Sustainable Catalyst Platform

Workbench

A computational workspace for mathematics, graphing, scientific modeling, engineering analysis, simulation, code, and reproducible technical work.

Start with an equation, dataset, model, technical problem, or experiment. Workbench connects the computation, visualization, assumptions, evidence, and resulting technical record.

Open Workbench → See what it can do →

Workbench v5.2.0 Symbolic CAS Interactive Graph Mathematics 30 Technical Studios

Start with the work

One workspace, several ways in

You do not need to choose a technical stack first. Start with the problem you are trying to solve and move into deeper tools as the work develops.

Mathematics

Solve & graph

Work with symbolic expressions, equations, calculus, parameters, functions, and interactive graphs.

Analysis

Explore data

Inspect datasets, statistics, signals, uncertainty, patterns, distributions, and scientific visualizations.

Modeling

Simulate systems

Build scenarios, dynamic models, Monte Carlo studies, controls, state-space systems, and digital twins.

Engineering

Build & validate

Connect code, devices, electronics, instrumentation, experiments, validation, and technical documentation.

Live workspace

Open the Workbench

Use the unified interface to move between mathematics, graphing, engineering tools, modeling, scientific analysis, programming, experiments, and project records.

Activating Workbench studios…

Computational Blackboard

restricted symbolic translation · CAS 5.1

Write mathematics naturally or symbolically

SYMBOLIC TRANSLATION

∫ x² dx

EXACT9

DECIMAL9.00000000000000

OBJECTmathematics · waiting

Automatic translation ready.

Graph link ready.

Sound & Mathematics

Hear the structure of a number

Acoustics engine

Mode NoteFrequency (Hz)Second frequency (Hz) Waveform

NOTEA4

FREQUENCY440 Hz

WAVELENGTH0.7795 m

Mathematics & Form

Turn relationships into geometry

parametric form engine

Form family abphase

Explore symmetry, resonance, phase, ratio, and periodic form as mathematics rather than decoration.

x = sin(3t + φ) · y = sin(2t)

Physical Prototyping

Move from mathematics to hardware scaffolds

export-only · human controlled

ProjectSignal frequency (Hz)Sample rate (Hz)Clock (MHz)

MATHEMATICS→SIGNAL→LOGIC→DEVICE

arduino.inoArduino

// Generate an allowlisted prototype scaffold.

Public Workbench does not flash or program hardware automatically.

EXAMPLES

EXPRESSION STACKUp to 8 linked functions

domain≤ x ≤

Piecewise functions can be built by stacking expressions with different domain restrictions.

Analysis

Roots Extrema Intersections Asymptotes Discontinuities

Tangent at x Normal line

Inequality / region

Expression

Parameters

a1.00

b1.00

c0.00

Viewport

x min x max y min y max

Ready.

ADVANCED CARTESIAN · MULTI-SERIESx −10…10 · y −10…10

GRAPH OBJECT—

EXAMPLES

CONSTRUCTION0 points · 0 objects

CONSTRAINTSbounded solver

Constraint Point IDs Value

TRANSFORMaffine matrix

DYNAMIC PLANEx −10…10 · y −7…7

MOVE · drag points

Ready.

GEOMETRY OBJECT—

Expression

MinMax

Method

Expression

LowerUpper

Method

Expression

xOrder

x values y values Method

dy/dt

y(0)t max

Method

Matrix A Vector b Operation

Objective Variables Initial Bounds Goal

SCIENTIFIC COMPUTING OUTPUTready

METHOD—

RESULT—

DIAGNOSTIC—

Select a method and run a bounded numerical calculation.

Sample rate (Hz)

Tone (Hz) Harmonic

Samples CSV (optional)

Window Detrend

Family Response

Order Sample rate

Cutoff Hz Ripple dB (Chebyshev)

Numerator coefficients Denominator coefficients

Min Hz Max Hz

Step duration (s)

Open-loop numerator Open-loop denominator

Gain min Gain max

A matrix (rows separated by new lines)

B C

D Duration

Plant numerator Plant denominator

Kp Ki Kd

Setpoint Duration

Signal Kernel

Mode Normalize

SIGNALS / SYSTEMS / CONTROL OUTPUTREADY

METHOD—

PRIMARY RESULT—

DIAGNOSTIC—

{
  "status": "Ready for a bounded signals/control computation"
}

Universal mathematics foundation

This first gap-closing build makes one mathematical object usable across exact algebra, numeric evaluation, solving, and calculus. Interactive linked graphing is available in the v5.2 Graph Mathematics studio.

