The γ(3,4) triangle

Mark Burgess's Semantic Spacetime in one picture: three node kinds and four edge kinds — enough, in our reading, to sketch any observer's view of anything in space and time.

The ipm etc-LPXN triangle: event (e, orange), thing (t, green) and concept (c, blue) vertices, joined by L (leads-to), P (part-of), X (expresses) and N (near-to) edges and self-loops.

The three corners are e (event), t (thing) and c (concept). The arrows and self-loops show every legal edge; the dotted circles (N_e, N_t, N_c) are near-to — undirected similarity between two nodes of the same kind.

The three node kinds

Kind	Symbol	What it is	Examples
Event	e	A transient happening — fast at the model's timescale	“User clicks button”, “Build runs”, “Plum murders Scarlet”
Thing	t	A persistent participant — slow at the model's timescale	“Alice”, “my laptop”, “service A container”, “knife K1”
Concept	c	A quasi-invariant pattern; a property that events or things express	“human”, “microservice”, “production”, “murder”

The four edge kinds

Sym	Render	Name	Meaning	When to use
L	orange	LEADS-TO	Temporal / causal flow	One event causes or precedes another
P	green	PART-OF	Containment / participation	A thing inside an event, a sub-event inside a parent event, or a sub-part inside a bigger thing
X	blue dashed	EXPRESSES	Property (a single promise)	An event or thing expresses a concept as a property; a concept can express another. Not is-a
N	gray dotted	NEAR-TO	Similarity / proximity (undirected)	Two same-kind nodes are alike but you don't want to merge them

All 11 allowed edges

Every legal source → target combination, matching the triangle above. The syntax column shows the most common ipmt form.

#	Source → Target	Edge	ipmt syntax	Reads as
1	event → event	L	`e1 ::e --> e2 ::e`	e1 leads to e2
2	event → event	P	`inner ::e --::P--> outer ::e`	inner event is part of outer event
3	event → event	X	`e1 ::e --::X--> e2 ::e`	e1 expresses e2
4	event — event	N	`e1 ::e --- e2 ::e`	e1 is similar to e2 (and vice versa)
5	thing → event	P	`tA --> e1 ::e`	tA participates in (is part of) e1
6	thing → thing	P	`subpart --> whole`	subpart is part of the whole (physical composition)
7	thing — thing	N	`tA --- tB`	tA is near / similar to tB (and vice versa)
8	event → concept	X	`e1 ::e --> cX ::c`	e1 expresses property cX
9	thing → concept	X	`tA --> cX ::c`	tA expresses property cX
10	concept → concept	X	`cX ::c --> cY ::c`	cX expresses property cY
11	concept — concept	N	`cX ::c --- cY ::c`	cX is similar to cY (and vice versa)

The edge symbols L / P / X / N are ipm's mnemonic. Burgess's original SST uses L / C / E / N — ipm renames C→P (and reverses its direction) and E→X.

Two rules baked into the table

No thing --> thing arrow except part-of. To say “Alice owns the car”, create an event that co-locates both participants and let it express the relation as a concept-property (Ownership ::c). The event is the temporal container; the concept names what the co-location means.
The bare --> arrow defaults to the relation that fits the two node kinds: leads-to for event→event, part-of for thing→event and thing→thing, expresses for event→concept, thing→concept and concept→concept.

Full walkthrough — infinite.pm/intro → ← back to the lab