"Forge" = CREATE new formulas through verified derivation
π English | ηΉι«δΈζ
NSForge is NOT a formula database β it's a derivation factory that CREATES new formulas.
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
β β
β π¨ FORGE = Create new formulas through derivation β
β β
β Input: Base formulas Output: NEW derived formulas β
β βββββββββββββββββββββββ βββββββββββββββββββββββββββββββββββββββ β
β β β’ One-compartment β β Temperature-corrected elimination β β
β β β’ Arrhenius β βββ β Body fat-adjusted distribution β β
β β β’ Fick's law β β Renal function dose adjustment β β
β β β’ ... β β Custom PK/PD models β β
β βββββββββββββββββββββββ βββββββββββββββββββββββββββββββββββββββ β
β (from sympy-mcp) (stored in NSForge) β
β β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
| Capability | Description | Tools |
|---|---|---|
| DERIVE | Create new formulas by composing base formulas | substitute, simplify, differentiate, integrate |
| CONTROL | Full step control: review, edit, rollback, insert | get_step, update_step, rollback, delete_step, insert_note |
| VERIFY | Ensure correctness through multiple methods | check_dimensions, verify_derivative, symbolic_equal |
| STORE | Save derived formulas with full provenance | formulas/derivations/ repository |
NSForge works WITH other MCP servers, not against them:
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
β MCP Scientific Computing Ecosystem β
β π’ 108 Tools Total π’ β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ€
β sympy-mcp (32 tools) β
β βββ Base formulas: F=ma, PV=nRT, Arrhenius... β
β βββ Physical constants: c, G, h, R... (SciPy CODATA) β
β βββ Symbolic computation engine (ODE, PDE, matrices) β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ€
β nsforge-mcp (76 tools) β YOU ARE HERE β
β βββ π¨ Derivation framework: compose, verify, generate code β
β βββ π Derivation repository: store CREATED formulas with provenance β
β βββ β
Verification layer: dimensional analysis, reverse verification β
β βββ π Formula search: Wikidata, BioModels, SciPy constants β
β βββ π Optimization bridge: prepare formulas for USolver β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ€
β medical-calc-mcp (75+ tools) β
β βββ Clinical scores: APACHE, SOFA, GCS, MELD, qSOFA... β
β βββ Medical calculations: eGFR, IBW, BSA, MEWS... β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ€
β usolver-mcp (Optional collaboration) β
β βββ π― Find optimal values for NSForge-derived formulas β
β βββ Solvers: Z3, OR-Tools, CVXPY, HiGHS β
β βββ Use case: dose optimization, circuit parameter selection β
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What NSForge stores:
| β BELONGS in NSForge | β Does NOT belong (use other tools) |
|---|---|
| Temperature-corrected drug elimination | Basic physics formulas (sympy-mcp) |
| Body fat-adjusted volume of distribution | Physical constants (sympy-mcp) |
| Renal function dose adjustments | Clinical scores (medical-calc-mcp) |
| Custom composite PK/PD models | Textbook formulas (references) |
NSForge provides features not available in SymPy-MCP by directly leveraging SymPy modules:
| Feature | SymPy Module | Application | Status |
|---|---|---|---|
| Statistics & Probability | sympy.stats |
PopPK variability, uncertainty | β v0.2.1 |
| Limits & Series | sympy.limit, sympy.series |
Steady-state, accumulation | β v0.2.1 |
| Inequality Solving | sympy.solvers.inequalities |
Therapeutic window | β v0.2.1 |
| Assumption Queries | sympy.assumptions |
Auto-validation | β v0.2.1 |
| Advanced Algebra | sympy.expand/factor/apart... |
Expression manipulation | β v0.2.4 |
| Integral Transforms | sympy.laplace_transform/fourier_transform |
ODE solving, frequency analysis | β v0.2.4 |
| Derivation Workflow | NSForge exclusive | Step tracking, provenance | β Available |
| Verification Suite | NSForge exclusive | Dimension analysis | β Available |
π Details: See NSForge vs SymPy-MCP Comparison for complete analysis.
