CENTL / CentL26

Exact-first mathematics, physics, chemistry, and offline STEM computing environment.

Good maths should be free.
Never manufacture mathematical certainty.

CentL26 · freecomputation.org · Apache-2.0

CentL26 is the flagship standalone scientific computing environment of CENTL.
The "26" represents the 2026 flagship product line. CentL26 provides a calm, offline, deterministic scientific workbench that combines exact rational arithmetic, canonical polynomial algebra, physics kernels, chemical stoichiometry, in-app hackability, 2D function plotting, interactive STEM animated visualizer & theorem studio, academic search engine, and a comprehensive offline natural language problem solver.

CentL26.13-AG is the official latest release across all supported desktop and web environments.

---

Simple & Easy Setup Across All Ecosystems

CentL26 runs natively on Windows 11, macOS Arm64, and Debian/Fedora Linux distros with 100% feature parity. All modes run the exact same offline Rust core engine with zero cloud dependencies.

1. macOS (Apple Silicon Arm64 & Intel)

# 1-Command Universal Setup:
./install.sh

# Or build native AppKit/WebKit application:
./desktop/centl26/macos/build.sh
open build/centl26/macos/CentL26.app

2. Linux (Debian, Ubuntu, Fedora, RHEL, Arch)

# 1-Command Universal Setup (Installs binary, desktop launcher, and hicolor icons):
./install.sh

# Or build standalone package:
./desktop/centl26/linux/build.sh
./build/centl26/linux/CentL26

3. Windows 11 (PowerShell & Terminal)

# 1-Command PowerShell Setup (Installs binary, Start Menu & Desktop shortcuts):
.\install.ps1

# Or 1-click batch launcher:
.\desktop\centl26\windows\CentL26.bat

4. Cross-Platform Local Web Browser

cargo run --release --bin centl26
# Open http://127.0.0.1:2626

---

Key Highlights in CentL26.10

1. Continuous Jupyter-Grade Notebooks & Export

• Seamless Interactive Multi-Step Calculations: Execute multi-statement computation cells with live reactive output, inline cell editing, cell deletion, re-running, and persistent state history.
• Direct Jupyter Notebook (.ipynb) Export: Export computational notebooks directly to standard Jupyter Notebook format with full input/output cell mapping for immediate sharing with research teams.
• Multi-Notebook Tabs & Workspaces: Organize independent computations across named tabs with safe keyboard shortcuts (⌥ W / ⌘ ⇧ W).

2. Smooth In-App Paper & Documentation Scrolling

• Integrated FCF Knowledge Center: Offline indexed document browser with responsive Markdown rendering and smooth scrolling for all FCF operator manuals, mathematical architecture specifications, and theoretical research preprints (Bryan Recursive Entanglement Calculus v1.0, Erdős–Straus Modular Decomposition, Collatz Modular Trajectory Dynamics, and Ramanujan Tau asymptotics).

3. Complete Windows 11 Build & 1-Command Universal Installation

• Automated Windows 11 Packaging: Native desktop/centl26/windows/build.ps1 produces standalone CentL26-Windows-x64.zip / CentL26-Windows-x86_64.zip distributions with 1-click batch launcher (CentL26.bat), native application icon, and SHA-256 integrity verification.
• 1-Command Universal Setup: Fast cross-platform setup on macOS (./install.sh), Linux (./install.sh), and Windows 11 (.\install.ps1).

