Next-Generation Databases — Research Overview

Overview

This repository contains experimental database systems built on mathematical foundations that go beyond traditional relational or document models.

The shared goal is:

to treat semantic identity as primary, rather than raw data equality.

These systems store and operate on structured objects where identity is determined by equivalence under transformation.

Core Idea

Traditional databases treat identity as:

• equality of rows

• equality of documents

• equality of keys

In contrast, these systems treat identity as:

equivalence classes of structured objects.

This enables:

• deduplication based on structure, not representation

• queries over equivalence classes

• indexing by invariants rather than raw values

• explicit tracking of transformation history

Projects

QuandleDB

An algebraic database using quandle structures as a semantic identity layer.

• Objects are indexed by algebraic invariants derived from their structure

• Designed for equivalence detection under transformation (e.g. knot isotopy)

Status: early-stage; core extraction and fingerprinting in progress.

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Skein.jl

A persistence and indexing layer for topological objects.

• Stores canonical representations (e.g. TangleIR)

• Maintains invariant caches

• Tracks rewrite history and provenance

Status: active, undergoing refactoring.

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VeriSimDB / VanguardDB

A self-normalising multimodal database with formal verification goals.

• Rust core with Elixir/OTP orchestration

• Focus on correctness and reliability guarantees

Status: design phase.

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Lithoglyph / Glyphbase / GQL

A narrative-first database system aimed at documentary and structured storytelling.

• GQL (Glyph Query Language) provides the query layer

• Dependent-type extensions planned

Status: specified.

Common Principles

Across these systems:

• Structured objects are primary, not rows or documents

• Equivalence is a first-class concept

• Invariants are used for indexing and identity

• Provenance and transformation history are explicitly stored

• Query systems operate over equivalence classes

Relationship to Languages

These databases are designed to pair with languages in nextgen-languages:

• KRL → QuandleDB / Skein (topological objects)

• Other languages → domain-specific storage and verification systems

The broader goal is a unified ecosystem where:

• languages define construction and transformation

• databases define identity and retrieval

Status

This repository represents ongoing research work.

Components vary in maturity:

• some systems are partially implemented

• others are specified but not yet built

• formal obligations are documented but not fully discharged

See proof and specification documents for current guarantees and gaps.

Suggested Entry Points

• QuandleDB proof obligations — mathematical and systems requirements for equivalence

• Skein.jl documentation — persistence and indexing design

• KRL integration — example of language ↔ database interaction