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
β β
β User Question NSForge Processing Pipeline β
β βββββββββββββ βββββββββββββββββββββββββββ β
β β
β "Drug concentration in 1οΈβ£ Query Formula Knowledge Base β
β a 38Β°C fever patient?" βββ ββ One-compartment PK: C(t) = CβΒ·e^(-kβt)
β ββ Arrhenius equation: k(T) = AΒ·e^(-Ea/RT)
β β
β 2οΈβ£ Compose Derivation β
β ββ Substitute k(T) into PK model β
β ββ Obtain temperature-corrected formulaβ
β β
β 3οΈβ£ Symbolic Computation (SymPy) β
β ββ C(t,T) = CβΒ·exp(-kβ,refΒ·tΒ·exp(...)) β
β β
β 4οΈβ£ Verify Results β
β ββ T=37Β°C reduces to standard model β β
β ββ Dimensional analysis passed β β
β β
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NSForge now provides full CRUD control over derivation steps:
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β ποΈ STEP CONTROL - Navigate and Edit Your Derivation! β
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ€
β β
β Step 1 β Step 2 β Step 3 β Step 4 β Step 5 β Step 6 (current) β
β β β
β β β
β "Wait, step 3 looks wrong..." β
β β
β ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β π READ β derivation_get_step(3) β View step details β β
β β βοΈ UPDATE β derivation_update_step(3, notes="...") β Fix notes β β
β β βͺ ROLLBACKβ derivation_rollback(2) β Return to step 2 β β
β β π INSERT β derivation_insert_note(2, "...") β Add explanation β β
β β ποΈ DELETE β derivation_delete_step(6) β Remove last step β β
β ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β
β After rollback: Step 1 β Step 2 (now current) β
β β Continue derivation from step 2, try a different path! β
β β
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
| Tool | Operation | Description |
|---|---|---|
derivation_get_step |
Read | Get details of any step (expression, notes, assumptions) |
derivation_update_step |
Update | Modify metadata (notes, assumptions, limitations) - NOT expression |
derivation_delete_step |
Delete | Remove the LAST step only (safety constraint) |
derivation_rollback |
Rollback | β‘ Jump back to any step, delete subsequent steps |
derivation_insert_note |
Insert | Add explanatory note at any position |
π‘ Key Insight: Expressions can't be edited directly (that would break verification). Use
rollbackto return to a valid state, then re-derive with corrections.
- Peer Review: "Step 5's assumption is questionable" β
update_step(5, notes="Validated for T<42Β°C only") - Wrong Path: "We should have used integration instead" β
rollback(3)β start fresh - Add Context: "Need to explain the Arrhenius substitution" β
insert_note(4, "Temperature effect on enzyme kinetics...") - Clean Up: "Last step was a mistake" β
delete_step(8)
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β β
β Problem: LLMs doing math directly β
β βββββββββββββββββββββββββββββββββ β
β β
β β May calculate wrong β Different results β Unverifiable β
β (hallucinations) each time β
β β
β βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ β
β β
β Solution: LLM + NSForge β
β βββββββββββββββββββββββ β
β β
β LLM handles: NSForge handles: β
β βββββββββββββββββββββββ βββββββββββββββββββββββ β
β β β’ Understand query β β β’ Store verified β β
β β β’ Plan derivation β βββ β formulas β β
β β β’ Explain results β β β’ Precise symbolic β β
β βββββββββββββββββββββββ β computation β β
β "Understanding β β’ Track derivation β β
