magnus919_agent-skills/semantic-spacetime/references/agent-coordination.md

# Agent Coordination — SST and Promise Theory for Multi-Agent Systems

**Load this file when you need to design or diagnose coordination between AI agents** — modeling an agent team in SST terms, choosing a coordination substrate, detecting drift between agents' world models, or using SST's machinery to reason about delegation, shared meaning, and temporal blindness. This is the agentic-AI companion to [foundations.md](foundations.md) (formal model and γ(3,4) definitions) and [patterns.md](patterns.md) (named patterns to apply).

**What belongs here:** Burgess's 2025–26 agent papers (arXiv:2604.10505, 2512.19084, 2507.10000), the working software (SSTorytime, MCP-SST), the drift and temporal-blindness literature, spatial-temporal world models and the neuroscience substrate, the MCP/A2A coordination substrate, the honest industry record (including Anthropic's documented delegation failure), and — explicitly labeled `[EXTRAPOLATION]` — five synthesis patterns for using SST as an agent-coordination model. What does **not** belong here: the CFEngine/infrastructure lineage (see [applications-infrastructure.md](applications-infrastructure.md)); the full γ(3,4) formalism (see [foundations.md](foundations.md)); the diagnosis procedure (see [diagnosis-and-debugging.md](diagnosis-and-debugging.md)); and the promise-level machinery of offers, acceptances, and trust (see [promise-theory](../../promise-theory/SKILL.md) — linked, not restated).

**Provenance.** `[VERIFIED]` = confirmed in a fetched primary source (arXiv abstract/full text, official docs, GitHub); `[UNVERIFIED]` = secondary or inferred; `[EXTRAPOLATION]` = this skill's original synthesis, labeled wherever it appears and grounded in verified sources.

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## 1. Burgess's agent-cooperation program: the four load-bearing concepts

*Cooperation in Human and Machine Agents: Promise Theory Considerations* (arXiv:2604.10505, April 2026) is Burgess's explicit "revisit[ing] [of] established principles of agent cooperation, as applied to humans, machines, and their mutual interactions" in the era of AI agents [VERIFIED — arXiv:2604.10505, full text read]. Four concepts carry the paper, all `[VERIFIED]`:

1. **No agent may promise anything on behalf of any agent but itself.** "Autonomy is the base state of any operational entity, human or machine," and the fundamental tenet is that no agent may promise on behalf of any other; attempts to work around this "account for almost all misunderstandings and errors in agent systems" [VERIFIED — arXiv:2604.10505]. This is the coordination-layer statement of promise-theory's autonomy axiom — for the promise-theory treatment, see [promise-theory](../../promise-theory/references/foundations.md).
2. **The Downstream Principle (Def. 1).** "Agents downstream… have the ultimate power of decision over the outcome." For autonomous agents causality is inverted: the receiver decides what it accepts, and responsibility flows downstream (a client is responsible for its own use of a service) [VERIFIED — arXiv:2604.10505].
3. **Offer / acceptance with an overlap.** Coordination is voluntary: offer `Ai →+bi Aj` plus acceptance `Aj →−bj Ai`; influence flows only if both are kept, and the propagated content is the overlap (mutual information) `b∩ = bi ∩ bj`. Impositions are "generally ineffective" [VERIFIED — arXiv:2604.10505]. (The offer/acceptance machinery itself is promise-theory territory — link to [promise-theory](../../promise-theory/references/foundations.md), do not re-derive here.)
4. **Trust as energy.** Trustworthiness is a potential `V`; mistrust drives kinetic sampling at rate `v = √(2(VR−VS−risk)/ρ)` — "trust is really a form of work or energy in the physics sense," whose function is to reduce the overhead of managing a promise dependency [VERIFIED — arXiv:2604.10505; the model is developed in Burgess & Dunbar, *European Economic Review*, 2025].

