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 (formal model and γ(3,4) definitions) and 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); the full γ(3,4) formalism (see foundations.md); the diagnosis procedure (see diagnosis-and-debugging.md); and the promise-level machinery of offers, acceptances, and trust (see promise-theory — 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.
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, 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 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 §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; 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 §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 and 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 §5 and 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. 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 and its agent-coordination and patterns references; for the formal γ(3,4) definitions, foundations.md; for patterns to apply, patterns.md; for diagnosis, diagnosis-and-debugging.md.