SSMS Master Recurrence: State Space Model Synthesis

Authors: Research Stack Team
Date: April 2026
Domain: TTM Layer J (Dynamics)
OTOM Version: 2.2

Abstract

The SSMS (State Space Model Synthesis) Master Recurrence provides the unified evolution equation for all agent states in the OTOM framework. It combines selective state space mechanisms with structured evolution rules.

1. Introduction

The Master Recurrence unifies all temporal evolution in OTOM through a single equation that governs agent state transitions across the manifold.

2. The Master Equation

S_{t+1} = \text{MLGRU}(\text{Gossip}(\text{Prune}(\text{Stabilize}(\text{Score}_{\Sigma+NK}(\text{Expand}(S_t))))))

2.1 Components

Component	Function
Expand	Generate candidate successor states
Score	Evaluate candidates using Σ+NK coupling
Stabilize	Apply conservation constraints
Prune	Remove unstable trajectories
Gossip	Share state across agents
MLGRU	Update via multi-layer gated recurrence

3. Unified Manifold-Blit Equation

For manifold-space shortcuts:

\mathcal{M}_{t+1} = \text{Blit}_{\text{manifold}}(\mathcal{M}_t, \Delta_{\text{field}})

4. Implementation

Lean 4 Modules:

SSMS.lean — Core state space mechanics
SSMS_nD.lean — N-dimensional extension
MasterEquation.lean — Formal verification
MLGRU.lean — Recurrence implementation

5. Theoretical Properties

Conservation: Energy and information invariants preserved
Convergence: Guaranteed under ACI conditions
Completeness: All valid states reachable

6. References

Gu, A., & Dao, T. (2023). Mamba: Linear-time sequence modeling.
Research Stack, OTOM Ontology v2.2.

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