A persistent world engine must evolve its latent field without drifting into inconsistency or collapsing into rigidity. This creates a fundamental design tension:
- If updates are purely neural, the system becomes expressive but unstable.
- If updates are purely symbolic, the system becomes stable but non-generative.
The dynamics module Δψ must resolve this tension.
Δψ is not the physics of the system.
It is a proposal operator acting within a constrained dynamical system.
The actual physics emerges from:
- the constraint manifold C
- the invariants governing admissibility
- the projection operator Π_C
Field evolution is defined as a combination of intrinsic dynamics and neural forcing:
dM/dt = F_phys(M) + F_ψ(M, p, a, o)
Where:
- F_phys — intrinsic RSVP field dynamics (Φ, v, S coupling)
- F_ψ — neural forcing term (Δψ)
This produces a proposed update, not a valid one.
The system enforces consistency via projection:
M_{t+1} = Π_C( M_t + Δψ )
This ensures:
- invalid updates are corrected
- invariants are preserved
- global structure remains coherent
The projection acts as a semantic pressure solve, analogous to constraint enforcement in physics simulations.
The update can be expressed as a constrained optimization:
M_{t+1} = argmin_{Y ∈ C} ||Y - (M_t + Δψ)||²
This yields:
- maximal fidelity to the neural proposal
- strict adherence to admissibility
The system continuously balances:
- exploration (Δψ)
- correction (Π_C)
Without projection:
- drift accumulates
- conservation laws break
- topology becomes inconsistent
This manifests as hallucination and structural instability.
Without neural forcing:
- no new structure is generated
- system becomes rigid
- generalization fails
The system enforces rules but cannot create.
A stable system separates concerns into three layers:
-
Proposal Layer (Δψ)
- Generates candidate updates
- High expressivity
- May violate constraints
-
Constraint Layer (C)
- Defines admissible states
- Encodes invariants
-
Projection Layer (Π_C)
- Enforces global consistency
- Maps proposals onto valid states
This forms the fundamental loop:
proposal → projection → commit
Physics is encoded in:
- constraint manifold C
- conservation laws
- RSVP field coupling (Φ, v, S)
- projection operator Π_C
Δψ is allowed to temporarily violate these constraints, but violations cannot persist.
- mass consistency
- identity persistence
- causal locality
- topological admissibility
These define the manifold C.
- deformation behavior
- texture evolution
- motion patterns
- affordance transitions
These are modeled by Δψ and F_phys.
Each agent contributes:
- local forcing Δψ
- shared field M_t
- shared constraint manifold C
Conflicts are resolved through admissibility:
- only updates satisfying constraints survive
- no explicit consensus protocol required
This yields causal field synchronization instead of state replication.
A stable world satisfies:
M* = Π_C( M* + Δψ )
At this point:
- updates reinforce structure
- contradictions are eliminated
- the system becomes self-consistent
Traditional systems:
- state is primary
- rules act on state
RSVP–Polyxan systems:
- constraints are primary
- state is whatever satisfies them
Δψ acts as a perturbation within this constraint-defined space.
Δψ must be:
- neural in proposal (to generate structure)
- symbolic in admissibility (to enforce invariants)
- variational in resolution (to reconcile both)
Collapsing these roles leads to failure:
- pure neural → chaos
- pure symbolic → rigidity
Only the three-stage loop ensures stability:
proposal → projection → commit
This is the minimal architecture required for persistent, coherent, and generative world simulation.