4. Robust Algebraic Engine & Canonical Polynomial Solver

• Arbitrary-Precision Rational Root Theorem Solver: Exact root extraction for linear, quadratic, cubic, quartic, and higher-degree polynomials with synthetic division (synthetic_divide_root) and exact radical isolation.
• Direct Algebraic Equation Auto-Solving: Free variable analysis automatically differentiates variable assignment (x = 5) from equations (2x + 3 = 7 $\rightarrow x = 2$, x^2 - 5x + 6 = 0 $\rightarrow x = 2, x = 3$).
• Constant Mathematical Equality Verification: Immediate truth-value validation (2 + 3 = 5 $\rightarrow true$, 2 + 3 = 6 $\rightarrow false$, 2^10 = 1024 $\rightarrow true$).
• Polynomial Expansion & Factorization:
  • factor(x^2 - 9) $\rightarrow (x + 3)(x - 3)$
  • factor(x^2 - 5x + 6) $\rightarrow (x - 2)(x - 3)$
  • factor(x^3 - 6x^2 + 11x - 6) $\rightarrow (x - 1)(x - 2)(x - 3)$
  • expand((x - 1)*(x + 1)) $\rightarrow x^2 - 1$
• Smart Implicit Multiplication: Natural parsing of mathematical notation (2x, 5x^2, 3(x+1), (x-1)(x+1), 4pi, 2sin(x)) while preserving English natural language sentences.

5. Advanced Calculus, Discrete Mathematics & Series

• Higher-Order Differentiation: diff(f, x, n) (e.g. diff(x^4, x, 3) $\rightarrow 24x$).
• Definite & Indefinite Integration: integrate(3x^2 + 2x, x, 0, 3) $\rightarrow 36$.
• Symbolic Limits & L'Hôpital's Rule: limit((x^2 - 1)/(x - 1), x, 1) $\rightarrow 2$.
• Taylor Series Expansion: taylor(exp(x), x, 0, 3) $\rightarrow 1 + x + \frac{1}{2}x^2 + \frac{1}{6}x^3$.
• Discrete Summations & Products: sum(k^2, k, 1, 5) $\rightarrow 55$, product(k, k, 1, 5) $\rightarrow 120$.

6. Interactive STEM Animated Visualizer & Theorem Studio

• Engage directly with dynamic mathematical theorems, Fourier harmonics, ODE wave animations, Lorenz chaotic attractors, particle physics simulations, and Bravais crystal lattice geometry.

7. STEM Academic Search Engine Omnibar

• Omni-routing academic queries directly to Google Scholar, arXiv, PubMed, Wolfram MathWorld, OEIS, NIST Chemistry WebBook, and NASA ADS with intelligent domain detection.

8. Resilient Multi-Model Gemini AI Co-Pilot

• Multi-model automatic fallback (2.5-flash $\rightarrow$ 2.0-flash $\rightarrow$ 1.5-flash $\rightarrow$ 1.5-pro), persistent cross-platform API key management, and atomic JSON decomposition with exact offline CAS verification.

9. Exhaustive 100-Test Automated Non-Regression Suite

• Dedicated offline test verification across arithmetic, linear/quadratic/polynomial algebra, calculus, stoichiometry, and modern physics.

---

Quick Start CLI Examples

# Exact rational mathematics
./target/release/centl26 "0.1 + 0.2"                    # → 3/10
./target/release/centl26 "catalan(6)"                   # → 132
./target/release/centl26 "totient(36)"                   # → 12
./target/release/centl26 "diff(x^3 * sin(x), x)"        # → 3*x^2*sin(x) + x^3*cos(x)
./target/release/centl26 "plot sin(x) from -3.14 to 3.14"

# Direct STEM problem solving
./target/release/centl26 "What is the pH of a 0.05 M HCl solution?"
./target/release/centl26 "Dilute 50 mL of 2 M HCl to 200 mL, what is the final concentration?"
./target/release/centl26 "Calculate kinetic energy of a 1500 kg car moving at 25 m/s"
./target/release/centl26 "Hypotenuse of right triangle with legs 3 and 4"
./target/release/centl26 "Dot product of (1, 2, 3) and (4, 5, 6)"

---

Architecture

Component	Path	Description
SCi Plain-English Solver	src-web/engine/sci.rs	Offline natural language parser, unit solvers, and hybrid Gemini bridge.
In-App Programmability	src-web/engine/extensions.rs	In-app user function builder, AST compiler, parameter validator, and macro engine.
2D Function Plotter	src-web/engine/plot.rs	2D discrete coordinate sampler and ASCII/Unicode grid renderer.
Mathematics & Calculus	src-web/engine/	Exact rational arithmetic, symbolic differentiation, integration, linear algebra, and statistics.
Physics Kernel	src-web/physics/	Mechanics, quantum physics, thermodynamics, radiation, relativity, and physical constants.
Chemistry Engine	src-web/server/	Element catalog, reaction balancing via rational nullspace, and stoichiometric calculations.
Design Contract	design/centl26/	Automated visual and layout regression assertions (57 invariants).