Two further results matter for coordination design. **Convergent fixed points as the safety pattern**: CFEngine engineered certainty via mathematical fixed points — iterative evaluation `π̂|q⟩ ↦ |qπ⟩` converges on the promised state, and "convergent fixed-point outcomes are the only plausible safeguard in safety critical goals" [VERIFIED — arXiv:2604.10505]. **Swarms vs. teams (Def. 6)**: "a swarm is an ensemble of agents, which are basically similar, and has no leader"; a team has differentiated roles and clear promises — microservices are "a team structure applied to information technology" [VERIFIED — arXiv:2604.10505]. The paper also quantifies proxy chains: fully-promised delivery through N intermediaries costs O(N²), and at minimal trust the promise graph must be complete [VERIFIED — same source]. See [promise-theory's agent-coordination reference](../../promise-theory/references/agent-coordination.md) for the operational mapping of these concepts onto multi-agent engineering practice.

## 2. γ(3,4) "Attention" in cognitive agents: graphs preserve intentionality

*γ(3,4) 'Attention' in Cognitive Agents: Ontology-Free Knowledge Representations with Promise Theoretic Semantics* (arXiv:2512.19084, December 2025) applies the γ(3,4) representation to cognitive agents without relying on LLMs implicitly [VERIFIED — arXiv:2512.19084]. The load-bearing claim: **"while vectorized data are useful for probabilistic estimation, graphs preserve the intentionality of the source even under data fractionation"** [VERIFIED — arXiv:2512.19084]. The γ(3,4) graph "avoids complex ontologies in favour of classification of features by their roles in semantic processes" and "favours an approach to reasoning under conditions of uncertainty" [VERIFIED — same source]; "appropriate attention to causal boundary conditions may lead to orders of magnitude compression of data required for such context determination" [VERIFIED — same source, Burgess's claim, not independently benchmarked]. The full formal definition (3 node meta-types × 4 link types, the nine typing rules) belongs to [foundations.md](foundations.md) §2 — this file only summarizes and routes.

The intentionality-vs-vectorization contrast is the key design trade for agent systems: embeddings are good for probabilistic estimation but their "interior spaces" have "inscrutable property models"; a typed γ(3,4) graph keeps the *kind* of relation (causal, containment, attribute, similarity) explicit even when data is fragmented across agents [VERIFIED — arXiv:2512.19084; arXiv:2506.07756].

## 3. Working software: SSTorytime and MCP-SST

The SST line ships real, current software — evidence it is "working software, not vaporware" [VERIFIED — GitHub, fetched 2026-08-12]:

- **SSTorytime** (github.com/markburgess/SSTorytime): "an independent Knowledge Graph, based on Semantic Spacetime… aims to be both easier to use and more powerful than RDF" [VERIFIED — GitHub]. A Go library + Postgres knowledge-graph store with the **N4L note query language** and the `searchN4L`, `pathsolve`, `graph_report` tool set; ~158 stars and active through 2026-08-12 [VERIFIED — GitHub]. It ships an embedded Agent Skills-format skill — a `SKILL.md` under `.claude-plugin/skills/SSTorytime/` with `name`, trigger-style `description` (TRIGGER when the user asks about notes on a subject; SKIP for RDF questions), and `allowed-tools` — a real-world instance of the Agent Skills pattern inside the SST ecosystem [VERIFIED — GitHub].
- **MCP-SST** (github.com/markburgess/MCP-SST): "an MCP to SST proxy" — a Model Context Protocol server advertising the **`N4Lquery`** tool on `tools/list`, so "an LLM client like Claude Code can drive the SSTorytime knowledge graph in natural language — no hand-crafted JSON-RPC needed" [VERIFIED — GitHub]. The README shows an LLM generating an SVG orbit visualization of the word "brain" from one MCP tool call [VERIFIED — GitHub]. Note the direction: MCP-SST is **agent ↔ tool** (an LLM client querying a graph tool), not agent ↔ agent — it wires SST into modern agentic infrastructure as a tool substrate [VERIFIED — GitHub; MCP spec].
- Community spinoffs: Simon Frost's Julia `SemanticSpacetime.jl` and `CQL.jl` ("From Causal SQL to Semantic Spacetime via CQL") [VERIFIED — SSTorytime README].

## 4. Intentionality, co-language, and the three-languages problem

**Intentionality measurement.** *On The Role of Intentionality in Knowledge Representation: Analyzing Scene Context for Cognitive Agents with a Tiny Language Model* (arXiv:2507.10000, July 2025) applies SST as an effective Tiny Language Model: agents can detect "a degree of latent 'intentionality' in data by looking for anomalous multi-scale anomalies and assessing the work done to form them"; **scale separation** sorts content into "intended" vs "ambient context," using spacetime coherence as a measure — "at very low computational cost, without reference to extensive training or reasoning capabilities" [VERIFIED — arXiv:2507.10000]. This is the measurement arm: intentionality is detected, not assumed, by separating scales.

