Find a concept
Search for electron. Every match is marked; the highest-ranked result opens in Details.
Search electron1. Quick start
Choose a starting method based on what you want to do. Each example below opens real atlas content and, where relevant, a complete saved application state.
Read one concept
Open Group with its canonical concept URL, then follow its recorded relations.
Open GroupFollow a guided Story
Start From sets to spaces, or jump directly to the Topological space step.
Open Story at step 5See the large-scale structure
Open Mathematics in Domains layout with Algebra selected. The aggregate arrows summarize the visible directed relations.
Open domain structureInspect a multi-input construction
Open the diamond where a group and total order jointly form a totally ordered group.
Open construction diamondReproduce a filtered view
Open only Algebra, with Group selected. The compact share tokens encode the complete filter and display state.
Open saved Algebra state2. Read the graph
The atlas is an editorial map of structural, mathematical, physical, chemical, historical, and evidential relationships. Position supports interpretation, but it is not a proof and horizontal distance is not a metric.
Concept node
One solid rounded node represents one concept. Its fill and lane use its primary domain.
Additional domains
Small colored markers show secondary memberships. The concept remains one node, not a duplicate.
Construction diamond
A diamond is an AND construction: every listed input and the compatibility condition are required.
Levels and lanes
In Layered layout, authored vertical levels generally move from less structure near the top toward specialization, added data or axioms, composition, approximation, physical realization, collective organization, or emergence below. Mathematics occupies the upper formal band. Physics and Chemistry share the lower scientific band while retaining their authored relative levels. Horizontal lanes group primary domains; their separation is organizational rather than quantitative.
Relations
An arrow has three parts: its direction, its relation type, and its specific annotation. Do not infer that every downward edge means “derived from,” or that experimental support is logical proof. Select an edge to read its exact meaning and sources.
Prerequisite context
When you select a subset of domains, the atlas can retain required prerequisite concepts from outside that subset. Those nodes are normally faded. They are context, not direct matches. Hide prerequisites removes this closure; domain and field suppression can restrict it more selectively.
Construction diamonds
When construction junctions are visible, incoming branches meet at a diamond and an outgoing branch reaches the result. When junctions are hidden, the atlas contracts the diamond into dashed direct branches. Labels beginning with jointly still mean every associated branch is required.
Complete relation key: 25 active meanings
Arrow direction and edge type are authored claims. The exact annotation on an edge states what changes in that particular relation.
Add data
Equip an existing carrier or structured object with additional chosen data, when such compatible data exists. Use a construction junction when several independently meaningful inputs must coexist on the same carrier or interact compatibly.
Impose axiom
Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.
Induced / forgotten
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
Canonical construction
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
Quotient construction
Identify elements by a stated equivalence relation and equip the quotient with the induced structure. The edge detail must state the representatives and equivalence relation.
Canonical embedding
Map one structure injectively into another by the standard structure-preserving inclusion or representation. This records a canonical copy, not necessarily literal set containment.
Combine compatible structures
Feed several structures into a construction junction and impose compatibility between them.
Representation / equivalence
Reinterpret an object, pass to an equivalent presentation, or relate canonically corresponding structures; the carrier may change.
Theorem implication
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
Mathematical formulation
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
Framework specialization
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
Quantization
A classical system or field theory is used to construct a quantum theory through a stated quantization procedure. Quantization need not be unique and is not guaranteed to preserve every classical structure.
Theory component
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
Describes / governs
A theory, law, or interaction describes the behavior of the target within a stated regime. The edge detail must state important limits or qualifications.
Physical constitution / realization
The source is a material constituent, structural component, or underlying quantum field whose excitation realizes the target physical system or particle. The edge label and detail must distinguish composition from field excitation; neither implies a simple classical sum of parts.
Classification
The target is a member or subtype of the broader source class.
Physical interaction / binding
The source field, particle, charge, current, or interaction couples to, acts on, binds, forms, or stabilizes the target in the stated regime. The edge label and detail must identify the exact coupling, interaction, or binding claim and its qualifications.
Limit / controlled approximation
The target is recovered from the source either in a stated mathematical or asymptotic limit, or through a quantitatively controlled approximation with identified small parameters or omitted terms. The edge label and detail must state which case applies and its regime of validity.
Effective theory / model
The target retains the degrees of freedom and interactions relevant below a stated scale or within a stated regime, while higher-energy or unresolved degrees of freedom from the source are integrated out, coarse-grained, or encoded in effective couplings.
Model / approximation method
The target is a model, idealization, restricted ansatz, approximation scheme, phenomenological fit, or historical representation used for the source system or theory. It need not have a universal small error parameter and is not thereby a controlled limit or effective theory. The edge label and detail must identify the precise status.
Emergent / collective behavior
The target is a collective, organizational, or scale-dependent phenomenon of the source constituents and interactions; it is not a mere list or classical sum of constituents.
