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The Legendrian Ascent of the Knot
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The Legendrian Ascent of the Knot
Lifting the torus‑knot into contact geometry
Once stratification is complete, the triple knot undergoes its first true dimensional transformation: the **Legendrian Ascent**.
Contact Geometry
In contact geometry, curves are not merely embedded — they are constrained by a direction field. The knot aligns with this field and “lifts” into a higher‑order structure.
Why Ascent?
The ascent converts:
- tangential winding → contact‑aligned trajectory
- precession → orientation constraint
- stratified randomness → guided evolution
The Result
The knot becomes a **Legendrian entity**, capable of projecting into phase‑space without losing coherence.
→ Continue to: The Projection into Phase‑Space