Part 3: Application — Predicting How People Behave

Part 2 established the person-side object. It distinguished the inherited seed from the realized individual structure, the realized structure from the momentary phenomenal state, the momentary phenomenal state from the general predictive response state, and that ideal response state from the finite object the model can actually estimate. Part 3 now asks what can be done with it.

The claim of this section is narrower than a final proof about mind. It is not that we already possess the exact universal transition law for human beings. It is that we can define a mathematical program in which an actor, a proposition, the actor’s environment, and the history between them can be represented through a shared coordinate arena, and that inside this program we can iteratively improve our estimate of how one state gives rise to the next.

In other words: this section does not complete the science; it specifies the playground in which the science can be built.

Everything the model computes on eventually becomes vectors, tensors, distributions, or tuples of those things. Raw inputs can still be text, categories, histories, metadata, prices, organizational charts, people, products, and context objects. A vector is the representation entering an operation. It is not the claim that the original thing was secretly a vector before we touched it.

The canonical symbol definitions are in Canonical Notation and Mathematical Conventions.

Towards a Universal State Transition Function

In the ideal philosophical form of the theory, the object of interest is still the next phenomenal state.

Let \(\phi_{i,t}\) denote the full phenomenal state of person \(i\) at time \(t\), let \(T_{i,t}\) denote the slowly changing realized Transcendental Embedding of that person, let \(c_{i,t}\) denote the active role-and-institution context, let \(w_t\) denote world state, and let \(x_t\) denote the proposition confronting the observer at decision time \(t\).

Here “proposition” is meant broadly. It may be a sentence, an email, a product, a person, a meeting, a threat, a market signal, a price, or a whole local arrangement of circumstances. For the observer, what matters is not bare matter but presented structure.

Define the complete ideal actor–world state

The familiar deterministic silhouette

is the phenomenal component of a fuller transition in which the slow person, context, and world may also change. Let \(\boldsymbol\Xi_{t+1}\) denote the random exogenous change between decision epochs and \(\boldsymbol\xi_{t+1}\) a realized or supplied scenario value. The notation below evaluates a transition kernel at the supplied scenario value; it does not require the singleton event to have positive probability. The operationally honest ideal law is

I keep the deterministic equation because it is the motivating silhouette. It says that if the complete actor–world state and exact transition rule were known, the next state would follow. The stochastic kernel permits genuine randomness; our operational uncertainty is larger still because the complete state is not observed. A deterministic system is the special case in which the kernel places all of its mass on one next state.

The learned model therefore works with the operational state

Its recursively usable prediction is a distribution over the next operational state:

where \(\boldsymbol\Xi_{t+1}\) is the random exogenous change and \(\boldsymbol\xi_{t+1}\) is the realized or supplied scenario value between decision epochs.

The outcome associated with decision \(t\) and horizon \(\Delta\) has a separate predictive law:

For a one-step task, this law may be induced by the next state and its immediate observation. For a longer horizon, it is defined relative to a declared continuation policy, future candidate-set process, exogenous-path law, and censoring convention unless those variables are conditioned on explicitly. It may be induced by a rollout or represented by a direct head calibrated to that same regime. A 90-day close is not an immediate emission one step after an email.

The reply, the purchase, the rejection, the delay, the meeting, or the concession is not the state itself. It is a visible residue of a transition and, for longer horizons, of a trajectory. The model is not fundamentally about “will they buy?” It is about “what state will this actor enter next, and what future traces follow, at the resolution relevant to the task?”

It is useful to decompose the learned transition into four operations.

First, encode the current individual actor-state estimate:

Second, encode the external or symbolic proposition without yet pretending that this encoding is how the actor experiences it:

Third, produce the actor-relative proposition representation for the individual-state model:

Fourth, form the individual interaction representation:

The state transition can then be written

The individual actor-relative map \(\mathcal P_{s,\theta}\) need not be linear. It may contain projection, attention, retrieval, and nonlinear transformation. It stands for the fact that the same proposition is not available to every actor in the same way. The proposition is first represented, then reorganized through the distinctions, salience, language, role, relationship, and current state of the actor who receives it.

This factorization asserts that the fitted transition depends on the proposition through the joint interaction representation:

That is a model restriction, not a metaphysical theorem. It is what makes equality of actor-relative interaction representations imply equality of the fitted model’s predictions.

God’s Infinite Dimensional Space: Making All Realities Composable

“To make all realities composable” does not mean every object is one interchangeable vector or that every category receives its own permanent part of the Hilbert space.

GIDS is the common arena of possible distinctions. The things represented through it are constructions.

A person is represented through an inherited and developed organization of those distinctions. A proposition is represented through the features it presents to an actor. A category may be a region, prototype, distribution, or classifier over those coordinates. A corporation is assembled from people, internal structure, memory, facts, statistics, incentives, and environment. None of these needs to be a primitive type inside the space.

The composability claim is therefore about a common formal grammar:

1. encode relevant distinctions;
2. project or gate them through an actor’s available structure;
3. combine them with the current state;
4. apply a transition law;
5. read out observable consequences;
6. update from what actually happened.

Some operations will be linear. Most interesting interactions will not be.

A dot product between two vectors is meaningful only when the encoders and training objective have made it meaningful. Adding two representations is legitimate only when the result has a defined interpretation. The fact that two objects occupy the same Hilbert arena gives us the capacity to relate them; it does not grant every possible piece of vector arithmetic philosophical significance.

If two external propositions differ physically but produce the same task-relevant joint interaction representation, then they are equivalent for that actor and task under the fitted model. Formally, if

then, holding the operational actor-state and exogenous input fixed,

This is a statement about the fitted model because the factorization above makes the actor-relative proposition representation the only proposition-side input to the transition kernel. It is not a metaphysical theorem that two physically distinct propositions must have the same real-world effect.

This captures a number of cases at once. A distinction associated with dark matter may be absent from unmediated human perception even though humans can infer dark matter through instruments, theory, and its observable effects. A table made of wood and a table made of stone may differ physically, yet remain interchangeable for a task in which material never enters the observer’s next state. A price stated as a percentage and the same price stated as a dollar amount may be economically equivalent while producing different human representations because framing activates different coordinates.

The world is therefore not composable because everything is the same. It is composable because differences can be represented, transformed, ignored, or made consequential under one formal program.

Composite actors

A corporation requires a separate construction.

Let \(C\) be a corporation and let \(\mathcal J_C(t)\) be the set of relevant people participating in it at time \(t\). For each member \(j\), define the abstract person-state available to the conceptual construction by

Let

• \(\mathsf{Facts}_{C,t}\) denote facts and statistics about the corporation;
• \(\mathsf{Org}_{C,t}\) denote role, authority, governance, and communication structure;
• \(\mathsf{Mem}_{C,t}\) denote institutional memory;
• \(\mathsf{Inc}_{C,t}\) denote incentives, constraints, and active objectives;
• \(\mathsf{EnvHist}_{C,t}\) denote historical environmental exposure already absorbed into the corporation’s organization.

Define the conceptual composite state by

\(\mathcal A_{\mathrm{corp}}\) is not an average. It is an aggregation mechanism that should respect authority, information flow, coalition structure, veto rights, incentives, and the fact that most employees do not contribute equally to every corporate action.

Once this amalgamation has persistence, memory, a boundary, channels through which propositions enter, and a repeatable way of producing outward responses, it acquires a characteristic—almost feel-like—way of dealing with the world. For a corporation, “experience” means the state made institutionally available through its people, records, systems, incentives, and communication paths; it does not automatically mean phenomenal consciousness. The construction only needs to justify treating the corporation as an actor at the level of prediction.

The model never observes the complete conceptual state. Let \(\mathcal J_C^{\mathrm{obs}}(t)\subseteq\mathcal J_C(t)\) be the usable member subset, let \(\mathbf u_{C,t}^{\mathrm{corp}}\) collect measurable company-side evidence, and let \(\mathbf m_{C,t}^{\mathrm{miss}}\) encode missing membership, authority, and company fields. The learned estimate is

Let \(\boldsymbol\Xi_{C,t+1}\) denote the random exogenous corporate change before the next decision epoch and \(\boldsymbol\xi_{C,t+1}\) a realized or supplied scenario value. Its fitted transition law can then be written in the same outer form:

The outer algebra is shared. The internal construction is not.

For the present paper, however, humans remain the first target. Corporations enter the first application as structured context around the people acting through them. Later, the same data can be reorganized so that the corporation itself becomes the center of prediction.

Creating the World Model

A world model, in the present sense, is not a copy of physical reality. It is a learned simulator of actor, company, and relationship transitions under propositions.

The first application domain is go-to-market interaction because it produces repeated transitions, clear timestamps, and measurable outcomes.

Consider the actual problem.

Salesperson A, working at Company A, is trying to sell a product to Executive B, working at Company B. To keep the formal labels from eating each other, I will write the salesperson as \(a\), the executive as \(b\), the salesperson’s company as \(C_a\), and the executive’s company as \(C_b\).

The system must rank a sequence of propositions using the history of both people, the features of both companies, the relationship between them, and the environment in which the transaction is unfolding.

For each human \(i\in{a,b}\), define the estimated person-side substate by

The current world vector will appear once at the dyadic level rather than being copied into each person tuple.

Let

be the relevant company-state representations, and let

denote the estimated relationship state between the two sides: prior contact, familiarity, trust, perceived authority, commitments, objections, response history, sender reputation, channel history, and prior commercial interaction.

Define the filtered operational dyadic state by

This is the state type the first world model should operate on. The hats matter: this is the estimate available to the system before proposition \(x_t\), not the unknowable complete state of either person or corporation.

When a focal person also contributes to the learned company summary, the dyadic tuple contains a deliberate redundancy. An implementation should either exclude that focal person from the company-context summary, or estimate the person and company states jointly so the duplicate path is not treated as independent evidence.

The proposition is also structured. Write

Let \(\boldsymbol\Xi_{t+1}\) denote random exogenous changes between decision epochs and \(\boldsymbol\xi_{t+1}\) a realized or supplied scenario value: market movement, personnel change, company change, or anything else that is not generated by the dyadic action alone. Expressions of the form \(K(\cdot\mid\boldsymbol\Xi=\boldsymbol\xi)\) mean kernel evaluation at a supplied scenario value, not conditioning on a necessarily positive-probability point event. The notation \(K_{D,\theta}\) below is shorthand for the typed encoder–interaction–transition factorization defined explicitly in Algorithm 2. The single-step transition is

The immediate observable trace is

This readout makes the usual state-space assumption that the simulated next state is sufficient for the immediate trace. If that assumption is too strong for an implementation, use the more general kernel \(R_{O,\theta}(\cdot\mid\widetilde D_{ab,t+1},\widehat D_{ab,t},X_t=x_t)\) and test whether the extra conditioning is needed.

The trace variable \(O_{t+1}\) summarizes the records attributed to the interval \((t,t+1]\); several timestamped records may contribute to one trace bundle. It may include reply, silence, objection, meeting acceptance, forwarding behavior, a change in deal stage, a change in sentiment, or an internal action at Company \(C_b\).

The output of the transition is the same state type needed by the next transition. This is what makes the model recursively usable rather than a one-step decoder that cannot be composed.

Before an outcome is observed, the model simulates:

After actual records arrive, the model filters or updates its estimate:

where \(\mathcal H_{(t,t+1]}\) is the collection of response, company, relationship, and environmental records that became available between the two decision epochs. Actual exogenous changes are included in this record set rather than passed to the filter a second time.

Simulation and filtering are different operations. The first asks what might happen. The second changes what we believe after something actually happened.

For a sequence of propositions \(x_t,\ldots,x_{t+H-1}\), and an exogenous scenario path \(\boldsymbol\xi_{t+1:t+H}\), repeated application of the transition and readout kernels defines the trajectory law

Exogenous changes in the market, personnel, company condition, or world state must be supplied or modeled along the way. We do not get to pretend the future environment freezes merely because the recursion is convenient. When candidate propositions are compared under one ranking regime, they must be evaluated against the same declared exogenous scenario or the same action-invariant exogenous law. Otherwise a change in the assumed environment can be mistaken for an effect of the proposition. Any future variable that is itself caused by the proposition belongs inside the state transition, not inside an exogenous law that is held fixed across candidates.

For a task outcome measured at horizon \(\Delta\), write the fitted predictive law as

This law may be implemented by a direct head or induced by rolling the state model forward and applying an outcome functional to the resulting trajectory. For a horizon extending beyond the next decision epoch, it is defined only relative to a declared continuation policy, future candidate-set process, exogenous-path law, and censoring convention unless those quantities are conditioned on explicitly. A direct head must be calibrated to the same regime. The notation does not pretend that a 90-day close is literally an immediate emission one step after an email.

Nothing in this framework commits us to one architecture. The transition kernel may be implemented by a linear state-space model, a recurrent model, an attention-based model, a structured probabilistic model, or a neural system that combines several of these. Sequence models in the Mamba family are one candidate because they compress long histories into an evolving state, but they do not define the theory. They are implementation options inside it.

What matters most at the outset is not architectural ambition but a working procedure.

Algorithm 1: Estimate the actor and relationship state

Choose a task \(\tau\) and a horizon \(\Delta\).

Estimate the slow and fast person-side states for salesperson \(a\) and executive \(b\). Construct company representations from available organizational facts, statistics, roles, incentives, member states, and histories. Construct relationship state from all pre-proposition interactions.

This produces

Algorithm 2: Encode the proposition and predict the transition

Encode the structured proposition:

Compute its actor-relative representation for executive \(b\) inside the full dyadic context:

Encode the current dyadic state and form the interaction:

Then predict the next state distribution:

The shorthand

will be used whenever the encoder–interaction factorization is not the point.

Decode immediate traces from the next state:

For delayed primary outcomes and auxiliary probes that must be used jointly, define a coherent regime-specific law

The horizon-specific primary and probe heads

are marginals or conditionals of this joint law when a joint law is modeled. Separate marginal heads are adequate for separate losses and marginal expectations; they do not define cross-head dependence unless a coupling or conditional-independence assumption is declared.

Algorithm 3: Update from error

Observe the matured primary outcomes and probe labels. Minimize

with

Masks, censoring weights, or survival likelihood contributions belong inside the relevant head loss. The positive signs matter. These are losses and penalties being minimized. Writing negative signs would reward the model for making them larger.

Update the parameters by gradient descent,

or update a posterior distribution over parameters in a Bayesian implementation.

Then update the fast person states and relationship state using the actual observed records. Refresh slow person and company states only when durable evidence accumulates.

Algorithm 4: Detect drift and reopen discovery

No implementation should be assumed stable forever. If the market changes, the product changes, the organization changes, incentives shift, or a once-inert distinction becomes active, model quality will decay.

Compare recent loss and calibration with reference windows. When degradation persists, reopen the discovery process: add candidate features, revise the company aggregation, reweight existing coordinates, expand the proposition representation, or rebuild the task projection.

This is the correct sense in which the framework is open-ended. The framework is not rescued from every failure by saying the first implementation was weak. Specific implementations are falsified when they fail. The broader program survives only if it keeps generating better testable representations rather than excuses.

From Forecasting to Proposition Search

This is the place where I stop pretending the point of the machinery is merely to admire prediction metrics.

The practical purpose of the framework is not only to forecast outcomes, but to compare admissible candidate propositions by their expected effect on the next state and downstream objective. Otherwise why the hell are we building it.

Let \(\mathcal X_t^{\mathrm{adm}}\) denote the admissible proposition universe and let \(\varnothing\ne\mathcal X_t^{\mathrm{cand}}\subseteq\mathcal X_t^{\mathrm{adm}}\) be the set actually available for scoring at decision \(t\). Let \(U_\tau\) be a declared measurable utility over predicted trajectories, outcomes, probe variables, cost, and policy constraints, and assume it is integrable under every model and evaluation regime being compared.

A value over more than one future decision is undefined until the evaluation regime is declared. Let \(\mathfrak e\) contain at least:

• a continuation policy \(\pi^{\mathrm{cont}}\) after the candidate proposition;
• the process that supplies future candidate sets;
• an exogenous-path law \(\mathbb Q_{\Xi}\);
• and the outcome, censoring, and terminal-utility convention used by the score.

For model-based predictive ranking, define

The tilded outcome and probe bundles are either measurable functionals of the same simulated trajectory or draws from the coherent joint kernel \(P_{YZ,\theta,\mathfrak e}\). If only marginal heads exist, the utility uses marginal expectations or an explicitly declared coupling. They are not independent duplicate futures. Candidate ranking chooses

This argmax exists automatically for a nonempty finite candidate set. For a continuous candidate space, existence requires conditions such as compactness and upper semicontinuity; otherwise the mathematically correct target is a supremum or an approximate optimizer. In deployment the score should also be constrained by support, uncertainty, policy rules, and the cost of simulator exploitation; the highest unconstrained point estimate should not automatically win.

But the actual sales problem concerns a sequence of propositions. The best first move may not be the message with the highest immediate meeting probability. It may be the message that reveals uncertainty, establishes legitimacy, changes perceived risk, or makes a later proposition more effective.

Let the policy be

Let \(\mathfrak P_{\mathrm{adm}}\) be the nonempty admissible policy class, let \(\gamma\in[0,1]\), and let \(\mathbb Q_{\Xi}\) be the declared exogenous-path law and \(\mathbb Q_{\mathcal X}\) the future candidate-set law. For a planning length \(H\), define a step utility \(u_\tau^{\mathrm{step}}\) and terminal value \(V_\tau^{\mathrm{term}}\). Then

where the expectation also covers the future candidate-set process declared by the planning regime. The policy-search problem is

when a maximizer exists; otherwise write \(\sup_{\pi\in\mathfrak P_{\mathrm{adm}}}\). This avoids the common stupidity of copying one eventual close backward and awarding it independently to every prior message. Credit assignment belongs to the trajectory.

The first implementation does not need to solve unconstrained long-horizon persuasion. A reasonable progression is:

1. one-step ranking among controlled proposition families;
2. ranking short predefined sequences;
3. adaptive next-best-action after each observed response;
4. longer-horizon policy optimization after the transition model and intervention design are trustworthy.

This gives us three distinct epistemic regimes.

First, there is forecasting: estimate what is likely to happen after the proposition that was actually delivered.

Second, there is model-based ranking: use the forecasting model to simulate and order candidate propositions. This is useful, but it is still only as good as the model and the support of the data.

Third, there is interventional policy improvement: choose propositions and claim that choosing them causes better outcomes. This requires an experimental or otherwise defensible causal identification design. When logged data are used, it also requires the assignment probabilities or densities recorded at decision time, sufficient overlap, consistency, appropriate handling of interference and censoring, and an estimator matched to the one-step or sequential regime.

The predictive conditional quantity is

The causal quantity is

or equivalently the potential-outcome law

where \(\mathfrak e\) fixes the downstream continuation, candidate-set, exogenous, and censoring regime after the current proposition. The corresponding causal value under that same declared regime is

These are not interchangeable without an identification argument. The causal ambition is to choose propositions that change behavior. The engine underneath that ambition is forecasting. The causal claim begins only when the data collection process and assumptions let the forecasting architecture estimate an interventional law.

Until then, leave the causal swagger out of it. The system may still be useful. It is useful as a forecasting, simulation, and ranking device rather than as a proven controller.

Closing Part 3

Part 1 argued that reality, as it appears to an organism, is not a mirror of noumena but the output of an evolved representational structure. Part 2 showed how that structure can be individualized, historically deformed, estimated from observable traces, and split into slow and fast state. Part 3 completes the descent into an operational world model.

The ideal object remains the next phenomenal state. The practical object is a predictive actor-state. GIDS supplies coordinates of possible distinction; it does not contain a warehouse of primitive people, propositions, and corporations. Those objects are constructed from patterns and relations in the space. Their interaction is modeled as a state transition. The resulting state can be simulated, compared against outcomes, decoded into probes, and updated under error.

For the first domain, the whole ambition can be written as

The three lines are simulation, delayed prediction, and filtering. They are related; they are not the same operation.

And if proposition search is turned on,

That is the whole ambition of this section. Not a complete algebra of mind, but a way to build one without lying about what has and has not been solved.

OK, it is time to get serious now.