ExactPreserve fractions, radicals, constants, and symbolic forms.

ComputeSimplify, expand, factor, solve, differentiate, integrate, limit, and series.

ReusableEvery result carries LaTeX, free symbols, precision, operation provenance, and a content hash.

One canonical projectConnect requirements, evidence, data, calculations, experiments, workflows, reviews, evaluations, and release records.

All platform surfacesCoordinate Workbench, Lab, Site Intelligence, Decision Studio, Research Librarian, Knowledge Library, WordPress, and offline nodes.

Human-controlled releaseRequire integrity, traceability, security, evaluation, professional review where applicable, backups, rollback, and named approval.

Project titleDomains (JSON)Surfaces (JSON)Requirements (JSON)

Ready to prepare an integrated platform record.

{}

Connected Overview

Connected project

Create one canonical project contract across every Workbench and Sustainable Catalyst surface.

Capability registry

Audit studios, runtimes, domains, services, and required capabilities before a workflow begins.

Integration health

Check required and optional platform connections while preserving offline fallback.

Release manifest

Assemble traceability, evaluation, review, and human-approval evidence without publishing automatically.

Connected recordBrowser-local fallback active

{}

Project HubAudit the unified project manifest, studio state, evidence, artifacts, dependencies, and readiness.

Platform handoffsPackage selected records for Site Intelligence, Decision Studio, Research Librarian, or another Workbench project.

Recovery safeguardsExport versioned packages and require explicit confirmation before clearing saved workspace data.

Project manifest (JSON) Dependencies (JSON)

{}

Review boundary: project health, migration, handoff, package, and reset records are planning and evidence-management aids. They do not establish technical correctness, regulatory compliance, safety, certification, or professional approval. Export a backup before destructive actions and revalidate imported records in every destination system.

Local firstProjects save in this browser even when no account or backend is available.

Private persistenceSigned-in editors can store private project records and revisions in WordPress.

AutosaveDirty project records save after an idle delay and before page exit.

Revision safetyManual and server saves create recoverable, content-hashed snapshots.

No active project loaded.

Search projects Status Pinned only

Project ID Title Status Storage mode Tags, comma separated Pin this project Description Project metadata and shared studio state (JSON)

Not modified.

Revision reason

Browser records0

Local revisions0

Estimated usage0 B

Server accessSign in to enable

This session is using browser-local storage. Sign in with editing access to enable private WordPress synchronization.

Conflict strategy

{}

Persistent workspace ready.

Storage boundary: browser projects remain tied to the current browser profile unless exported or synchronized. WordPress projects are private application records, not certified records of engineering approval. Export backups before account changes, cleanup, migration, or reset.

Organization and teamsPrivate organizational boundaries, team membership, invitations, and role-based capabilities.

Shared project spacesAuthenticated team projects with revisions, ownership, activity records, and explicit access checks.

Local-first fallbackAnonymous and offline users retain browser-local projects. No paid database is required.

Organization nameTeam nameProject titleMembers (JSON)

Ready for authenticated collaboration planning.

{}

Browser-local mode.Sign in with an authorized WordPress account to create private hosted organizations, teams, invitations, and team projects.

Collaboration boundary: invitations, access changes, conflict resolution, deletion, publication, and professional sign-off require authenticated human authorization. Workbench does not automatically escalate roles, accept invitations, delete projects, or expose private records publicly.

Choose a workflowStart from a scientific, engineering, measurement, analytics, sustainability, or connected Lab-to-decision template.

Build traceability earlyCreate requirements, milestones, evidence placeholders, validation gates, deliverables, and recommended studio routes before execution.

Prepare for teamsAdd role bindings and private WordPress storage without making hosted services mandatory.

Keep humans in controlTemplates never authorize experiments, device control, publication, certification, or professional sign-off.

Project titleTemplate IDDomainObjectiveConstraints, one per lineTeam role bindings JSON

Ready to create a guided project plan.

{}

Local-first mode.Sign in with an authorized WordPress account to preserve private templates and guided projects on this site.

Guidance boundary: templates organize work but do not execute experiments, operate devices, approve findings, publish records, certify compliance, diagnose people, or replace qualified scientific, engineering, medical, legal, or professional review.