**Co-language / three-languages.** From arXiv:2604.10505: each agent pair has three languages — the sender's, the receiver's, and the exchange *co-language*; translation between them is generically non-unitary, so "agents should expect to misunderstand one another's intentions to some level," and decompressing discourse to approximate unitarity is risky ("saying too much could make things worse"); the key line is "autonomous agents are never certain" [VERIFIED — arXiv:2604.10505]. This is the meaning-negotiation substrate of the whole SST line — and it is promise-theory's three-languages/meaning-negotiation problem. Per the no-duplication rule, the full treatment lives in [promise-theory](../../promise-theory/references/agent-coordination.md); this file uses the concept and links rather than restating the machinery.

**Two labeled synthesis connections** (both `[EXTRAPOLATION]`, grounded in §4's sources): (a) the co-language machinery is the micro-mechanism underneath the shared-semantic-ground synthesis (§8.1) — agents converge on a working overlap `b∩` by negotiating a co-language, and the shared manifold is that overlap made persistent [EXTRAPOLATION — grounded in arXiv:2604.10505]; (b) it is also the diagnosis lens for delegation failure — Anthropic's documented vague-delegation failure (§7) is a small overlap `b∩` between the orchestrator's instruction language and the subagent's comprehension language, exactly what "agents should expect to misunderstand one another's intentions to some level" predicts [EXTRAPOLATION — grounded in arXiv:2604.10505 and Anthropic's engineering post].

## 5. Drift literature: the empirical evidence closest to SST

Three papers form the empirical core of agent drift — each with its central construct, its metric, and an explicitly labeled SST mapping [paper facts `[VERIFIED]`; mappings `[EXTRAPOLATION]`]:

### 5.1 Context drift (arXiv:2606.21666, June 2026)

*Hallucination as Context Drift: Synchronization Protocols for Multi-Agent LLM Systems* argues "a significant class of these failures arises… from context drift: the divergence of internal knowledge states between concurrent agents" [VERIFIED — arXiv:2606.21666]. Central constructs: a **Context Divergence Score (CDS)** over "spatial, temporal, and task dimensions," and a **Shared State Verification Protocol (SSVP)** in which "agents periodically exchange compressed state summaries and flag high-divergence conditions before joint reasoning" [VERIFIED — same source]. Key finding: naive full-broadcast sync *increases* hallucination by **34%** (contamination); selective sync reduces it (HR 0.463) with 58% fewer API calls — "refram[ing] hallucination mitigation as a distributed systems problem… context synchronization as a first-class primitive" [VERIFIED — same source]. **SST mapping [EXTRAPOLATION]**: context divergence is divergence between agents' world states in a semantic spacetime; the SSVP is an evaluation loop correcting toward promised (shared) states; contamination from full-broadcast sync is an information-leaking absorbing process — broadcasting unaccepted offers floods every agent with data that leaks its intentionality [EXTRAPOLATION — grounded in arXiv:2606.21666 and the absorbing-states doctrine of arXiv:2506.07756].

### 5.2 Agent drift (arXiv:2601.04170, January 2026)

*Agent Drift: Quantifying Behavioral Degradation in Multi-Agent LLM Systems* defines drift as "progressive degradation of agent behavior, decision quality, and inter-agent coherence over extended interaction sequences," with three manifestations: **semantic drift** (deviation from original intent), **coordination drift** (breakdown of consensus), and **behavioral drift** (unintended strategies) [VERIFIED — arXiv:2601.04170]. Central metric: the **Agent Stability Index (ASI)** over twelve dimensions, with mitigations including episodic memory consolidation, drift-aware routing, and adaptive behavioral anchoring [VERIFIED — same source]. **SST mapping [EXTRAPOLATION]**: the three drift types are three axes of divergence in semantic spacetime — semantic drift is displacement along the meaning coordinates, coordination drift is inter-agent trajectory separation, behavioral drift is divergence between the promised and actual path [EXTRAPOLATION — grounded in arXiv:2601.04170 and §8.2].

