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?

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