Missing Mathematics§1.8Priority #2
Differential Geometry
Framework Established
The Gap
UL uses flat Euclidean geometry, but meaning space is curved. No metric, geodesics, or curvature.
Why It Matters
The gauge field A(x,t) formalizes context — essential for pragmatics. Without connection/gauge field, UL cannot express how meaning changes with context.
Resolution
Trivial fiber bundle E = X × G constructed. Connection A defined. Polysemy-Holonomy theorem PROVEN.
Expedition Status
- Expedition:
- Expedition One
- Front:
- Front A
- Status:
- FRAMEWORK + PROVEN
- Source:
- frontier/expedition-one/gauge-bundle-of-meaning.md
Impact
high
Tractability
high
Effort
medium
Category
mathematics
Related Problems
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