:PROPERTIES:
:CREATED:  [2026-05-24 Sun]
:ID:       0d1e2f3a-4b5c-6d7e-8f9a-0b1c2d3e4f5a
:END:
#+title: The Middle Domain as World Models
#+filetags: :ideas:passepartout:world-models:

The middle of the knowledge tree — layers 8 through 14, from quantum chemistry approximations to molecular design heuristics — corresponds almost exactly to what the AI and robotics communities call world models. Recognizing this connection reveals a structural requirement for Passepartout that the current architecture does not explicitly address.

**What a world model is.**

In the AI sense, a world model is a predictive representation that an agent uses to anticipate the consequences of actions. It answers the question: if I do X, what happens next? The classic formulation decomposes this into:

1. A sensory encoder that compresses observations into a latent state
2. A dynamics predictor that predicts the next latent state given an action
3. A reward or value predictor that evaluates states

Every layer of the knowledge tree from 8 upward fits this description — it predicts how some aspect of reality evolves given initial conditions, parameters, and boundary conditions.

**The deductive world models (layers 0-7).**

Logic, algebra, analysis, classical mechanics, quantum mechanics, statistical mechanics, electrodynamics — these are world models where the dynamics are deductively complete. Given the state (a wavefunction, a phase space point, a metric tensor) and the equations of motion (Schrödinger equation, Hamilton's equations, Maxwell's equations), the time evolution is determined. No parameters to fit. No learning required. The model is provably correct against its axioms.

These are the world models that ACL2 can verify. The prover can confirm that the Schrödinger solver correctly implements the Schrödinger equation for any input. The correctness is total — not statistical, not empirical.

**The empirical world models (layers 8-14).**

Quantum chemistry approximations, molecular mechanics, molecular dynamics, solvation models, docking scoring functions, reaction mechanism models, molecular design heuristics — these are world models where the dynamics are known in form but empirically parameterized. The functional form of the force field (bond stretching + angle bending + torsions + non-bonded) is a modeling choice. The parameters (force constants, equilibrium lengths, partial charges) are fitted to data. The solvation model has a mathematical structure, but its parameters are calibrated against measured solubilities.

These world models cannot be verified against axioms. They can only be validated against experiment. The validation is always provisional — valid for the molecules and conditions tested, uncertain outside that domain.

**The composition is layered world models, not a single one.**

The critical structural insight: the world models are not independent. They form a dependency hierarchy.

A docking prediction (layer 12) depends on:
- A solvation model (layer 11) with its own parameters and validity domain
- A molecular dynamics simulation (layer 10) that samples conformational space
- A force field (layer 9) that predicts energies and forces
- Quantum chemistry calculations (layer 8) that parameterize the force field
- Statistical mechanics (layer 6) that relates ensemble averages to binding free energies
- Classical mechanics (layer 4) that governs the MD integration

Each layer's uncertainty propagates upward. The docking prediction's error is not the scoring function's error in isolation — it is the compound uncertainty of the force field, the solvation model, the conformational sampling, the MD integrator, and the scoring function, all composed.

**The Passepartout world model formula.**

A world model in Passepartout's architecture is a triple:

**World Model = Verified Equations ⊗ Provenance-Tracked Parameters ⊗ Validity Envelope**

- **Verified Equations** — the formal skeleton: the differential equations, the integration scheme, the force field functional form. Verified by the ACL2 prover against the deductive layer below. This is what the gate can definitively check.

- **Provenance-Tracked Parameters** — the numbers that make the model match reality: force constants, partial charges, solvation parameters, scoring weights. Each carries a source (experimental paper, QM calculation, benchmark dataset), a confidence interval, a validity regime (temperature range, molecular class, solvent type), and a last-validation date.

- **Validity Envelope** — the region of input space where the model has been experimentally validated. A force field parameterized for soluble proteins at 298K in water is valid there; applying it to a membrane protein at 350K in ethanol may produce plausible numbers with no physical meaning. The validity envelope is a learned or specified boundary that the gate checks.

