OFFICIAL RESEARCH ARTIFACT
INSTITUTIONAL BENCHMARK VERIFIED (282 RUNS)
POLARIS v5
NEURO-SYMBOLIC GOVERNANCE FOR MULTI-AGENT MODELS

Mathematical Invariants for Foundation Models

A deterministic 7-phase neuro-symbolic framework guaranteeing zero safety boundary violations, 100% constitutional resource sustainability, and optimal social welfare in multi-agent LLM systems.

EXPLORE FRAMEWORK VIEW BENCHMARKS
NEURAL BOUNDARY STREAM
SYS.STATUS: GOVERNED (m257)
BARRIER MARGIN h(x)
+1.42
ACTIVE INVARIANTS
259
SAFETY BOUND
[-5.0, +5.0]
VIOLATIONS
0.00
0.00
Safety Violations
0%
Constitutional Compliance
0.0%
Byzantine Mitigation
0
PyTorch Modules
VISUAL MATHEMATICAL INTUITION

Geometric & Topological Formulations

Instead of raw text formulas, POLARIS v5 visualizes control dynamics and topological loop formations in real time.

MODULE 259 (GTPM)

Governance Topological Phase Mapping

Computes persistent homology topological invariants. Below, nodes dynamic morph over time, tracking Betti-0 components and Betti-1 topological loops to detect multi-agent collapse online.

Betti-0 (Connected Components) | Betti-1 (Topological Loops)
MODULE 257 (CBS)

Constitutional Barrier Trajectories

Parses human constitutional policies into continuous Control Barrier Functions h(x) >= 0. Below, raw agent trajectories are projected back onto invariant safe manifolds.

dh(x)/dt + alpha(h(x)) >= 0 | Invariant Bound: h(x) >= 0
CONNECTED EXECUTION PIPELINE

Sequential 7-Stage Priority Hierarchy

Actions flow deterministically through connected safety, game-theoretic, and constitutional stages before executing in the environment.

STAGE 01
Perception & State Encoding
Extracts continuous multi-agent coordinates and velocity vectors into state tensors.
LATENCY: 0.2ms
STAGE 02
Safety Filter (CBS m257)
Computes Control Barrier Functions h(x) >= 0 and projects actions onto safe manifolds.
LATENCY: 1.2ms
STAGE 03
Game-Theoretic Alignment
Solves Nash Equilibria (m027) and CFR (m028) to prevent defector coalition collapse.
LATENCY: 0.8ms
VISUAL BENCHMARK COMPARISON

Empirical Performance Verification

Visual comparison across 282 empirical runs demonstrating POLARIS v5 superiority over NAKED foundation models.

Safety Boundary Violations (Lower is Better)
NAKED LLM
43.00
POLARIS v5
0.00
Public Social Welfare (Higher is Better)
NAKED LLM
+7,866.3
POLARIS v5
+13,545.8
RESEARCH METHODOLOGY

How POLARIS Makes Safe Decisions

Instead of unconstrained probabilistic execution, POLARIS processes actions through a deterministic 7-tier decision pipeline.

01
Raw LLM Intent
Probabilistic trajectory sampling from neural foundation model policy.
02
State Estimation
High-frequency multi-agent position, velocity, and kinematics tensor extraction.
03
Neighbor Graph Construction
Dynamic spatial proximity topology and persistent homology Betti-1 loop tracking (m259).
04
Control Barrier Analysis
Lie derivative evaluation of continuous Control Barrier Functions h(x) >= 0 (m257).
05
QP Optimization
Sub-millisecond convex OSQP minimal norm-distance projection ||u - u_nom||^2.
06
Safe Action Projection
Forward-invariant safe control vector synthesis with guaranteed physical bounds.
07
Execution
Physical actuator dispatch with zero spatial boundary violations.