This category contains database systems built on mathematical foundations that go beyond the relational and document models. The common thread is semantic identity: each system represents objects in a way that captures structural and algebraic meaning, not just data fields.
Algebraic database using quandle structure as the semantic identity layer. Quandles provide a canonical fingerprint for equivalence classes under transformation, grounded in knot-theoretic coloring invariants.
Primary role in the KRL stack: semantic equivalence search and fingerprinting.
Persistence, indexing, and query layer for topological objects (tangles, knots, links).
Stores canonical TangleIR objects, caches invariants, indexes by algebraic fingerprint,
and maintains a rewrite-step graph for provenance and simplification tracking.
Primary role in the KRL stack: the database engine.
Self-normalising multimodal database with formal verification properties. Rust core, Elixir/OTP orchestration, Podman deployment.
Narrative-first database for documentary journalism. Dependent types extension; GQL (Glyph Query Language) front-end. Glyphbase is the web interface layer over Lithoglyph.
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Mathematical objects as primary storage units, not rows
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Structural and semantic fingerprinting for identity and deduplication
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Equivalence as a first-class database concept, not a post-query computation
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Invariant caches as indexed columns, not application-layer lookups
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Provenance and rewrite history stored alongside objects
The databases in this category are designed to be driven by the languages
in nextgen-languages. In particular:
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KRL (Knot Resolution Language) is the surface language for QuandleDB and Skein.jl
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Eclexia is the language for resource-constraint databases
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Phronesis is the language for multi-agent ethical constraint systems
| Project | Status | Notes |
|---|---|---|
QuandleDB |
Active — early stage |
Quandle extraction and fingerprinting in progress |
Skein.jl |
Active — refactoring |
Migrating to TangleIR as primary stored type |
VeriSimDB |
Active — design phase |
Rust core skeleton in place |
Lithoglyph |
Specified |
GQL grammar defined; implementation pending |
