Update README.md

README.md

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 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.
+
+---
+
+🔥 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.
+
+---
+
+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.
+
+---
+
+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.
+
+---
+
+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.
+
+---
+
+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.
+
+---
+
+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.
+
+---
+
+🧭 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.
+
+---
+
+🧩 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.
+
+---
+
+🛠️ 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.
+
+---
+
+📦 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
+
+
+---
+
+🧠 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.
+
+---
+
+🏁 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