Register sourcesPreserve connector type, host allowlists, licensing, citations, refresh cadence, and stable source hashes.

Build reproducible pipelinesPlan transformations, dependencies, schemas, validation, freshness, and outputs without silently changing data.

Work offlineCreate content-addressed dataset snapshots and portable packages for local analysis and later synchronization.

Keep humans in controlNetwork retrieval, credentials, overwrites, publication, cloud upload, and deletion require explicit external action.

Dataset titleDataset IDSource IDs JSONColumns JSONPipeline steps JSON

Ready to prepare a reproducible data record.

{}

Local-first mode.Sign in with an authorized WordPress account to preserve private source and dataset records on this site.

Data boundary: connector records and pipeline plans do not automatically fetch network data, store credentials, overwrite datasets, upload to cloud services, publish records, delete source material, or certify data quality.

Define benchmarksPreserve metrics, directions, datasets, protocols, baselines, units, and review boundaries.

Compare candidatesSummarize repeated trials, uncertainty, practical differences, and regressions without overstating causality.

Verify reproducibilityCheck seeds, runtime, environment, dataset, protocol, and repeated-run consistency.

Gate human decisionsLeaderboards, baseline replacement, release approval, and certification remain explicitly human controlled.

Benchmark titleBenchmark IDMetric nameMetric directionCandidates JSONParameter grid JSONSeeds JSON

Ready to prepare an auditable evaluation record.

{}

Local-first mode.Sign in with an authorized WordPress account to preserve private benchmark and evaluation-run records on this site.

Evaluation boundary: plans and reports do not automatically execute experiments, publish leaderboards, replace baselines, approve releases, establish causation, or certify scientific, engineering, safety, regulatory, or professional conclusions.

Define an extensionCreate a versioned manifest with explicit capabilities, hooks, compatibility bounds, provenance, licensing, and package integrity.

Restrict privilegesUse least-privilege capability scopes, hostname allowlists, project boundaries, and explicit approval for high-risk operations.

Validate lifecycle changesPlan installation, activation, updates, deactivation, and uninstall with compatibility, signature, backup, and receipt checks.

Package reproduciblyPreserve file hashes, tests, documentation, compatibility reports, security audits, and human review records.

Extension IDNamePublisherVersionCapabilities JSONHooks JSON

Ready to prepare a capability-scoped extension record.

{}

Local-first mode.Sign in with an authorized WordPress account to preserve private extension and release records on this site.

Extension boundary: manifests, hooks, packages, and lifecycle records never authorize arbitrary code execution, remote shells, automatic installation, automatic activation, privilege escalation, publication, device execution, or safety-control bypasses.

Article-aware projectsTurn a Library article into a persistent Workbench project with source, formula, citation, and topic context.

Formula-aware embedsRegister article equations and produce reviewable compact-calculator shortcode plans.

Grounded routingSend an article question to a relevant Workbench studio through a site-scoped Research Librarian packet.

Human-reviewed returnSave generated reports as private or draft WordPress records, never automatic public posts.

No article record loaded.

Article ID WordPress ID Article title Article URL Topics, comma separated Excerpt Article record JSON

Formula records JSON

Generated shortcodes are placement recommendations. Review calculator maturity, article context, and responsible-use boundaries before publishing.

Question grounded in this article Requested action

Draft title Project ID Visibility Evidence IDs, one per line Artifact IDs, one per line Draft content (Markdown)

{}

Publication boundary: article links, formula matches, calculator placements, Research Librarian routes, citations, and generated drafts require human review. Workbench does not automatically publish or certify content.

Build a cross-application handoff

Source application Target application Handoff type Source project ID Target project ID Handoff title Objective Payload JSON

Handoff recordReady.

{}

Build a technical review record

Review calculations, code, models, experiments, hardware evidence, requirements, and documents without treating internal approval as professional certification.

Project ID Review ID Review title Revision Review state Owner ID Reviewers JSON Review items JSON Requirement IDs, one per line

Review recordReady.

{}

Local runner connection

Runner URL

Pair once through the v2.0.0 Local Go Runner panel. v2.1.0 reuses that origin-bound browser token.

Structured task plan

Task I consent to this allowlisted local device task.

Device discovery has not run.

Prototype and research support only. Confirm electrical limits, pin assignments, device permissions, calibration, model behavior, latency, memory use, environmental conditions, and safety requirements on the actual hardware.