### 5.3 Drift as bounded equilibrium (arXiv:2510.07777, 2025)

*Drift No More? Context Equilibria in Multi-Turn LLM Interactions* formalizes drift as turn-wise **KL divergence** from a goal-consistent reference, evolving as "a bounded stochastic process with restoring forces"; it finds "stable, noise-limited equilibria rather than runaway degradation," and reminder interventions reliably reduce divergence [VERIFIED — arXiv:2510.07777]. **SST mapping [EXTRAPOLATION]**: bounded equilibria with restoring forces are CFEngine's fixed-point attractors in the semantic domain — the same "ball rolling into a potential well" (§1, applications-infrastructure §2) with reminders acting as reaffirmed acceptance promises [EXTRAPOLATION — grounded in arXiv:2510.07777 and arXiv:2604.10505's fixed-point convergence].

## 6. Temporal blindness, spatial-temporal world models, and the neuroscience substrate

Four verified results anchor SST's claim that relational knowledge and space/time share substrate:

1. **LLM agents are temporally blind** (arXiv:2510.23853, ACL 2026 Findings): agents "by default assume a stationary context, failing to account for the real-world time elapsed between messages," causing over- or under-use of stale context in tool-use decisions; in a benchmark, **no model achieving a normalized alignment rate better than 65% when given time stamp information** [VERIFIED — arXiv:2510.23853]. (The 65% figure is benchmark-specific; do not over-generalize it into "models are ≤65% at temporal tasks" [UNVERIFIED — generalization beyond the benchmark].)
2. **LLMs build linear spatial-temporal world models** (Gurnee & Tegmark, *Language Models Represent Space and Time*, arXiv:2310.02207, ICLR 2024): Llama-2 learns linear representations of space and time across scales, robust to prompting, with identifiable "space neurons" and "time neurons"; "modern LLMs… possess basic ingredients of a world model" [VERIFIED — arXiv:2310.02207].
3. **The Tolman-Eichenbaum Machine** (Whittington et al., *Cell* 2020) unifies spatial and relational memory: the same code supports "where" and "what relates to what" — semantics and space share a substrate [VERIFIED — Cell 2020; Behrens et al., *Neuron* 2018]. Burgess's γ(3,4) claims "human concepts ultimately derive from concepts about space and time" [VERIFIED — arXiv:2506.07756].
4. **Grid cells furnish a Euclidean metric** (Banino et al., *Nature* 557, 2018): emergent grid-like cells provide agents "with a Euclidean spatial metric and associated vector operations" [VERIFIED — Nature 2018].

The SST tie, labeled per provenance rules: these are independent lines of evidence that space and meaning share machinery — which is exactly what SST formalizes as a graph in which *both* coordinates and semantic relations live on one structure [EXTRAPOLATION — grounded in the four verified results above; the "share substrate" sentence is the neuroscience literature's own framing, the SST identity is this skill's reading].

