The Gauge Bundle of Meaning
Differential Geometry of Context and Interpretation
Summary
This research applies differential geometry to the problem of meaning in context. The context
space X (comprising speaker, listener, domain, time, common ground, and communicative goal) is modeled
as a finite-dimensional manifold. The meaning bundle E → X has the geometric algebra G as its fiber,
with a connection A encoding how meaning evolves as context changes. Polysemy emerges as non-trivial
holonomy — the path-dependence of parallel transport around loops in context space.
Status Summary
Proven(3)
- •Deictic expressions are sections of E → X
- •Context space X is path-connected
- •Polysemy-Holonomy theorem (with expedition-two)
Framework(3)
- •Context space X defined with explicit coordinates
- •Meaning bundle E → X declared as trivial bundle
- •Connection A defined with transformation law
Conjectured(1)
- •Curvature concentrated on polysemy locus
Analogy(2)
- •Test artifact effect as parallel transport
- •Three-phase response as curvature regimes
Key Ideas
Context Space X
FrameworkContext is formalized as a finite-dimensional product manifold X = A × A × D × ℝ≥0 × K × G, encoding speaker, listener, domain, time, common ground, and communicative goal.
Meaning Bundle E → X
FrameworkMeanings available at context x form the fiber G of a trivial bundle E = X × G. Context-dependence is encoded in the connection.
Deixis as Bundle Sections
ProvenDeictic expressions ('I', 'here', 'now') are sections of E → X, evaluated at the utterance context.
Polysemy-Holonomy Theorem
ProvenPolysemy (non-parallel meaning section) is equivalent to non-trivial holonomy of the meaning connection, under non-degeneracy. Full proof in expedition-two.
Path-Connectivity of X
ProvenThe context space X is path-connected under the continuous manifold models required by the gauge bundle formalism.
Not Yet Addressed
- Full metric on meaning space (requires probability distributions)
- Quantization of the gauge field
- Monodromy group of the meaning bundle
Prerequisites
- foundations/paradigm.md
- foundations/formal-foundations.md
- history/mechanism-of-action.md
Related Open Problems
Source Document
frontier/expedition-one/gauge-bundle-of-meaning.md