Orchestration overview

Build an auditable local-device workflow. No arbitrary shell execution is exposed.

1. InventoryRecord device identity, transport, firmware, state, and capabilities.

2. ConsentAllowlist devices and operations with expiration and sensitive-action confirmation.

3. RunPlan ordered tasks, rollback steps, stop conditions, and simulation fallbacks.

Device orchestration recordReady.

{}

Project name HDL Board profile Clock frequency (MHz)

Top-level HDL Pin and timing constraints Implementation report

Generated HDL and constraints will appear here.

No implementation report has been analyzed.

Engineering support only. Verify component ratings, electrical clearances, grounding, thermal behavior, constraints, timing, fabrication rules, standards, and safety on the actual target hardware with qualified review.

Drive model Wheel diameter (mm) Track width / wheelbase (mm) Left wheel speed (RPM) Right wheel speed (RPM) Payload mass (kg)

Enter project values and run the analysis.

Prototype and analytical support only. Verify loads, voltages, current limits, torque, speed, stopping behavior, fault handling, interlocks, mechanical clearances, control stability, and safe states on the actual system with qualified engineering review.

Instrumentation

Range, resolution, bandwidth, accuracy, interface, and isolation review.

[sc_workbench_instrumentation_studio project="default"]

Data Acquisition

Sampling, Nyquist, throughput, buffering, storage, and timing planning.

[sc_workbench_data_acquisition project="default"]

Signal Analysis

Time-domain statistics, drift, filtering, noise estimates, and previews.

[sc_workbench_signal_analysis project="default"]

Frequency Analysis

Windowed spectrum, dominant frequencies, frequency resolution, and aliasing checks.

[sc_workbench_frequency_analysis project="default"]

Calibration and Uncertainty

Linear calibration, residuals, uncertainty budgets, and expanded uncertainty.

[sc_workbench_calibration_uncertainty project="default"]

Measurement Validation

Timestamp integrity, sample-rate accuracy, jitter, completeness, and channel statistics.

[sc_workbench_measurement_validation project="default"]

Dynamic Simulation

First-order, logistic, and damped-system simulations with Euler or RK4 integration.

[sc_workbench_simulation_studio project="default"]

Digital Twin

Compare measured streams to model behavior and calibrate a transparent first-order twin.

[sc_workbench_digital_twin project="default"]

Systems Modeling

Simulate coupled linear state systems with explicit matrices, states, and forcing.

[sc_workbench_systems_modeling project="default"]

Scenario Sweep

Run parameter sweeps and identify sensitivity, monotonicity, and outcome ranges.

[sc_workbench_scenario_sweep project="default"]

Monte Carlo

Propagate parameter uncertainty through a transparent linear response model.

[sc_workbench_monte_carlo project="default"]

Model Validation

Calculate residual metrics, acceptance checks, and linear correction records.

[sc_workbench_model_validation project="default"]

Instrument or sensor name Instrument type Engineering units Range minimum Range maximum Accuracy (% full scale) ADC resolution (bits) Instrument bandwidth (Hz) Expected signal minimum Expected signal maximum Input / output interface Isolation required

Enter the measurement or acquisition parameters, then run the analysis.

Research and prototyping support only. Verify instrument ratings, isolation, grounding, probes, wiring, sampling assumptions, calibration traceability, uncertainty budgets, environmental limits, and all safety-critical measurements against the actual equipment and applicable standards.

Dynamic Simulation

First-order, logistic, and damped-system simulations with Euler or RK4 integration.

[sc_workbench_simulation_studio project="default"]

Digital Twin

Compare measured streams to model behavior and calibrate a transparent first-order twin.

[sc_workbench_digital_twin project="default"]

Systems Modeling

Simulate coupled linear state systems with explicit matrices, states, and forcing.

[sc_workbench_systems_modeling project="default"]

Scenario Sweep

Run parameter sweeps and identify sensitivity, monotonicity, and outcome ranges.

[sc_workbench_scenario_sweep project="default"]

Monte Carlo

Propagate parameter uncertainty through a transparent linear response model.

[sc_workbench_monte_carlo project="default"]

Model Validation

Calculate residual metrics, acceptance checks, and linear correction records.

[sc_workbench_model_validation project="default"]

Scientific Visualization and Engineering Dashboard Studio

Turn simulation, instrumentation, runtime, and validation records into auditable scientific figures, dashboards, uncertainty overlays, system-state views, and accessible exports.