## 7. The coordination substrate: MCP, A2A, the unformalized gap, and the honest industry record

- **MCP (Model Context Protocol)** is the agent ↔ tool substrate (Anthropic, Nov 2024): JSON-RPC standardizing **Resources** (context/data), **Prompts** (templated workflows), and **Tools** (functions the model executes), plus client-side Sampling, Roots, and — in the 2026 release-candidate extensions — Tasks and MCP Apps [VERIFIED — MCP spec 2025-11-25; MCP blog 2026-07-28]. "MCP is for agent-to-tool communication" [VERIFIED — MCP spec].
- **A2A (Agent2Agent Protocol)** is the agent ↔ agent substrate (Google, April 2025; Linux Foundation, June 2025): "an open protocol enabling communication and interoperability between opaque agentic applications" — agents "interact without needing to share internal memory, tools, or proprietary logic" [VERIFIED — a2a-protocol.org]. The **AgentCard** is the capability manifest: a machine-readable JSON document describing an agent's name, skills, endpoints, auth, and transports [VERIFIED — same source]. A2A and MCP are complementary: agent↔agent vs. agent↔tool [VERIFIED — same source].
- **The unformalized gap**: neither substrate formalizes *what the common semantic ground between two agents is* or how to measure its absence; A2A keeps agents opaque, leaving semantics to per-exchange negotiation [EXTRAPOLATION — grounded in the A2A docs' opacity design and the drift literature's divergence measures]. This is precisely where SST adds value.
- **Anthropic's documented delegation failure**: the orchestrator-worker engineering post reports that delegation quality depends on detailed task descriptions — without them "subagents misinterpret the task or perform the exact same searches" [VERIFIED — anthropic.com/engineering/multi-agent-research-system]. This is a documented operational failure mode, not a ranking: the research does not support a "#1" ranking of coordination substrates, and none is asserted here [VERIFIED — the research's own searches found no such ranking]. It is also subagents performing duplicated work, which in SST terms is two trajectories toward the same absorbing region without a shared anchor (§8.3, §8.5).
- **The honest negative result**: no mainstream LLM-agent framework, observability platform, or enterprise multi-agent system uses SST or promise theory as its coordination model [VERIFIED — negative result of this research phase's searches]. The limitation must be stated with it: this is absence of evidence from a bounded search session, not proof of impossibility [VERIFIED — research report §2.8; the caveat is the report's own framing]. SST remains a small, deep-specialist program (Burgess's papers and software, a 2025 self-published book, a 2018 UiO thesis, data-pipeline startups, and 5G interest) [VERIFIED — agentic-ai report §2.8].

## 8. Synthesis: five patterns for SST as a coordination model

Each pattern below is this skill's **original synthesis — labeled `[EXTRAPOLATION]`** — and each names the verified research it builds on. None is implemented or measured at scale yet; treat them as hypotheses to test (see §9).

### 8.1 Shared semantic manifold with causal-temporal structure as coordination substrate `[EXTRAPOLATION]`

Give a multi-agent system a shared γ(3,4)-structured representation (nodes = events/things/concepts; links = near/leads-to/contains/expresses) as the coordination substrate, instead of raw token contexts or opaque agent cards. Each agent maintains its own projection of the shared manifold plus its interior state; coordination happens by comparing projections, not by exchanging full context. **Grounding**: γ(3,4) and "graphs preserve the intentionality of the source" (arXiv:2512.19084); A2A's opacity + AgentCard manifests (a2a-protocol.org); GraphRAG's LLM-generated graphs (arXiv:2404.16130); Tolman-Eichenbaum showing spatial and relational memory share machinery (Cell 2020); MCP-SST already demonstrating the plumbing (an LLM querying an SST graph through MCP). **Value-add**: a typed, directional shared representation lets agents agree on *what type of relation* a statement claims — the ambiguity the context-drift literature shows is costly (arXiv:2606.21666).

### 8.2 Agent trajectories through semantic space as first-class observables `[EXTRAPOLATION]`

Treat every agent as tracing a trajectory through semantic spacetime: a sequence of {position, intent (promise), time} steps. Drift = displacement from the promised path; divergence = inter-agent trajectory separation; convergence = approach to a shared fixed point; absorbing state = task dead-end requiring boundary injection (human input / a new promise). **Grounding**: intent as "an agent's 'direction of travel' in some space of possibility" (arXiv:2604.10505); absorbing states and division-by-zero (arXiv:2506.07756); linear space/time coordinates in LLMs (arXiv:2310.02207); drift and divergence metrics (arXiv:2601.04170, arXiv:2606.21666); observability/evals as trajectory recording (OpenTelemetry GenAI conventions; LangSmith/Langfuse; Anthropic's end-state evals). **Value-add**: gives observability a geometry — "how far am I from my promised state?" and "how far apart are our world models?" with a defined semantic metric, going beyond turn-wise KL divergence (arXiv:2510.07777).

### 8.3 Promise propagation through semantic spacetime as inter-agent commitments `[EXTRAPOLATION]`

Model delegation as promise propagation: an orchestrator's task description is an offer (+b); a subagent's acceptance is acceptance (−b); the effective task is the overlap `b∩`; the Downstream Principle makes the accepting agent responsible for the outcome; long chains inherit the O(N²) assurance cost; "trust" sets the monitoring/sampling rate. **Grounding**: offer/acceptance, Downstream Principle, proxy chains, contracts as bilateral promise collections, fixed-point convergence (arXiv:2604.10505); Anthropic's finding that vague delegation causes misinterpreted/duplicated work — i.e., low offer/acceptance overlap (multi-agent research system); A2A task delegation (a2a-protocol.org). **Value-add**: a principled diagnosis for a documented failure — the promise overlap was small; the fix is explicit negotiation/expansion of the co-language (§4).