β & Planning" β sources β β
β β β’ Verify results β β
β βββββββββββββββββββββββ β
β "Computation β
β & Verification" β
β β
β β
Guaranteed correct β
Reproducible β
Fully traceable β
β β
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NSForge stores derived formulas with full provenance tracking:
formulas/
βββ derivations/ β All derived formulas go here
βββ README.md β Documentation
βββ pharmacokinetics/ β PK model derivations
βββ temp_corrected_elimination.md β Temperature-corrected k
βββ fat_adjusted_vd.md β Obesity-adjusted Vd
Each derivation result contains:
- LaTeX mathematical expression
- SymPy computable form
- Derived from: which base formulas were combined
- Derivation steps: the actual derivation process
- Verification status: dimensional analysis, limiting cases
- Clinical context and usage guidance
- YAML metadata for programmatic access
Example Derivations:
| Derivation | Domain | Description |
|---|---|---|
| Temperature-Corrected Elimination | PK | First-order elimination + Arrhenius temperature dependence |
| NPO Antibiotic Effect | PK/PD | Henderson-Hasselbalch + Emax model for pH-dependent absorption |
| Temperature-Corrected Michaelis-Menten | PK | Non-linear saturable kinetics with temperature effects |
| Cisatracurium Multiple Dosing | PK | Hydrolytic drug accumulation with temperature correction |
| Physiological Vd Body Composition | PK/PBPK | PBPK-based Vd adjustment for body composition (logP > 2) |
Example: NPO (Fasting) Impact on Antibiotic Efficacy
id: npo_antibiotic_effect
name: NPO Impact on Oral Antibiotic Efficacy
expression: E_0 + (E_max * C_eff^n) / (EC_50^n + C_eff^n)
where: C_eff = F_base * D / (Vd * (1 + 10^(pH - pKa)))
derived_from:
- henderson_hasselbalch # pH-dependent ionization
- emax_model # Pharmacodynamic effect
verified: true
verification_method: sympy_symbolic_substitution
clinical_context: |
Predicts reduced antibiotic efficacy in NPO patients due to
increased gastric pH. Critical for weak acid antibiotics like
Amoxicillin (pKa=2.4) where NPO can reduce effect by >90%.See also: Python Implementation with clinical recommendations.
| Category | Capabilities |
|---|---|
| π’ Symbolic Computation | Calculus, Algebra, Linear Algebra, ODE/PDE |
| π Formula Management | Storage, Query, Version Control, Source Tracking |
| π Derivation Composition | Multi-formula composition, Variable substitution, Condition modification |
| β Result Verification | Dimensional analysis, Boundary conditions, Reverse verification |
| π Code Generation | Generate Python functions from symbolic formulas |
- Python 3.12+
- uv (recommended package manager)
# Using uv (recommended)
uv add nsforge-mcp
# Or using pip
pip install nsforge-mcpgit clone https://github.com/u9401066/nsforge-mcp.git
cd nsforge-mcp
# Create environment and install dependencies
uv sync --all-extras
# Verify installation
uv run python -c "import nsforge; print(nsforge.__version__)"// Claude Desktop config (claude_desktop_config.json)
{
"mcpServers": {
"nsforge": {
"command": "uvx",
"args": ["nsforge-mcp"]
}
}
}Calculus computation:
User: Calculate β«(xΒ² + 3x)dx and verify the result
Agent calls NSForge:
β Result: xΒ³/3 + 3xΒ²/2 + C
β Verify: d/dx(xΒ³/3 + 3xΒ²/2) = xΒ² + 3x β
β Steps: Split integral β Power rule β Combine
Physics derivation:
User: Work done by ideal gas in isothermal expansion?