[sc_workbench_scientific_visualization project="default"]

Workbench v2.8.0 workflow layer

Automate and reproduce this project

Turn measurements, simulations, and visualizations into structured protocols, dependency-aware workflows, checkpoints, version manifests, deviation records, and reproducible experiment bundles.

[sc_workbench_experiment_automation project="default"]

Dynamic model Numerical solver Initial state x(0) Input / forcing u Gain or growth rate Time constant / damping Capacity / natural frequency Time step Δt Duration Units

Enter model parameters, then run the analysis.

Research and prototyping support only. Treat models as explicit approximations. Verify equations, units, parameter ranges, numerical stability, calibration data, uncertainty assumptions, boundary conditions, and decision consequences against field evidence and qualified review.

Multi-Language Engineering Runtime Studio

Generate equivalent engineering calculations, inspect local runtimes, compare numerical behavior, and validate reproducibility across languages.

[sc_workbench_multilanguage_runtime project="default"]

Scientific Visualization and Engineering Dashboard Studio

Turn simulation, instrumentation, runtime, and validation records into auditable scientific figures, dashboards, uncertainty overlays, system-state views, and accessible exports.

[sc_workbench_scientific_visualization project="default"]

Workbench v2.8.0 workflow layer

Automate and reproduce this project

Turn measurements, simulations, and visualizations into structured protocols, dependency-aware workflows, checkpoints, version manifests, deviation records, and reproducible experiment bundles.

[sc_workbench_experiment_automation project="default"]

Auditable predictive workflow

Workbench separates data profiling, split design, feature decisions, model evaluation, responsible-use audits, documentation, and human review.

1. FrameDefine task, target, intended use, exclusions, and review requirements.

2. ValidateUse held-out data, baselines, cross-validation, uncertainty, leakage, drift, and subgroup checks.

3. DocumentExport content-hashed model cards, experiment records, and cross-language fixtures.

Computational intelligence recordReady.

{}

Shared domain workflow

Calculate

Carry equations, inputs, units, assumptions, evidence, and equivalent implementations into a Lab domain.

Experiment

Translate research questions into protocols, controls, instruments, replicates, safety boundaries, and reproducibility records.

Validate

Apply domain-specific checks without claiming automatic certification, clinical diagnosis, or licensed approval.

Publish

Synchronize notebook entries and draft reports while retaining provenance, review state, and immutable hashes.

Workbench prepares and validates auditable records. It does not independently authorize physical experiments, diagnose patients, or replace licensed scientific and engineering review.

Choose a domain tool to build an auditable integration record.

{}

Offline Workbench architecture

Installable packages

Platform-specific launchers for macOS, Linux, and Raspberry Pi OS.

Loopback service

FastAPI and the Workbench backend bind only to 127.0.0.1 by default.

Persistent local storage

Projects, backups, revisions, and evidence remain usable without network access.

Portable synchronization

Explicit import/export bundles preserve hashes, conflicts, and rollback requirements.

Boundary: This interface prepares plans and records. It does not run arbitrary shell commands, expose a remote shell, or silently upload local projects.

Offline Workbench ready.

Select a tool to create a local-first installation, runtime, synchronization, or recovery record.

{}

Public-release evaluation system

Inclusive interface

Keyboard, focus, labels, landmarks, screen-reader smoke tests, motion, contrast, and mobile overflow.

Production budgets

Transfer, JavaScript, CSS, interaction, layout stability, API latency, and memory thresholds.

Operational resilience

Migration stress, corrupt data, storage exhaustion, interrupted updates, backend outages, and rollback.

Stable public contracts

Versioned schemas, hooks, routes, deprecations, compatibility floors, onboarding, and human release gates.

Boundary: A ready gate records evidence and human approval. It does not certify regulatory compliance or publish automatically.

Evaluation record

No evaluation has been generated.

{}

Runner URL One-time pairing code Primary language Execution mode Source filename Maximum duration (seconds) Source code

Enter the project or validation inputs, then run the analysis.

Engineering and research support only. Local execution requires explicit pairing and consent. Review source code, numerical methods, dependencies, compiler flags, runtime versions, units, tolerances, output parsing, and platform-specific behavior before relying on results.

Scientific Visualization and Engineering Dashboard Studio

Turn simulation, instrumentation, runtime, and validation records into auditable scientific figures, dashboards, uncertainty overlays, system-state views, and accessible exports.