---

Research

The CENTL research program includes active exploration of Erdős–Straus Diophantine Decomposition ($4/p = 1/x + 1/y + 1/z$):

• cbis.kernel: Production letter hunt engine.
• cbx.kernel: Finite search grade analysis and inverse-cover x-ray instrument.
• cbap.kernel: High-performance letter targeting engine.

./target/release/centl26 "solve 2521"

Erdős–Straus Hunt Classification Hierarchy

Hardness measures tell us where to look. Certificates tell us what is true.

interesting solved → unusually hard solved → unresolved → certified impossible

  LETTER          REMNANT           GOD'S LETTER        DIS TICKET
  (solved         (solved,          (incomplete         (complete
   hard prime)     hardness          residual —          finite region
                   proxy only)       not a disproof)     empty)
                                                              │
                                                    Victory certificate
                                                    (six Mordell classes)

Densities are staged, not complementary: elementary CC cover 7/8, intermediate modular 3/32, Mordell hard core 1/32.

Classification	Artifact	Condition
class_theorem	4 permanent identities	even, $4p+3$, $3p+2$, $8p+5$. Not counted per prime.
class_covered_instance	dual ledger (proof)	Prime cleared by applying a class theorem. Not a new class proof.
instance_proof	dual ledger (proof)	Constructive witness. Does not prove ES.
certified_counterexample	tickets/DIS-<p>.json	Complete finite region empty. One ticket disproves ES.
incomplete_residual / gods_letter	gods-letter/GL-<p>.json	Unresolved menu miss. Not a disproof.
letter	letters/L-<p>.json	Notable solved hard-prime decomposition
remnant	remnants/REM-<p>.json	Solved, with independent descent-hardness proxy
escape	escapes/ESC-<p>.json	Solved outside Letter admission
victory_certificate	none yet	Uniform covering of ${1,121,169,289,361,529}\pmod{840}$

The observatory is agnostic. Approximates never certify. Dual descent is a bounded hardness proxy, not a proof engine. Game status is OPEN until a Mordell covering or one DIS ticket. The census is not a verification record (Salez 2014: $10^{17}$).

Specification: research/erdos-straus/DUAL-LEDGER.md · research/erdos-straus/GODS-LETTER.md

God's Letter commands:

# Full certified domain scan (2 ≤ p ≤ 100,000) and persist artifact
centl es gods-letter --scan

# Print elimination tree
centl es gods-letter --explain

# Machine-readable evaluation
centl es gods-letter --json

Specification: research/erdos-straus/GODS-LETTER.md
Vault: gods-letter/

Documentation & Manuals

• CentL26 Architecture Guide
• CentL26.13-AG Release Notes
• CentL26.12-GL Release Notes
• CentL26.11-ES Release Notes
• CentL26.10.2 Release Notes
• CentL26.10.1 Orchid Release Notes
• Universal Multi-Platform Installation
• Exact Numerical & Algebraic Contract
• Exact Polynomial & Matrix Algebra Guide
• Symbolic Calculus & Series Manual
• CentL-SCi Natural Language Problem Solver
• Stoichiometry & Reaction Balancing Manual
• CAS Syntax & Functions Reference
• CentL26 Approved Design Contract
• Mathematician Onboarding Guide
• Physicist Onboarding Guide
• Native macOS Packaging

---

License

Software is licensed under Apache-2.0.
Documentation is licensed under CC BY 4.0 where identified.
Branding is reserved: see LICENSING.md.

Developed under the Free Computation Foundation.
Free for science.