Agent calls NSForge:
β W = nRT ln(Vβ/Vβ)
β Derivation: PV=nRT β P=nRT/V β W=β«PdV β Integrate
Algorithm analysis:
User: Analyze T(n) = 2T(n/2) + n
Agent calls NSForge:
β T(n) = Ξ(n log n)
β Method: Master Theorem Case 2
β Example: Merge Sort
- Design Evolution: Derivation Framework - Architecture evolution from templates to composable derivation framework
- Domain Planning: Audio Circuits - Audio circuits principles and modifications
- Original Design - Complete architecture and API design (reference)
- Power Amp Coupling Capacitor Design - Complete RC high-pass filter derivation
- From ideal formulas to practical considerations (output impedance, ESR, speaker impedance curve)
- Demonstrates NSForge "Principles + Modifications" framework in practice
- API Reference - MCP tool documentation (TBD)
NSForge provides 75 MCP tools organized into 7 modules:
| Tool | Purpose |
|---|---|
derivation_start |
Start a new derivation session |
derivation_resume |
Resume a previous session |
derivation_list_sessions |
List all sessions |
derivation_status |
Get current session status |
derivation_show |
π Display current formula (like SymPy's print_latex_expression) |
derivation_load_formula |
Load base formulas |
derivation_substitute |
Variable substitution |
derivation_simplify |
Simplify expression |
derivation_solve_for |
Solve for variable |
derivation_differentiate |
Differentiate expression |
derivation_integrate |
Integrate expression |
derivation_record_step |
Record step with notes ( |
derivation_add_note |
Add human insights |
derivation_get_steps |
Get all derivation steps |
derivation_get_step |
Get single step details |
derivation_update_step |
Update step metadata |
derivation_delete_step |
Delete last step |
derivation_rollback |
β‘ Rollback to any step |
derivation_insert_note |
Insert note at position |
derivation_complete |
Complete and save |
derivation_abort |
Abort current session |
derivation_list_saved |
List saved derivations |
derivation_get_saved |
Get saved derivation |
derivation_search_saved |
Search derivations |
derivation_repository_stats |
Repository statistics |
derivation_update_saved |
Update metadata |
derivation_delete_saved |
Delete derivation |
derivation_export_for_sympy |
π Export state to SymPy-MCP |
derivation_import_from_sympy |
π Import result from SymPy-MCP |
derivation_handoff_status |
π Check handoff capabilities |
derivation_prepare_for_optimization |
π Prepare for USolver |
| Tool | Purpose |
|---|---|
verify_equality |
Verify two expressions are equal |
verify_derivative |
Verify derivative by integration |
verify_integral |
Verify integral by differentiation |
verify_solution |
Verify equation solution |
check_dimensions |
Dimensional analysis |
reverse_verify |
Reverse operation verification |
| Tool | Purpose |
|---|---|
calculate_limit |
Calculate limits |
calculate_series |
Taylor/Laurent series expansion |
calculate_summation |
Symbolic summation Ξ£ |
solve_inequality |
Solve single inequality |
solve_inequality_system |
Solve system of inequalities |
define_distribution |
Define probability distribution |
distribution_stats |
Get distribution statistics (mean, var, skew) |
distribution_probability |
Calculate probability P(condition) |
query_assumptions |
Query symbol assumptions |
refine_expression |
Refine expression with assumptions |
evaluate_numeric |
Numerical evaluation |
symbolic_equal |
Symbolic equality check |
| Tool | Purpose |
|---|---|
parse_expression |
Parse mathematical expression |
validate_expression |
Validate expression syntax |
extract_symbols |
Extract symbols with metadata |
| Tool | Purpose |
|---|---|
generate_python_function |
Generate Python function |
generate_latex_derivation |
Generate LaTeX document |
generate_derivation_report |
Generate Markdown report |
generate_sympy_script |
Generate standalone SymPy script |
| Tool | Purpose |
|---|---|
expand_expression |
Expand products: (x+1)Β² β xΒ²+2x+1 |
factor_expression |
Factorize: xΒ²-1 β (x-1)(x+1) |