[sc_workbench_scientific_visualization project="default"]

Documentation and Product Dossier StudioConvert project records into traceable documentation, evidence registers, revision histories, and release-readiness dossiers.

Document title Project revision Owner or reviewer Sections (JSON) Assumptions, one per line Limitations, one per line Risks, one per line

{}

Documentation, readiness, compliance, manufacturing, certification, and verification records are planning and evidence-management aids. They do not establish regulatory approval, product safety, conformity, fitness for use, or professional sign-off. Validate every record against applicable standards, controlled source files, actual hardware and software revisions, qualified review, and organizational quality procedures.

Figure title Visualization type X-axis label Y-axis label Units Histogram bins / spectrum limit CSV data

Enter data and render a visualization.

A structured analysis record will appear here.

Scientific and engineering support only. Verify source data, units, sampling, transformations, axis scales, thresholds, uncertainty assumptions, visual encodings, accessible descriptions, and exported figures before using a visualization as evidence or in safety-critical work.

Workbench v2.8.0 workflow layer

Automate and reproduce this project

Turn measurements, simulations, and visualizations into structured protocols, dependency-aware workflows, checkpoints, version manifests, deviation records, and reproducible experiment bundles.

[sc_workbench_experiment_automation project="default"]

Experiment title Objective Pipeline tasks (JSON) Checkpoint rules (JSON) Observed checkpoint values (JSON) Runner URL Pairing code

{}

Automation support does not replace laboratory supervision, equipment interlocks, operating procedures, human review, or applicable safety and quality systems. Validate protocols, dependencies, schedules, code, instruments, checkpoints, data lineage, and failure handling before unattended or consequential use.

Documentation and Product Dossier StudioConvert project records into traceable documentation, evidence registers, revision histories, and release-readiness dossiers.

Document title Project revision Owner or reviewer Sections (JSON) Assumptions, one per line Limitations, one per line Risks, one per line

{}

Document title Project revision Owner or reviewer Sections (JSON) Assumptions, one per line Limitations, one per line Risks, one per line

{}

DiscoverInventory Workbench v1.x, v2.x, v3.x, unknown, and canonical browser-storage records.

PreviewBuild a migration map and canonical v3 project manifest without modifying browser storage.

ProtectCreate content-hashed backups and rollback points before every destructive operation.

RecoverValidate imported packages, resolve conflicts, restore safely, and audit the final workspace.

Source version Target project ID Preserve unknown Workbench-like keys in a legacy studio

Estimated browser quota in bytes

Backup label Previous backup hash

Backup file Conflict strategy: skip, overwrite, or rename Create rollback backup before restore

Cleanup scope: selected, duplicates, orphans, stale, or all-candidates Selected keys, one per line I downloaded a current backup Type CLEAN WORKSPACE

Rollback backup JSON I downloaded a backup of the current state Type ROLLBACK WORKBENCH

No storage operation has run.

{}

Recovery boundary: all migrations, restores, rollbacks, cleanup, and reset operations occur in the current browser profile. Download and verify a backup before changing storage. Imported records remain subject to studio-level validation, source review, and professional boundaries.

Interface diagnostics

Primary shortcodeRegistered by v5.7.0

Browser routerInitializing

Projectdefault

Available studios37 of 37

Universal Mathematics

Equation, graph, and analysis are now one computational object

Workbench combines a governed symbolic mathematics engine with interactive graph mathematics. Expressions remain connected to their graphical representation, parameters, solutions, derivatives, integrals, and analytical record.

Exact arithmetic Symbolic algebra Equation systems Calculus 2D graphing 3D surfaces

EXAMPLES

EXPRESSION STACKUp to 8 linked functions

domain≤ x ≤

Piecewise functions can be built by stacking expressions with different domain restrictions.

Analysis

Roots Extrema Intersections Asymptotes Discontinuities

Tangent at x Normal line

Inequality / region

Expression

Parameters

a1.00

b1.00

c0.00

Viewport

x min x max y min y max

Ready.

ADVANCED CARTESIAN · MULTI-SERIESx −10…10 · y −10…10

GRAPH OBJECT—

Interactive Graph Mathematics

Explore mathematical behavior instead of only calculating an answer

Symbolic

CAS mathematics

Simplify, expand, factor, substitute, evaluate, solve equations and systems, calculate limits and series, and perform symbolic differentiation and integration.

