = one observer persisting across three MOMENTS. K=3 is the third of ten axiom terms (the Decality). The ring Z/970200Z has 108 lattice structures.
| MEASURE | RESULT | MEANING |
|---|---|---|
| Spatial K | MAJ(agent A, agent B, agent C) | What 3 observers agree on RIGHT NOW |
| Temporal K | MAJ(origin, present, terminus) | What persists across 3 MOMENTS |
| Equivalence | Spatial = Temporal (converges) | Same operation, different framing |
| MECHANISM | EXPLANATION |
|---|---|
| MAJ = MAJ | Both spatial and temporal K use the same majority operation. The bit-level logic is identical. |
| Shared environment | Spatial result feeds temporal projection. Coupling makes them converge. |
| Agent convergence | K=3 agents converge to same pattern in ~3-5 steps. Once converged, spatial K = any agent = temporal K. |
| TEST | QUESTION | ANSWER |
|---|---|---|
| Equivalence | Do spatial and temporal K give same P5 rate? | YES - both converge to same attractors |
| Stacking | Does combining both create meta-structure? | YES - meta-P5 emerges from agreement |
| Nesting | Does K at level N force K at level N+1? | K propagates upward through levels |
| Life Braid | Does temporal K produce P5 attractor like life.c? | YES - LIFE=7 emerges from K=3 braid dynamics |
| PROPERTY | THIS DEMO | STANDARD VIEW |
|---|---|---|
| Space vs Time | Same operation (K=MAJ) | Fundamentally different |
| Consensus | K=3 minimum for closure | Arbitrary threshold |
| Dimension origin | K-binding creates dimension | Dimensions assumed a priori |
| Braid structure | Spatial/temporal strands weave | Braids = pure topology |
Source: braid.c (851 lines). K=3 = minimum for majority vote = minimum for closure. Triangle is the simplest polygon. The braid is not metaphor.
Standard view: Braid groups are abstract algebraic structures. The connection between spatial and temporal braiding is metaphorical.
Axiom view: K=3 strands IS the minimum for non-trivial braiding. Spatial K (topology) = temporal K (closure). Every interaction is a braid: two strands cross under a third's gaze. The axiom's closure principle K=3 is literally the structure of braiding.