**The neurosymbolic engine's role in world models.**

The neurosymbolic split maps onto world model construction and use as follows:

- The **ACL2 prover** verifies the equations — the form of the model, the correctness of the implementation, the composition of multiple world models into a pipeline. This is deductive assurance.

- The **LLM oracle** handles synthesis — selecting which world model to apply to a given problem, interpreting the model's output in natural language, generating hypotheses about why a prediction failed, proposing new parameterizations or model forms when the existing ones are insufficient.

- A **new provenance layer** (described below) handles the third component — tracking parameters, maintaining validity envelopes, propagating uncertainty, and validating predictions against experiment.

**What this changes in the architecture.**

The architecture describes verification (the gate) and knowledge (the memex). World models require a third subsystem: the **empirical knowledge base** — a structured store of fitted parameters, experimental benchmarks, and validity regimes, with full provenance.

The empirical knowledge base would:

1. Store every parameter used by every world model (force field parameters, DFT functional constants, solvation model coefficients, docking scoring weights).
2. Attach provenance to each parameter: the paper, dataset, or calculation it came from, the confidence interval, the validity domain.
3. Track validation history: which experimental measurements have been compared to this model's predictions, with what outcome, and whether the parameters were updated as a result.
4. Enforce validity regimes at the gate level: if a computation applies a model outside its validity envelope, the gate either blocks it (safe default) or flags it with a reduced confidence score.

This is not the same as the symbolic index (which stores formal facts) or the neural index (which stores embedding vectors). It is a third index over empirical knowledge — parameteric, uncertain, and provisional, but no less essential for its lack of deductive certainty.

**The connection to self-improvement.**

The neurosymbolic engine's self-modification capability applies differently to each part of the world model triple:

- **Verifying new equations** (updating the deductive core): the system generates a new algorithm, ACL2 proves it correct against the specification, it is hot-reloaded. This is the Mathematica-bootstrapping scenario — the system improves its own deductive world models autonomously.

- **Updating parameters** (improving the empirical core): the system compares predictions to experimental measurements, detects systematic bias in a force field, and proposes updated parameters. The update is validated by checking whether the new parameters improve predictions on a held-out benchmark. No proof, just statistical improvement. The provenance trail records the change.

- **Expanding the validity envelope** (learning where models work): the system accumulates computational predictions and experimental results, and learns the boundaries where each model is reliable. This is a continuous process, not a one-time formalization.

The self-improvement loop for empirical world models is slower and more uncertain than for deductive ones — it requires experimental feedback, not just formal verification. But it is equally essential for any system that needs to operate in the real physical world rather than inside a closed formal system.

**The test case.**

Schafmeister's spiroligomer pipeline is the test case for all three components:

- The **equations** — QM calculations (layer 8), force field predictions (layer 9), MD integration (layer 10), thermodynamic integration (layer 11), docking (layer 12), design rules (layer 14) — all need verified implementations.
- The **parameters** — force field parameters for novel monomer types, solvation parameters for non-standard solvents, scoring function weights for spiroligomer-protein binding — need provenance and validity envelopes.
- The **validation** — experimental binding assays, catalytic rate measurements, structural characterization (NMR, crystallography) provide the feedback that updates parameter confidence and expands validity regimes.

If Passepartout can handle this pipeline correctly — distinguishing what is verified from what is empirically parameterized, tracking provenance through the composition of multiple world models, and propagating uncertainty from the bottom of the hierarchy to the top — then the architecture is complete. If it cannot, then the architecture only works for pure mathematics.

**Summary.**

| Layer | Type of world model | Verification mode | Key data |
|---|---|---|---|
| 0-7 | Deductive | ACL2 proof against axioms | Theorems, equations, algorithms |
| 8-14 | Empirical | Validation against experiment | Parameters, benchmarks, validity envelopes |
| All | Composed | Provenance + correctness | Traceability through pipeline |

The middle domain is world models. The architecture needs to be built to reflect that.

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- [[id:9c0d1e2f-3a4b-5c6d-7e8f-9a0b1c2d3e4f][The Middle of the Knowledge Tree]] — the layers from logic to nanotechnology
- [[id:1c3ec48b-446c-50d2-b53e-126a81f5143f][Passepartout Architecture]] — current architecture
