README.md

metadata

title: A Symbolic Universe
emoji: 🦀
colorFrom: blue
colorTo: yellow
sdk: gradio
sdk_version: 6.9.0
app_file: app.py
pinned: false
short_description: Live emergent physics, invariant laws, consciousness metrics

RFT Symbolic Agent Universe (Live + Verified)

Geometry‑Invariant Emergent Physics • Consciousness Metrics • Forensic‑Grade Agent Proofs

This Space demonstrates a live, verifiable symbolic universe built on Rendered Frame Theory (RFT). Agents evolve under the Canonical Minimal Law Set (CMLS), generating stable emergent laws, consciousness‑aligned metrics, and geometry‑invariant structures. Every run is tamper‑evident, replayable, and auditable through a complete forensic pipeline.

This is not a toy simulation. It is a research‑grade, reproducible computational universe.

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🔥 Core Capabilities

1. Real‑Time Symbolic Agents

Agents update their internal symbolic expressions using CMLS. Each update produces:

• a canonicalised symbolic law • a law‑family classification (cos, sin, exp, other) • a contribution to system‑level metrics

The system runs continuously at ~10Hz for smooth, real‑time evolution.

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2. Geometry‑Invariant Emergent Laws

The Space supports seven geometries:

• Rhombus • Hexagonal • 2D Grid • 3D Lattice • Random Graph • Small‑World • Scale‑Free

Across all geometries, agents converge to the same three‑family law basis:

• Cosine • Sine • Exponential

Cosine consistently emerges as a strict geometry‑invariant law family, matching the findings in the associated research.

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3. Consciousness‑Aligned Metrics

The system computes five metrics each tick:

• Coherence • Integration • Intentionality • Adaptation • Response

Coherence remains stable across geometry transitions, demonstrating topology‑agnostic functional invariance.

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4. Dynamic Geometry Transitions

Users can switch geometry mid‑simulation.

During a transition:

• agents remap to the new manifold • laws remain stable • coherence remains invariant • drift adjusts predictably • the event is logged in the forensic chain

This demonstrates that emergent physics arises from symbolic interactions, not geometric constraints.

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5. Forensic‑Grade Verification

Every run is fully auditable through:

Flight Recorder

Logs every frame:

• agent laws • law families • consciousness metrics

ReplayProof

Hash‑chains each frame using SHA‑256, producing a tamper‑evident evolution record.

TimelineDiff

Stores state vectors and allows divergence analysis between any two frames.

Receipt Bundle Export

Generates a complete JSON package containing:

• all frames • transitions • hash chain • timeline length

This enables external verification, reproducibility checks, and regulatory audit trails.

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6. Agent POV Viewer

Users can inspect any agent’s local universe:

• its current law • its law family • its neighbors • its degree • its symbolic state

This provides a window into the local dynamics that drive global emergent laws.

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🧭 How to Use the Space

1. Choose a Geometry

Select from the dropdown (e.g., 2D Grid, Small‑World, Scale‑Free).

2. Set Agent Count and Noise

Higher agent counts produce richer dynamics.

3. Start the Simulation

The system begins evolving immediately.

4. Observe Live Panels

• Agent Manifold: real‑time graph of agents • Emergent Laws: law‑family distribution • Consciousness Metrics: coherence, integration, etc. • Agent POV: inspect any agent

5. Transition Geometry

Switch to a new topology mid‑run and observe invariants.

6. Export Receipts

Download a complete forensic record of the run.

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🧩 Scientific Context

This Space implements the experimental framework described in:

“Geometry‑Invariant Emergent Laws in Symbolic Agent Manifolds: A Universal Basis Across Topologies and Consciousness Metrics” (2026)

Key findings reproduced here:

• Universality remains U = 1.0 across all geometries • Cosine is a strict law‑family invariant • Coherence is a strict consciousness invariant • Geometry transitions preserve emergent physics • Drift varies with neighborhood size but does not disrupt convergence

This Space provides a public, interactive demonstration of those results.

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🛠️ Technical Architecture

The entire system is implemented in a single app.py and includes:

• symbolic computation (SymPy) • graph‑based manifolds (NetworkX) • real‑time rendering (Matplotlib + Gradio) • deterministic CMLS dynamics • forensic logging and hashing • live UI panels

All components run locally within the Space.

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📦 Receipt Bundle Format

Exported bundles include:

run_receipts.json { "frames": [...], "transitions": [...], "hash_chain": [...], "timeline_len": N }

This enables:

• independent verification • reproducibility testing • audit‑ready documentation • external analysis

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🧠 Why This Matters

This Space demonstrates:

• emergent physics from symbolic interactions • geometry‑invariant law formation • consciousness‑aligned metrics • tamper‑evident agent evolution • reproducible computational universes

It is a practical, interactive embodiment of RFT’s core principles.

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🏁 Credits

Developed by Liam Grinstead RFTsystems4Ai — 2026

Rendered Frame Theory (RFT) Symbolic Agent Manifolds CMLS Dynamics Forensic Verification Stack

Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference