Context Streaming Through Eventing: A Mathematical Framework for Behavioral Context as a Living Document

Every decision a human makes occurs within a context. Not a single variable or a flat feature vector, but a nested, hierarchical, temporally-evolving document that encodes beliefs, preferences, social dynamics, financial constraints, emotional states, and environmental conditions. When you choose a restaurant for dinner, your context includes your current mood, recent dietary preferences, the friend you are meeting (and their preferences), your financial state this month, the weather, recent social media discourse about food trends, and a dozen other factors -- most of which have changed since last week.

Current AI systems treat context as either (a) static user profiles, (b) retrieval-augmented snapshots fetched at inference time, or (c) conversation history within a single session. None of these approaches capture the continuous, event-driven nature of how context actually evolves. A person's financial anxiety after reading a news article about layoffs is a context mutation. A change in political opinion after a conversation with a friend is a context mutation. A shift in music taste after a breakup is a context mutation.

This paper makes three contributions:

1. A formal event-sourced model of human context as a living document, with Bayesian update semantics (Sections 3-4)
2. A mathematical proof that context mutation trajectories are isomorphic to behavioral shift functions, establishing that tracking context change is equivalent to tracking behavior (Section 4)
3. A document-store architecture and streaming protocol for real-time context publication, enabling any LLM to subscribe to a person's evolving context (Sections 6-7)

This work is a companion to our previous paper on Context Lineage [1], extending the framework from static entity context to dynamic human behavioral context. Where Paper I addressed how websites and APIs should present themselves to LLMs, this paper addresses how the humans using those LLMs can share their evolving context in a structured, private, and mathematically grounded way.

The central claim of this paper is deceptively simple but has profound implications for AI systems design:

Consider the behavioral science perspective. Traditional behavioral models [2, 3] define behavior as observable actions: clicks, purchases, movements. But actions are degenerate projections of a high-dimensional context state. The same click can mean curiosity, boredom, intent-to-buy, or accidental touch. What disambiguates these is the context in which the action occurred -- and more importantly, how that context has been changing leading up to the action.

We formalize this intuition. Let be a person's context state at time and let be their action. Traditional models estimate . We argue the correct model is:

where is the trajectory of context changes over the preceding window . The context trajectory -- not the context snapshot -- is the information-theoretically superior predictor. We prove this formally in Section 4.

We model a person's context as a probability distribution over a belief space, updated incrementally by a stream of typed events. This is philosophically aligned with the Bayesian brain hypothesis [4] and technically implemented as an event-sourced system [5].

The key insight is that this update rule admits a spectrum of responses to events. A low-salience event (background news, casual scroll) barely perturbs the context. A high-salience event (job loss, breakup, medical diagnosis) can dramatically reshape the entire distribution. This matches the cognitive science literature on attention-gated belief updating [6].

We now prove the central mathematical result: that context mutations contain strictly more behavioral information than action sequences, and that the KL divergence between successive context states is isomorphic to a well-defined behavioral shift function.

The behavioral shift is always non-negative, equals zero only when context is unchanged, and is unbounded above for radical belief revisions. This exactly mirrors our intuition about behavior: no change in context means no behavioral shift; dramatic context upheaval means large behavioral shift.

This theorem has a direct practical implication: any AI system that predicts behavior from actions alone is provably information-limited compared to one that tracks context trajectories. This is the formal justification for building context streaming infrastructure.

We define six primary event streams that compose the human context state. Each has distinct statistical properties (arrival rate, salience distribution, decay rate) that affect how the context document evolves.

The effective influence of stream on the composite context is the product of arrival rate and average salience:

By this metric, social streams have the highest volume but lowest per-event influence, while relational streams have the lowest volume but highest per-event influence. Financial and health streams occupy the middle ground with moderate rates and high salience. The total effective influence across all streams determines the rate of context evolution:

where is the average information content of events from stream .

We now specify the storage architecture for context documents. The choice of a document store over a relational database is not merely pragmatic -- it is dictated by the mathematical structure of the context state.

{
  "entity_id": "uuid",
  "version": 4217,
  "timestamp": "2026-03-04T15:32:00Z",
  "parent_version": 4216,
  "streams": {
    "social": {
      "sentiment": 0.62,
      "topics": ["AI", "climate", "music"],
      "influence_graph": { ... },
      "last_updated": "2026-03-04T15:30:00Z"
    },
    "financial": {
      "anxiety_index": 0.34,
      "liquidity_state": "comfortable",
      "recent_signals": [ ... ],
      "last_updated": "2026-03-04T12:00:00Z"
    },
    "health": { ... },
    "environmental": { ... },
    "professional": { ... },
    "relational": { ... }
  },
  "composite_entropy": 3.82,
  "behavioral_velocity": 0.15,
  "context_hash": "sha256:a1b2c3..."
}

We define a publish-subscribe protocol for real-time context distribution. The protocol is transport-agnostic (works over WebSocket, SSE, gRPC, or webhook) and is designed for LLM consumption.

The protocol guarantees at-least-once delivery with idempotent callbacks (using the context version number as a deduplication key). The drift threshold prevents noisy over-delivery -- LLMs are only notified when the context has shifted meaningfully.

A natural concern: does the context state converge to a stable distribution, or does it wander indefinitely? The answer depends on the stream statistics and reveals deep connections to behavioral psychology.

The stationary distribution represents a person's baseline behavioral profile -- their stable preferences, enduring beliefs, and default decision patterns. Deviations from are the interesting behavioral events: stress-induced changes, opinion shifts from social influence, life transitions.

This framework gives us a quantitative measure of how disruptive a life event is: compute the KL divergence between the pre- and post-transition stationary distributions. Job loss, divorce, and relocation are empirically the highest-magnitude transitions ( nats), while seasonal changes and routine social shifts are low-magnitude ( nats).

Context streaming raises immediate and serious privacy concerns. Our architecture is designed with privacy as a first-class constraint, not an afterthought.

Bayesian Cognition. The Bayesian brain hypothesis [4] posits that human perception and decision-making are well-modeled as Bayesian inference. Our framework extends this to the engineering domain, building infrastructure for maintaining and streaming the posterior beliefs.

Event Sourcing. Event sourcing [5] is an established pattern in distributed systems where state is derived from an append-only event log. We adapt this pattern to the domain of human context, adding salience-weighted Bayesian semantics to the state reconstruction.

Information Geometry. The use of Fisher information metric on statistical manifolds [8] provides coordinate-invariant measures of distributional change. We apply this to define behavioral path length as a reparameterization-invariant measure of behavioral change.

Contextual Bandits and RL. Contextual bandit algorithms [10] condition decisions on context features. Our contribution is orthogonal: we provide the infrastructure for streaming the context itself, which can then be consumed by any decision algorithm.

Personal Knowledge Graphs. Systems like Solid [11] and personal data stores give individuals control over their data. Our framework adds the mathematical semantics of context evolution and the streaming protocol for LLM consumption.

Context Lineage (Paper I). Our companion paper [1] addresses context lineage for static entities (websites, APIs). This paper extends the framework to dynamic human behavioral context, adding event-driven update semantics and the behavioral shift formalism.

We have presented a mathematical framework for treating human behavioral context as a living document, updated through event streams and persisted in a document store. The central result -- that context mutation trajectories contain strictly more behavioral information than action sequences (Theorem 4.1) -- provides the formal justification for building context streaming infrastructure.

The practical implications are significant. Today, when you use an AI assistant, it knows nothing about your context beyond what you explicitly type. Tomorrow, with consent-gated context streaming, your AI assistant will understand that you are financially stressed this month (financial stream), that you just had a difficult conversation with a colleague (relational stream), that you've been reading about career changes (social stream), and that it's raining outside (environmental stream). It will use this composite context to provide genuinely helpful, contextually appropriate responses -- without you having to explain your entire life situation in every prompt.

The technology to build this exists today. The mathematical framework is sound. What remains is the protocol layer -- the standardized, open, privacy-preserving infrastructure that connects human context to AI systems. That is what we are building.