collect_expression |
Collect terms by variable |
trigsimp_expression |
Trig simplify: sinΒ²+cosΒ² β 1 |
powsimp_expression |
Power simplify: xΒ²Β·xΒ³ β xβ΅ |
radsimp_expression |
Radical simplify |
combsimp_expression |
Factorial simplify: n!/(n-2)! β n(n-1) |
apart_expression |
π₯ Partial fractions (for inverse Laplace) |
cancel_expression |
Cancel common factors |
together_expression |
Combine fractions |
| Tool | Purpose |
|---|---|
laplace_transform_expression |
π₯ f(t) β F(s) for ODE solving |
inverse_laplace_transform_expression |
π₯ F(s) β f(t) multi-compartment PK |
fourier_transform_expression |
f(x) β F(k) frequency analysis |
inverse_fourier_transform_expression |
F(k) β f(x) signal reconstruction |
| Tool | Purpose |
|---|---|
formula_search |
π Unified search (Wikidata, BioModels, SciPy) |
formula_get |
π Get formula details by ID |
formula_categories |
π List available categories |
formula_pk_models |
π PK models (1/2-compartment, Michaelis-Menten) |
formula_kinetic_laws |
βοΈ Reaction kinetics (Hill, etc.) |
formula_constants |
π¬ Physical constants (from SciPy) |
NSForge includes 19 pre-built Skills that teach AI agents how to use the tools effectively:
| Skill | Trigger Words | Description |
|---|---|---|
nsforge-derivation-workflow |
derive, ζ¨ε°, prove | Complete derivation workflow with session management |
nsforge-formula-management |
list, ε ¬εΌεΊ«, find formula | Query, update, delete saved formulas |
nsforge-formula-search |
Wikidata, BioModels, η©ηεΈΈζΈ | π Search external formula sources |
nsforge-verification-suite |
verify, check, ηΆεΊ¦ | Equality, derivative, integral, dimension checks |
nsforge-code-generation |
generate, export, LaTeX | Python functions, reports, SymPy scripts |
nsforge-quick-calculate |
calculate, simplify, solve | Quick calculations without session |
Includes git-precommit, memory-updater, code-reviewer, test-generator, and more.
π Details: See NSForge Skills Guide for complete documentation.
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β Phase 1: SymPy-MCP executes computation β
β intro_many([...]) β introduce_expression(...) β β
β substitute/solve/dsolve... β print_latex_expression(...) β
βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ€
β Phase 2: NSForge records & stores β
β derivation_record_step(...) β derivation_add_note(...) β β
β derivation_complete(...) β
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Division of Labor:
| Task | Tool | Reason |
|---|---|---|
| Math computation | SymPy-MCP | Full ODE/PDE/matrix capabilities |
| Formula display | print_latex_expression |
User confirmation at each step |
| Knowledge storage | NSForge | Provenance tracking, searchable |
| Dimension check | NSForge check_dimensions |
Physical unit verification |
This project uses DDD (Domain-Driven Design) architecture with Core and MCP separation:
nsforge-mcp/
βββ .claude/skills/ # π§ Agent Skills (18 skills)
β βββ nsforge-derivation-workflow/ # Core workflow skill
β βββ nsforge-verification-suite/ # Verification skill
β βββ ... # 16 more skills
β
βββ src/
β βββ nsforge/ # π· Core Domain (pure logic, no MCP dependency)
β β βββ domain/ # Domain Layer
β β β βββ entities.py # - Entities (Expression, Derivation)
β β β βββ value_objects.py # - Value Objects (MathContext, Result)
β β β βββ services.py # - Domain service interfaces
β β βββ application/ # Application Layer
β β β βββ use_cases.py # - Use Cases (Calculate, Derive, Verify)
β β βββ infrastructure/ # Infrastructure Layer
β β βββ sympy_engine.py # - SymPy engine implementation
β β βββ verifier.py # - Verifier implementation
β β
β βββ nsforge_mcp/ # πΆ MCP Layer (Presentation)
β βββ server.py # - FastMCP Server
β βββ tools/ # - MCP tool definitions (76 tools)
β βββ derivation.py # - π₯ Derivation engine (31 tools)
β βββ calculate.py # - π’ Calculation (12 tools)
β βββ simplify.py # - π Advanced algebra (10+4 tools)
β βββ formula.py # - π Formula search (6 tools)
β βββ verify.py # - Verification (6 tools)
