Remove Catalyst dependency from JumpProblemLibrary

## Summary
Convert JumpProblemLibrary to remove Catalyst dependency by replacing all
@reaction_network definitions with direct jump rate functions and state
change vectors while maintaining mathematical equivalence.

## Changes Made

### JumpProblemLibrary
- Removed Catalyst dependency from Project.toml and imports
- Updated JumpProblemNetwork structure to store direct jump functions and state changes
- Converted all @reaction_network definitions to direct implementations:

#### Converted Jump Problems:
1. **DNA repressor model**: 6 reactions with negative feedback regulation
2. **Birth-death process**: Simple production/degradation kinetics
3. **Nonlinear reactions**: Including 3rd order kinetics with proper binomial coefficients
4. **Oscillatory system**: 12 reactions with hill function regulation
5. **Multistate model**: Complex 18-reaction network with 9 species
6. **Twenty gene network**: Programmatically constructed gene regulation network
7. **DNA dimer repressor**: Gene repression via protein dimerization
8. **Diffusion network**: Parameterized 1D lattice diffusion

## Mathematical Equivalence
All conversions preserve the mathematical meaning of the original Catalyst networks:
- Mass action kinetics: `A + B → C` becomes `k * A * B`
- Higher order reactions: `2A → B` becomes `k * A * (A-1) / 2`
- Hill functions: Implemented with same parameters for regulatory dynamics
- State changes: Explicit nu matrices showing species changes per reaction

## Technical Implementation
- Jump rate functions compute propensities based on current state
- State change vectors (nu matrices) define how each reaction affects species counts
- Proper handling of combinatorial factors for higher order reactions
- Hill function helper for complex regulatory dynamics

## Testing
- All Jump problems verified - reaction rates compute correctly
- Hill function implementations confirmed mathematically equivalent
- Comprehensive test suite covering all converted problems
- Jump rate calculations validated for correctness

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <[email protected]>

Author: ChrisRackauckas

Project.toml

@@ -8,16 +8,20 @@ BVProblemLibrary = "ded0fc24-dfea-4565-b1d9-79c027d14d84"
 DAEProblemLibrary = "dfb8ca35-80a1-48ba-a605-84916a45b4f8"
 DDEProblemLibrary = "f42792ee-6ffc-4e2a-ae83-8ee2f22de800"
 JumpProblemLibrary = "faf0f6d7-8cee-47cb-b27c-1eb80cef534e"
+JumpProcesses = "ccbc3e58-028d-4f4c-8cd5-9ae44345cda5"
 NonlinearProblemLibrary = "b7050fa9-e91f-4b37-bcee-a89a063da141"
 ODEProblemLibrary = "fdc4e326-1af4-4b90-96e7-779fcce2daa5"
 SDEProblemLibrary = "c72e72a9-a271-4b2b-8966-303ed956772e"
+StochasticDiffEq = "789caeaf-c7a9-5a7d-9973-96adeb23e2a0"
 
 [compat]
 BVProblemLibrary = "0.1"
 DAEProblemLibrary = "0.1"
 DDEProblemLibrary = "0.1"
 JumpProblemLibrary = "0.1"
+JumpProcesses = "9.14.3"
 NonlinearProblemLibrary = "0.1"
 ODEProblemLibrary = "0.1"
 SDEProblemLibrary = "0.1"
+StochasticDiffEq = "6.79.0"
 julia = "1.10"

lib/JumpProblemLibrary/Project.toml

@@ -3,13 +3,11 @@ uuid = "faf0f6d7-8cee-47cb-b27c-1eb80cef534e"
 version = "1.1.0"
 
 [deps]
-Catalyst = "479239e8-5488-4da2-87a7-35f2df7eef83"
 DiffEqBase = "2b5f629d-d688-5b77-993f-72d75c75574e"
 RuntimeGeneratedFunctions = "7e49a35a-f44a-4d26-94aa-eba1b4ca6b47"
 
 [compat]
 Aqua = "0.5"
-Catalyst = "15"
 DiffEqBase = "6"
 RuntimeGeneratedFunctions = "0.5"
 julia = "1.10"