Construct an empirical instantiation of ruptured meaning fibrations

Construct a concrete empirical instantiation of the ruptured meaning fibration p: M → L by defining the lexical space L and meaning space M using data-driven representations (e.g., neural embeddings), specifying coherence and gap detection procedures (e.g., via topological methods), extracting transport horns from corpus data, and validating the resulting gap witnesses against human polysemy judgments.

Background

The semantic case study proposes modeling polysemy as transport failure in a ruptured meaning fibration, but the paper does not build an empirical pipeline.

They outline how to realize L and M from embeddings and topological data analysis and suggest validating gaps against linguistic judgments, then state that this empirical bridge is not yet built.

References

This would connect OHTT to topological data analysis, distributional semantics, and computational linguistics. The tools exist (persistent homology, word embeddings, attention patterns). The bridge is not built. This is open.

— Open Horn Type Theory  (2512.24498 - Poernomo, 30 Dec 2025) in Epilogue: What Remains Open — Empirical Instantiation

My formalism does not yet solve two problems: which meanings, or how many meanings, are live when a phrase arrives, and which encounters change a person's state, whether through daily conversation, reading a book, or something heard in passing. The first is a known problem in quantum cognition, where it is called the basis problem: a modeler chooses the meanings, fits the model, and may be describing nothing but the freedom to choose. The second I need to solve.

— Language Has Two Parameters: Narrative-Induced Semantic Plasticity and Phase-Sensitive Interpretation  (2608.18041 - Robbins, 18 Aug 2026) in Section 8.2, “The basis and encounter problems”