State / property description
The target represents a state, property, observable, or state-dependent description associated with the source system or theory.
Transformation / process
A physical process transforms the source into, or produces, the target under the conditions stated in the edge detail.
Historically motivated
The source experiment, observation, anomaly, or problem materially motivated the development, revision, or acceptance of the target concept. Historical influence is not logical derivation; the edge detail states the documented role and avoids retrospective origin myths.
Experimentally tested / supported by
The source theory, law, entity, prediction, or structural claim is directly tested, supported, constrained, or established by the target experiment or observation. Experimental support is not final logical proof; the edge detail states exactly what was measured.
4. Search and scope
Search
- Press / or select the search box.
- Type a concept label, domain, field, or identifier. Suggestions are ranked as you type.
- Use the arrow keys to choose a result and press Enter, or select a suggestion directly.
- The atlas marks every match and opens the chosen concept. Search does not remove nonmatching concepts.
Try the real “electron” search →
Field and domain scope
The top navigation opens the entire atlas or a field route such as Mathematics, Physics, or Chemistry. Domain pages such as Algebra and Quantum mechanics are also interactive application routes with static, crawlable page content underneath.
The Directory is the complete static overview: field and domain summaries, all canonical concept links, the relation legend, and the all-in SVG.
5. Filters
Filters determine which concepts and relations are admitted. Display settings change how that admitted graph is presented. The URL records both groups independently.
Fields and domains
- Checkbox
- Adds or removes that field or domain from the direct selection.
- Linked name
- Isolates that field or domain. Selecting its linked name again while it is the sole selection chooses every other field or domain instead.
- all / none
- Selects every field and domain, or clears them all.
- Counts
- Field counts include all concepts belonging to the field. Domain counts include primary and secondary memberships.
Suppression states
The visibility button beside each domain cycles through three states. This is separate from whether its checkbox is selected.
Allowed
Ordinary direct matching and prerequisite context.
Excluded
A node whose primary domain is excluded is not admitted merely as prerequisite context. An enabled, non-excluded secondary membership may still select it directly.
Prohibited
A node with that primary domain is always hidden, including through secondary memberships and prerequisite closure.
Field suppression is two-state: allowed or excluded. Domain suppression cycles gray → yellow → red → gray.
Relation types
Relation checkboxes control both the edges drawn and the relation types allowed to participate in prerequisite closure. Selecting a relation-type name isolates that type; selecting the same isolated name again chooses every other active type.
Display controls
- Edge labels
- Shows or hides the authored annotations attached to relations.
- Edge interaction only when zoomed in
- Prevents overview-scale edges from capturing pointer input.
- Construction junctions
- Shows diamonds, or contracts them into dashed direct AND-branches.
- Hide prerequisites
- Disables transitive prerequisite context entirely.
- Show only primary domain matches
- Ignores secondary domain memberships when deciding direct matches.
- Hide isolates without filtered relations
- Removes nodes left with no incident relation under the current visibility and relation filters.
- Cross-field links: Contextual
- Shows cross-field relations for overview and the selected neighborhood, rather than all the time.
- Cross-field links: All / Hidden
- Shows every admitted cross-field relation, or none of them.
6. Layouts
Layered
Uses authored vertical levels and primary-domain lanes. It is the best layout for reading structural progression and cross-field placement.
Compact
Uses only currently visible nodes. Empty authored levels consume no rows, and deterministic ordering makes the same visible set reproduce the same arrangement.
Domains
Preserves the Layered concept positions as a dim substrate, then summarizes visible primary domains as centroid nodes connected by weighted directed aggregate relations.
Fields
Uses the same semantic-overview method at field scale. It is useful for seeing the overall flow among Mathematics, Physics, and Chemistry.
In Domains and Fields layouts, selecting a centroid hides unrelated aggregate arrows until the selection is cleared. Selecting a centroid or aggregate relation opens counts and supporting relations in Details. Arrow thickness records how many visible authored relations contribute to that aggregate direction.
Open the field structure with Physics selected →
Compact suggestion: the Compact toolbar button may briefly pulse amber when the current Layered graph is unusually wide and sparse. It is a suggestion, not an automatic layout change.
7. Details and sources
Details is the atlas’s reading surface. Select a concept, construction junction, edge, domain, field, or aggregate relation to inspect the corresponding record.
Concepts
Summary, field and domain memberships, type and scale metadata, carriers, data, axioms or constraints, induced structures, editorial sections, notes, relations, Stories, Views, and sources.
Relations
Source and target, edge type, the exact “what changes” annotation, interpretation of the type, and citations. In relation groups, the destination appears first and the annotation follows as via [annotation].
Construction junctions
All required inputs, the compatibility condition, and the resulting concept. Hidden-junction synthetic edges repeat the AND warning.
