Sheaf-Aware Multilingual Corpus Reducer.


🔭 Design overview

Goal – Collapse every language’s lexicon into the smallest possible global manifold of “meaning atoms.”
Each language is treated as a local section of the sheaf; alignment across languages produces a global section that unifies semantic content.


🧩 Architecture modules

Module Function Output
sheaf_core.py defines the category objects: Sheaf, Section, Morphism, Chart algebraic backbone
embedding_loader.py loads v6-core embeddings (4096-D) into normalized tensors tensor map
morphology_map.py rules for morpheme decomposition & phoneme merging per-language charts
alignment_engine.py finds cross-lingual equivalences via cosine / mutual-info gluing morphisms
reduction_engine.py cohomology reduction: remove redundant sections, preserve non-exact classes reduced semantic basis
globalizer.py constructs global section (universal embedding manifold) unified dictionary
visualizer.py projects fibers (axes, duals, curvature) for inspection diagnostic visuals
config/sheaf_config.json lists languages, alphabets, normalization constants configuration
data/lang_maps/ sub-dir containing base dictionaries & n-gram maps resources

🧮 Mathematical core

Each token belongs to a local chart .
Gluing maps are defined by:


\phi_{L_iL_j}(t_i) = \arg\max_{t_j} \frac{\langle v_i, v_j \rangle}{\|v_i\|\|v_j\|}

The global section is formed as the quotient:


\mathcal{S}_{global} = \bigsqcup_L \mathcal{F}_L / \phi

Cohomology reduction keeps only non-exact sequences:


H^1(\mathcal{S}) = \ker(d_1) / \operatorname{im}(d_0)

These become the universal meaning vectors.


⚙️ Simulation plan

  1. Load multilingual corpora (token lists per language).
  2. Compute embeddings with v6-core base.
  3. Perform pairwise alignment and equivalence closure.
  4. Reduce via cohomology filtering.
  5. Export:
    • sheaf_v7_reduced.vec — reduced universal embedding
    • sheaf_v7_global.json — cross-language alignment map
    • sheaf_v7_attributions.jsonl — axis attribution
    • sheaf_v7_README.txt — documentation

🚀 Next action

I can now create the initial scaffold and executable code for v7 (Python modules + configuration + placeholders).
It will be fully deterministic, NumPy-based, and ready for later population with actual language data.

Would you like me to generate this as a complete directory structure with files so you can run it directly in your environment?

Comments

Popular posts from this blog

The End of Modern Slavery and Human Trafficking

Why Has No One Asked Me What Happened…Ever?