β βββ expression.py # - Expression parsing (3 tools)
β βββ codegen.py # - Code generation (4 tools)
β
βββ formulas/ # π Formula Repository
β βββ derivations/ # - Human-readable Markdown
β β βββ pharmacokinetics/ # - PK derivation examples
β βββ derived/ # - YAML metadata (auto-generated)
β
βββ derivation_sessions/ # πΎ Session persistence (JSON)
βββ docs/ # π Documentation
β βββ nsforge-skills-guide.md # - Skills usage guide (588 lines)
βββ examples/ # π Python examples
β βββ npo_antibiotic_analysis.py # Clinical application
β βββ physiological_vd_model.py # PBPK body composition model
βββ tests/ # Tests
βββ pyproject.toml # Project config (uv/hatch)
- Core independently testable: No MCP dependency, can use
nsforgepackage standalone - MCP replaceable: Can support other protocols (REST, gRPC) in the future
- Dependency Inversion: Domain defines interfaces, Infrastructure implements
# Clone
git clone https://github.com/u9401066/nsforge-mcp.git
cd nsforge-mcp
# Create environment (uv will automatically use Python 3.12+)
uv sync --all-extras
# Run tests
uv run pytest
# Code checks
uv run ruff check src/
uv run mypy src/
# Start dev server
uv run nsforge-mcpNSForge can work with USolver to provide domain-expert formula derivation + mathematical optimization:
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β Problem: Find optimal Fentanyl dose for 65yo patient with 30% BF, β
β concurrent midazolam, targeting 2.5 ng/mL at t=5min β
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β Step 1: NSForge derives modified formula β
β ββ Consider: CYP3A4 competition (-30% CL) β
β ββ Consider: Body fat 30% (+25% Vd) β
β ββ Consider: Age 65 (-15% CL) β
β ββ Output: C(t, dose) = dose/15.875 Γ exp(-0.476Γt/15.875) β
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β Step 2: Prepare for optimization β
β ββ derivation_prepare_for_optimization() β
β β Variables: [dose], Parameters: {CL: 0.476, V1: 15.875} β
β β Constraints: dose β [0.01, 0.10], C(5) β [2.0, 4.0] β
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β Step 3: USolver finds optimal value β
β ββ usolver.solve(objective="C(5, dose) = 2.5", constraints=[...]) β
β β optimal_dose = 0.0354 mg (35.4 mcg) β
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| Tool | Strength | Output |
|---|---|---|
| NSForge | Domain knowledge (drug interactions, body composition) | Modified formula |
| USolver | Mathematical optimization (Z3, OR-Tools, CVXPY) | Optimal parameters |
| Together | Domain-smart + Math-precise | Best clinical decision |
- Install USolver:
uv run https://github.com/sdiehl/usolver/install.py - In NSForge, after completing derivation, call:
result = derivation_prepare_for_optimization() # Copy result.usolver_template to USolver
- USolver returns optimal values
- Use optimal values in NSForge-derived formula for final calculation
π Skill:
.claude/skills/nsforge-usolver-collab/SKILL.md
- Design documents
- MVP Implementation
- Derivation Engine (26 tools)
- SymPy Integration
- Verification Suite (6 tools)
- MCP Server
- Step Control System (v0.2.2)
- Read/Update/Delete steps
- Rollback to any point
- Insert notes at any position
- Agent Skills System
- 6 NSForge-specific workflows
- 13 general development skills
- Skills documentation
- Advanced Algebra & Transforms (v0.2.4)
- 10 simplification tools (expand, factor, apart...)
- 4 integral transforms (Laplace, Fourier)
- SymPy coverage: 85% β 92%
- External Formula Search (v0.2.4)
- Wikidata SPARQL adapter
- BioModels adapter
- SciPy constants
- Pharmacokinetics Domain
- Temperature-corrected elimination
- NPO antibiotic effect model
- Michaelis-Menten with temperature
- Multiple dosing accumulation
- Domain Expansion
- Physics formula library
- Audio circuits (in progress)
- Algorithm analysis
- Advanced Features
- Lean4 formal verification
- Automatic derivation planning
Contributions welcome! Please see CONTRIBUTING.md.
NSForge β Forge new formulas through verified derivation | Where Neural Meets Symbolic