Graphical

Multiple graph families

Work with Cartesian, parametric, polar, implicit and contour mathematics alongside vector fields and three-dimensional surface models.

Analytical

Graph-linked analysis

Inspect roots, extrema, intersections, derivative overlays, integral regions, parameter changes, and exact mathematical results without separating analysis from visualization.

Beyond the calculator

A technical environment that continues beyond mathematics

Workbench connects mathematical analysis to the other computational and engineering activities needed to investigate a real system.

Simulation

Models & digital twins

Dynamic systems, state-space models, scenario sweeps, Monte Carlo analysis, calibration, residuals, and model-versus-observation validation.

Scientific computing

Data & visualization

Statistics, time series, distributions, spectra, uncertainty, spatial views, engineering dashboards, and scientific plots.

Programming

Multi-language projects

Structured technical work across Python, JavaScript, R, SQL, Go, C, C++, Rust, Julia, Haskell, and additional engineering runtimes.

Physical systems

Hardware & controls

Embedded systems, Raspberry Pi, TinyML, FPGA, electronics, robotics, controls, telemetry, calibration, and instrumentation.

Experimentation

Repeatable workflows

Protocols, dependencies, checkpoints, run comparison, version manifests, deviation tracking, and reproducibility review.

Technical record

Document & export

Preserve formulas, graph objects, assumptions, calculations, source values, validation evidence, project files, and review boundaries.

Connected workflow

From technical question to reproducible result

Workbench preserves the relationship between the original problem, its computation, exploration, model, evidence, and final record.

Define Equation, dataset, model, or requirement
Compute Exact or numerical analysis
Explore Graphs, parameters, and scenarios
Model System behavior or implementation
Validate Assumptions, limits, and evidence
Export Reproducible technical record

Computational architecture

More power without exposing unrestricted execution

Workbench separates public interaction, browser computation, server-side analysis, and approved local execution into explicit technical boundaries.

Interface WordPress studios, project surfaces, embeds, navigation, and reports.

Browser Interactive graphing, parameter exploration, visualization, and local processing.

Compute Python / FastAPI mathematics, scientific analysis, and simulation.

Local engineering Origin-bound access to approved runtimes, instruments, devices, and tools.

Responsible use

Powerful technical work remains inspectable

Workbench supports research, learning, modeling, prototyping, experimentation, technical analysis, and validation planning. Results remain dependent on inputs, assumptions, data quality, model limitations, operating conditions, and appropriate human review.

Do not enter confidential or regulated information into the public Workbench. Calculations, models, simulations, code, engineering records, graphs, experiments, and reports do not replace qualified professional review where such review is required.

Open Workbench → Research Lab → View GitHub → Back to top ↑

One workspace, several ways in

Solve & graph

Explore data

Simulate systems

Build & validate

Open the Workbench

Universal mathematics foundation

Algebra / CAS

Equation solver

Calculus

Canonical math object

Connected Overview

Connected project

Capability registry

Integration health

Release manifest

Project Contract

Connection Graph

Workflow

Shared Context

Integration Health

Traceability

Dossier

Release Manifest

Build a cross-application handoff

Create a shared evidence record

Site Intelligence handoff

Decision Studio handoff

Research Librarian handoff

Compatibility and evidence merge

Portable handoff bundles

Build a technical review record

Reviewer queue

Record-level comments

Requested changes and resolutions

Revision comparison

Technical sign-off

Review and approval dossier

Local runner connection

Structured task plan

Orchestration overview

Connected-device inventory

Local consent and allowlist

Calibration schedule

Instrument sessions

Experiment-run orchestration

Logs and failure recovery

Hardware-absent simulation

Instrumentation

Data Acquisition

Signal Analysis

Frequency Analysis

Calibration and Uncertainty

Measurement Validation

Dynamic Simulation

Digital Twin

Systems Modeling

Scenario Sweep

Monte Carlo

Model Validation

Dynamic Simulation

Digital Twin

Systems Modeling

Scenario Sweep

Monte Carlo

Model Validation

Auditable predictive workflow

Dataset profile and split plan

Predictive modeling scaffold

Model validation

Time-series forecasting

Leakage, drift, and subgroup performance

Model card and review boundary

Cross-language reproducibility

Shared domain workflow

Domain registry

Calculation adapter

Experiment bridge

Domain validation contract

Notebook synchronization