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name: semantic-spacetime description: >- Model and analyze Semantic Spacetime (SST) graphs, distances, trajectories, drift, and model files. Do not use this skill for promise-theory vocabulary and fundamentals without SST modeling; use promise-theory for the substrate concepts. license: MIT

Semantic Spacetime

Semantic Spacetime (SST) is Mark Burgess's discrete, graph-theoretic model of meaning over time. A semantic element is one autonomous agent plus its scalar promises; a semantic spacetime is a collection of such elements in which a local change in state, promises, or configuration is a local unit of time. Time is proper time — there is no global clock (the precedence view Burgess credits to Lamport). Causality is cooperative: every adjacency requires an offer (+) and an acceptance (−) promise on both ends, so space is made of cooperating nodes and edges. The 2025 γ(3,4) formalism types the graph: three node meta-types (events, things, concepts) connected by four link types (0 = NEAR, ±1 = LEADS TO, ±2 = CONTAINS, ±3 = EXPRESSES). Absorbing states in partial graphs leak information, and intentionality enters at the boundary. SST is built on Promise Theory — for the promise vocabulary, load promise-theory instead of re-deriving it here. This skill is a thin router: load the dense material only when a row in Load By Need matches your task.

When to use

• When you need to design or analyze shared semantic ground between agents — model what "meaning" means in this system (what does a concept, term, or promise mean to whom), producing a γ(3,4) map of the shared semantic ground as the artifact.
• When you need to model intent or meaning over time — trajectories, drift, and convergence of understanding between agents, agents and humans, or agents and their instructions; the artifact is a semantic trajectory with recorded observations.
• When you need to design convergent, self-healing coordination — a loop in which state is continuously measured against a desired meaning and repaired toward it; model the loop as semantic elements whose local change is time.
• When you need to diagnose semantic drift, divergence, or dead-ends — absorbing states, meaning gaps, and non-converging agents; the artifact is a drift finding with the leaking boundary identified.
• When you need to map promises onto spacetime — trajectories, promise propagation, and causality between agents; model each promise as an edge and trace how intent propagates through the graph.
• When you need to analyze temporal blindness in agents — state tracking, event ordering, and causality failures where an agent cannot tell what happened before what; model event order via proper time instead of a shared clock.

When not to use

• Physics or relativity — SST is not a theory of quantum gravity or spacetime physics; it assumes no manifold structure and no momentum. Do not use it for physics problems; those belong to a physics domain.
• Pure vector embeddings, RAG, or semantic search without temporal-causal structure — a static embedding index has no proper time, no causality, and no trajectories to model; route to the embedding or semantic-search tool's own skill instead.
• Enforceable centralized control — if you can command and verify compliance directly, SST's cooperative-promise machinery is overhead, not insight (the same boundary promise-theory draws); route to promise-theory when you need the control-vs- cooperation discussion.
• Simple single-agent prompting — one model and one prompt with no delegation or meaning space to model needs no spacetime vocabulary.
• Tool manuals or framework documentation — routing to the tool's own skill is always better than framing the tool with SST.

Load By Need

Need	Load
Re-derive the formal model: semantic element, semantic spacetime, proper time, γ(3,4) typing rules, learning/knowledge formalism, promise substrate	references/foundations.md
Learn from the CFEngine and infrastructure lineage before designing convergent systems (convergence semantics, IaC/Kubernetes/GitOps/IBN lessons, promise-keeping-as-data, SLOs, the record axis)	references/applications-infrastructure.md
Model an agent team in SST terms or design agent coordination (Burgess's agent papers, drift/temporal-blindness literature, MCP/A2A substrate, synthesis patterns)	references/agent-coordination.md
Apply a named pattern — semantic anchor, trajectory, convergence loop, promise propagation, drift detection, absorbing-state detection, shared semantic manifold, γ(3,4) modeling, distance metrics, reconciliation	references/patterns.md
Diagnose semantic drift, divergence, dead-ends (absorbing states), or meaning gaps with a bounded procedure	references/diagnosis-and-debugging.md
Hit an unfamiliar term while modeling or diagnosing	references/glossary.md
Find or verify a primary source — the papers, project pages, and adjacent work behind a claim	references/bibliography.md

Quick Start

The bundled CLI (scripts/semantic-spacetime.py) is stdlib-only — any python3 runs it, nothing to install — and every command is read-only. Run the commands below from the repository root; the CLI resolves no files relative to its own location, so the same commands work from any directory with absolute paths.

1. Draft an SST model. Copy templates/sst-model.yaml.tmpl to a working file (for example sst-model.yaml) and replace the example values: declare agents (id, role, promises), semantic nodes (id, type in {event, thing, concept}), edges (from, to, link in -3..3), acceptances, trajectories, and observations. The machine-delimited block between # --- example --- and # --- end example --- shows a complete, valid model to imitate; the same model is committed, fully filled, at tests/fixtures/sample-model.yaml.
2. Lint it against the sst-model-v1 format — exit 0 prints a coverage summary, exit 1 prints named violations: python3 semantic-spacetime/scripts/semantic-spacetime.py model lint semantic-spacetime/tests/fixtures/sample-model.yaml
3. Map the γ(3,4) graph (--format is one of text | mermaid | json): python3 semantic-spacetime/scripts/semantic-spacetime.py model map semantic-spacetime/tests/fixtures/sample-model.yaml --format mermaid
4. Measure semantic distance — weighted hop count (each hop weighs |link| + 1): python3 semantic-spacetime/scripts/semantic-spacetime.py model distance semantic-spacetime/tests/fixtures/sample-model.yaml --from report-event --to drift-concept
5. Trace trajectories — every simple path with link types annotated; cycles are noted and the enumeration terminates on any finite model: python3 semantic-spacetime/scripts/semantic-spacetime.py model trajectory semantic-spacetime/tests/fixtures/sample-model.yaml --from report-event --to drift-concept
6. Diff two snapshots — added/removed/changed semantic regions; identical snapshots report no drift. Point the command at your two snapshot files (running it on the same file twice demonstrates the no-drift case): python3 semantic-spacetime/scripts/semantic-spacetime.py model drift semantic-spacetime/tests/fixtures/sample-model.yaml semantic-spacetime/tests/fixtures/sample-model.yaml
7. Machine-readable output. Append --json to any command for a single JSON object on stdout. --dry-run is accepted everywhere as a no-op guard.
8. Draft the analysis report. Copy templates/sst-analysis.md.tmpl to a working file (for example sst-analysis.md) and fill the skeleton: system description → semantic spacetime map → drift/divergence/absorbing-state findings → interventions → verification/measurement plan.
9. Diagnose drift when agents disagree. If agents diverge, treat the disagreement as an observation, measure the semantic distance between their interpretations, and locate the absorbing state or leaking boundary where information stops flowing.

