Adding more notes on the project

notes/qa-session.md

@@ -90,3 +90,64 @@ The mechanisms handle all standard geometric logic axioms:
 - Category laws, Petri net rules, graph reachability
 
 The gaps only matter for axioms with complex record/product operations in conclusions.
+
+---
+
+## Q3: Is Geolog inspired by an existing tool or software?
+
+**Answer: Geolog is an AI-generated project that combines ideas from several fields. No single tool is its direct ancestor.**
+
+### Origin
+
+The README states:
+
+> "This README was synthesized automatically by Claude Opus 4.5. As was this entire project, really."
+
+Geolog was created by Claude Opus 4.5, Anthropic's AI model.
+
+### Technical Influences
+
+The project draws from several established areas:
+
+**Egglog / Egg**
+- Uses `egglog-union-find` and `egglog-numeric-id` crates
+- Equality saturation and e-graph techniques for congruence closure
+
+**Database Theory**
+- Chase algorithm: a classical method for computing fixpoints in databases
+- Relational algebra for query compilation
+
+**SMT Solvers**
+- Model enumeration follows SMT solver patterns
+- Automated search with forward chaining and equation propagation
+
+**Category Theory / Topos Theory**
+- Geometric logic with semantics in topoi
+- Lean4 formalization uses the `model-theory-topos` library
+
+**Formal Verification**
+- Petri net reachability (similar to model checking)
+- Diagrammatic rewriting
+
+### No Single Predecessor
+
+The codebase doesn't name a specific tool as direct inspiration. Geolog is a novel combination of:
+
+| Concept | Source Field |
+|---------|--------------|
+| Geometric logic | Mathematical logic |
+| Chase algorithm | Database theory |
+| Tensor algebra | Linear algebra / sparse computation |
+| Equality saturation | Program optimization (egg/egglog) |
+| Congruence closure | Automated theorem proving |
+
+### Related Tools (for context)
+
+While not cited as inspirations, similar tools exist in adjacent spaces:
+- **Alloy** - relational logic model finder
+- **Datalog** - logic programming for databases
+- **CQL** - categorical query language
+- **Z3** - SMT solver
+- **Egg** - equality saturation toolkit
+
+Geolog occupies a unique niche: geometric logic with topos semantics applied to practical problems like workflow orchestration and Petri nets.

notes/summary.md

@@ -0,0 +1,81 @@
+# Geolog Summary
+
+*Date: 2026-03-19*
+
+## What Is Geolog?
+
+Geolog is a **Geometric Logic REPL** — a reasoning engine written in Rust that implements type theory with semantics in topoi. It was AI-generated by Claude Opus 4.5.
+
+## Core Concepts
+
+### Axioms
+
+An axiom is an "if-then" rule: "If premises are true, then conclusion must be true."
+
+```
+forall x, y, z. friends(x,y), friends(y,z) |- knows(x,z)
+```
+
+Similar to Datalog rules, but extended with:
+- Existentials in conclusions (`|- exists x. R(x)`)
+- Disjunctions (`|- A \/ B`)
+- Equality conclusions (`|- x = y`)
+
+### Chase Algorithm
+
+Repeatedly applies axioms until no new facts can be derived (fixpoint). Basic blocks:
+
+1. **Axioms** — the rules to apply
+2. **Structure** — carriers (element sets), functions, relations
+3. **Bindings** — variable-to-element mappings
+4. **Tensor system** — finds violations (premises true, conclusion false)
+5. **Fire conclusion** — adds relations, defines functions, creates elements, adds equations
+6. **Congruence closure** — union-find for tracking element equality
+
+### Union-Find
+
+Data structure for tracking equivalence classes. Used for congruence closure when axioms conclude `x = y`. More efficient than naive dictionary + sets approach:
+- Naive: O(n) per union
+- Union-find: O(1) amortized per union
+
+### Language Syntax
+
+Geolog's syntax is not based on any single existing language. Influences:
+- **Postfix application** (`x f` not `f(x)`) — category theory
+- **Sequent notation** (`premises |- conclusion`) — proof theory
+- **Path separators** (`/` not `.`) — unique to Geolog
+
+## Skeptical Assessment of Applications
+
+### Claimed Use Cases
+- Business process workflow orchestration
+- Formal verification
+- Database query design
+- Petri net reachability
+
+### Reality
+
+| Claim | Assessment |
+|-------|------------|
+| Workflow orchestration | No APIs, no integrations, no distributed execution — just a REPL |
+| Formal verification | Lean4 proofs "in progress"; not comparable to Coq/Lean/TLA+ |
+| Database query design | Not a database — no persistence at scale, no SQL, no transactions |
+| Petri net reachability | Toy examples only, not industrial-scale |
+
+### What It Actually Is
+
+A **research/educational tool** for:
+- Learning geometric logic and chase algorithms
+- Experimenting with category-theoretic ideas
+- Prototyping constraint systems
+- Academic exploration
+
+**Not suitable for:** Production systems, real workflow orchestration, industrial formal verification, or database replacement.
+
+## Project Status
+
+- Version: 0.1.0
+- 30,000+ lines of Rust
+- 168 tests (all passing)
+- 30 example files
+- Well-documented but unproven in real-world use