Structure overlays
Visible concept counts, aggregate in/out counts, and the authored relations contributing to a selected domain, field, or aggregate arrow.
Header actions
- Link copies a permalink containing the current selection, filter state, display state, and active comparison.
- Edit opens the corresponding source record on GitHub. This is for readers who want to propose corrections or additions.
- Compare appears when Experimental features are enabled and pins the selected concept into the comparison workspace.
Taxonomy badges and relation links are navigable. A relation link can reveal a concept currently hidden by ordinary filters, but it does not silently override a prohibited-domain setting.
8. Stories and Views
View
A curated graph configuration: fields, domains, relation types, display options, layout, and optional core nodes.
Story
A View with an ordered concept sequence. Numbered badges mark its nodes, and Previous/Next controls move through the sequence while leaving the rest of the graph available for exploration.
- Open Stories & Views from the toolbar or the static directory.
- Select a card. A Story begins at its first step; a View opens its curated configuration.
- Expand the banner for the narrative and sequence controls.
- Change filters or display options as needed. The changes remain attached as URL overrides while required Story or core nodes stay visible.
- Use the explicit exit action at the top of Filters. For a core-node Story or View, Use primary domains converts the core nodes into their ordinary domain scope.
9. Compare and connect (experimental)
Enable Experimental features in Preferences to reveal Compare in the toolbar and concept Details.
Overview
Contrasts two concepts’ recorded definitions, taxonomy, source overlap, direct enabled relations, relation-type profile, and shared adjacent concepts.
Connections
Finds up to three short paths through the currently visible graph. Choose either traversal direction while preserving arrow meaning, or follow authored arrows from A to B only.
Connections never silently re-enable hidden concepts or relation types. A path is limited to twelve relations. You can choose an alternative path, fit it, select its nodes or edges, and copy its node sequence in Story-authoring format.
10. Preferences
Preferences are saved only in the current browser. They are intentionally excluded from shared URLs.
- Theme
- Dark and Light select a fixed appearance. System follows the operating system and updates when its color scheme changes. The interactive atlas and generated HTML pages use the same saved choice. Authored domain colors retain their meaning while text, relation colors, label fills, outlines, and backgrounds adjust for contrast. The Preferences default is System; before a choice has been saved, standalone static pages follow the system scheme.
- High resolution
- Uses the browser’s full device pixel ratio. Turn it off to cap rendering resolution on dense or high-DPI displays.
- Fade transitions
- Animates opacity and style changes over a short interval.
- Animate graph
- Animates node motion and fitting during layout changes. Off by default.
- Auto-fit
- Refits after filter or layout changes. Turn it off to preserve your current viewport.
- Mark additional domains
- Shows small markers for secondary domain memberships.
- Overlay domains
- Shows domain-name overlays at useful zoom ranges in Layered and Fields modes.
- Hide edges while moving
- Temporarily suppresses edges during pan and zoom to improve interaction performance.
- Dim prerequisites
- Fades prerequisite-only context. Turning it off leaves those nodes at ordinary opacity.
- Highlight prerequisite path
- Highlights the selected concept’s transitive prerequisite nodes and edges.
- Experimental features
- Reveals Compare and gates Motion blur and Allow node dragging.
- Motion blur
- Uses the renderer’s motion-blur mode. It has no effect unless Experimental features is also enabled.
- Allow node dragging
- Lets you move individual nodes. It has no effect unless Experimental features is also enabled; ordinary dragging pans the graph.
Reset restores the default preference set. It does not change filters or the shareable display state.
12. Static pages and data
The atlas is interactive, but its principal routes also publish static HTML for search engines, citation, accessibility, and no-script browsing.
- /directory/
- Complete semantic directory plus the exact all-in SVG.
- /math/, /physics/, /chemistry/
- Field landing pages with interactive scope and static SVG previews.
- /math/algebra/ and other domains
- Domain landing pages scoped to primary-domain concepts.
- /concepts/<id>/
- Canonical concept pages. Example: Molecule.
- /views/
- Static Story and View directory, with one crawlable page per entry.
- /data/
- Dataset landing page with stable JSON URLs, checksums, and AI-use guidance.
- /static/atlas.svg
- Standalone vector map with links back to concept routes.
- Data section in Filters
- Published graph, schema, Story/View data, share codec, provenance, content license, Directory, and standalone SVG.
The graph is editorially selective and source-backed. Use the citations attached to each record for technical verification rather than treating the map’s geometry as evidence by itself.
13. Keyboard and mobile
Keyboard
/ focuses search · F fits the graph · Escape clears search and closes open mobile panels. Search suggestions and Compare tabs support arrow-key navigation.
Mobile and touch
Pinch to zoom and drag to pan. Filters enter from the left; Details rises from the bottom. The active Story or View context moves into the Details surface when necessary.
All toolbar buttons and filter controls have accessible names. The static Directory and this guide remain usable without JavaScript.