Available Scripts

This skill bundles one script; there are no others to discover. Every command is read-only (--dry-run is accepted everywhere as a no-op guard), and --json on any command produces a single JSON object on stdout.

Script	Purpose	Invocation
scripts/semantic-spacetime.py	Lints, maps, and analyzes SST models in the sst-model-v1 format. Subcommands: model lint (validate against the schema), model map --format text|mermaid|json (render the γ(3,4) graph), model distance --from X --to Y (weighted hop count, each hop weighs |link| + 1), model trajectory --from X --to Y (enumerate simple paths with link types), and model drift file-a file-b (diff two snapshots into added/removed/changed regions). Run lint after drafting or every edit of a model until it exits clean, then use the analysis subcommands when mapping shared semantic ground, measuring distance between interpretations, tracing intent propagation, or diagnosing drift between snapshots.	python3 semantic-spacetime/scripts/semantic-spacetime.py model lint <model.yaml>

Exit codes: 0 = valid/covered, 1 = named violations or missing/unreachable ids, 2 = usage or IO errors.

Related Skills

Skill	Route when...
promise-theory	You need the substrate vocabulary SST builds on: promises, offers and acceptances, convergence, the Downstream Principle, and coordination diagnosis (also routed from references/foundations.md)
agent-evals-and-observability	You need to turn measurement and verification of semantic claims into evals, traces, and release gates (also routed from references/foundations.md)
agent-council	You want structured multi-agent debate as a mechanism for negotiating shared meaning between agents
workflow-architect	You want to encode a semantic-spacetime-informed workflow as a reusable skill bundle
artifact-pyramids	You need to structure SST evidence — models, maps, observations — as summaries → analysis → evidence dossiers
agent-skills	You are authoring or editing an Agent Skills-format skill — the format this skill follows
cli-builder	You are building or refactoring the bundled CLI for SST models (it will follow cli-builder conventions: non-interactive, --json, --dry-run)

Gotchas

1. Provenance honesty. The theory files tag every factual claim [VERIFIED] (confirmed in a primary source fetched during research) or [UNVERIFIED] (secondary or inferred), and label original synthesis EXTRAPOLATION. Preserve those markers when you reuse the material; dropping a marker silently upgrades a claim. See the provenance block in references/foundations.md.
2. The theory is semi-formal and unrefereed. Burgess published the series as self-published notes with no intention of seeking refereed publication, and "some proofs [are] left to the reader." Use SST as a reasoning aid, not a proof system. See the status section in references/foundations.md.
3. Local time ≠ global clock. Proper time is per semantic element: a local change is that element's unit of time. There is no shared clock ordering all events; global order is an observer-relative artifact. See the proper-time section in references/foundations.md.
4. Semantics requires measurement. Meaning cannot be asserted before it is measured at the right scale — "dynamics always trumps semantics" (the CFEngine-lineage lesson in references/applications-infrastructure.md). SST's spacelike (repeated trials, constant state) and timelike (continuously adapting) measurements are the two ways to stabilize observation; see the measurement-duality section of references/foundations.md.
5. Promise-keeping must be stored as data. The gap documented in the CFEngine lineage — reporting whether a promise is kept right now without ever storing promise-keeping as queryable data — is exactly the gap SST's semantic-time record axis addresses (see the promise-keeping-as-data gap in references/applications-infrastructure.md). Record observations as versioned data or trust cannot accumulate.

Prerequisites

• Python 3 with standard library only; the CLI has nothing to install.
• A model file to analyze: copy templates/sst-model.yaml.tmpl and replace the example values (a complete, valid example lives at tests/fixtures/sample-model.yaml).
• The CLI resolves no files relative to its own location, so commands work from any directory — use paths relative to where you run them.

Limitations

• The theory is semi-formal and unrefereed; the CLI is a reasoning aid for models you author, not a proof system (see Gotchas).
• distance and trajectory exit 1 when an id is missing or no path connects two nodes; trajectory enumeration covers simple paths only (no repeated nodes) and terminates on any finite model.
• The CLI reads and analyzes model files only: it does not observe running agents, measure live systems, or store observations — recording measurements as versioned data stays your responsibility.

Exit Conditions

Stop when the system is modeled as a semantic spacetime — semantic elements, γ(3,4) edges, trajectories, and acceptances recorded — drift/divergence/ absorbing-state findings are written down, and a verification/measurement plan is stated. When diagnosing drift, stop after three non-converging passes and report the evidence instead of re-litigating the same model.