### 8.4 Semantic-distance metrics for delegation decisions `[EXTRAPOLATION]`

Use semantic distance in the shared manifold (typed, not just cosine) to route tasks: delegate to the agent whose capability region (AgentCard → concepts/things it can act on) is nearest to the task's required concepts; prefer redundant providers for critical promises (Downstream Principle); escalate when distance to a trusted solution exceeds a risk budget. **Grounding**: embeddings/RAG distance machinery (arXiv:2005.11401; Anthropic's research system); Gärdenfors conceptual spaces (convex regions, prototypes); A2A AgentCards as capability manifests; promise-theory redundancy doctrine (arXiv:2604.10505); Context Divergence Score as a proto-metric (arXiv:2606.21666). For the formal definition of semantic distance (metric vs. semantic), see [foundations.md](foundations.md) §8.

### 8.5 Detection of semantic drift between instruction, implementation, and reality `[EXTRAPOLATION]`

The highest-value diagnostic: track three trajectories — *instruction* (promised state), *implementation* (the agent's actual path), *reality* (observed world state) — and alert when their pairwise semantic distances exceed a threshold, or when an agent's path enters an absorbing state (hallucination, task collapse) that leaks information. **Grounding**: semantic/agent drift (arXiv:2601.04170); context drift and synchronization protocols (arXiv:2606.21666); context equilibria and reminder interventions (arXiv:2510.07777); absorbing states as "boundary information where intentionality can enter" (arXiv:2506.07756); CFEngine fixed-point convergence — "keep applying the map until |qπ⟩" (arXiv:2604.10505); Anthropic's end-state evaluation. **Value-add**: a convergence-based correction loop (re-apply the promise map, re-affirm acceptance, inject boundary information when stuck) — the mechanism CFEngine proved at datacenter scale and the drift literature is rediscovering empirically. This is the diagnostic pattern developed in [patterns.md](patterns.md) and [diagnosis-and-debugging.md](diagnosis-and-debugging.md).

## 9. Caveats on the synthesis

- SST is a formal theory with a small empirical footprint; the mappings in §8 are interpretive, not yet implemented or measured [EXTRAPOLATION].
- Burgess labels his own strong claims as hypotheses — "this remains a hypothesis for now" for the claim that four relation types suffice (arXiv:2506.07756) [VERIFIED — arXiv:2506.07756].
- The theory is semi-formal and deliberately unrefereed; use the synthesis here as a reasoning aid, not a proof system (full disclosure in [foundations.md](foundations.md) §5 and [applications-infrastructure.md](applications-infrastructure.md) §10) [VERIFIED — markburgess.org].
- Adoption barriers to name honestly: SST's formalism is dense; its tooling (SSTorytime/MCP-SST) is early-stage with a small community; the mainstream stack is embedding/vector-first [VERIFIED — GitHub activity; UNVERIFIED — the market-readiness assessment is opinion].

## Sources and routing

The full annotated source list with URLs is in [bibliography.md](bibliography.md). Key sources for this file: arXiv:2604.10505, 2512.19084, 2507.10000, 2506.07756, 2606.21666, 2601.04170, 2510.07777, 2510.23853, 2310.02207, 2404.16130, 2005.11401, 1803.10122; Banino et al. (Nature 2018); Whittington et al. (Cell 2020); Behrens et al. (Neuron 2018); a2a-protocol.org; modelcontextprotocol.io; anthropic.com/engineering/multi-agent-research-system; github.com/markburgess/SSTorytime; github.com/markburgess/MCP-SST. For promise-level machinery (offer/acceptance, Downstream Principle, trust calibration), load [promise-theory](../../promise-theory/SKILL.md) and its [agent-coordination](../../promise-theory/references/agent-coordination.md) and [patterns](../../promise-theory/references/patterns.md) references; for the formal γ(3,4) definitions, [foundations.md](foundations.md); for patterns to apply, [patterns.md](patterns.md); for diagnosis, [diagnosis-and-debugging.md](diagnosis-and-debugging.md).