Holonomy‑Induced Narrative Manifold • Reversible Story Physics • Geometric AI
🎨 Color Tiles Legend Documentation‑only tiles (not runtime glyphs):
- 🟦 A‑Layer — Geometric substrate
- 🟩 B‑Layer — Structural physics
- 🟧 C‑Layer — World + runtime
- 🟪 D‑Layer — UI documentation (system‑agnostic)
- 🟫 Phase‑D — Mathematical spine (preprint + appendices)
✨ Overview
The Fun‑Sphere Engine is a geometric narrative engine built on reversible operator flow, holonomy‑induced curvature, and trace‑preserving world‑state physics.
Instead of branching logic or scripted events, Fun‑Sphere treats narrative as
manifold traversal:
- Story actions → reversible operators
- Plot twists → holonomy curvature
- Zones → invariant submanifolds
- Factions → operator bundles
- Monsters → spectral perturbations
- Quests → reversible operator sequences
This repository contains:
- the geometric substrate (Wave‑A)
- world topology + spectral ecology scaffolds (Wave‑C)
- reversible quest compiler (Wave‑C)
- runtime stubs (Wave‑C)
- system‑agnostic UI documentation (Wave‑C)
- Phase‑D mathematical spine (complete) — preprint.md, appendices, glossary, references, provenance
It does not contain rendering logic, glyphs, HUD routing, or Godot Mobile UI.
🧠 Core Concepts
🟦 Neutral Manifold
Flat ND manifold with identity metric.
All narrative evolution begins here.
🟧 Holonomy Loops
Closed operator sequences that return to the same point
but transform the frame → narrative curvature.
🟩 Sovereign Submanifolds (Fun‑Spheres)
Regions where holonomy is non‑trivial.
These become zones, biomes, story pockets, or spectral wells.
🟥 Safety Membrane
Gradient‑based firewall preventing runaway instability.
If breached, the engine resets to equilibrium.
🧩 Features
🔹 Reversible Operator Engine Trace‑preserving diffusion + unitary operator flow.
🔹 Holonomy Zone Generator Detects curvature and forms sovereign narrative regions.
🔹 Spectral Monster Ecology
Eigenvectors → monster families
Eigenvalue drift → monster evolution
🔹 Faction Operator Bundles Operator‑bias families that shape world dynamics.
🔹 Reversible Quest Compiler Quests are operator paths with invertible outcomes.
🔹 System‑Agnostic UI Documentation Structural placeholders for future UI work (Fantasy Engine repo).
🟫 Phase‑D: Mathematical Spine (Complete) The geometric foundations are now fully documented:
- preprint.md
- Appendices A–E
- Glossary + overview
- Full references section
- Provenance clarification
This phase establishes the system‑agnostic geometric substrate for game engines and geometric AI research.
📦 Repository Structure
`
fun-sphere-engine/ │ ├── engine/ # geometric physics layer (Wave‑A) ├── world/ # zones, factions, monsters (Wave‑C) ├── quests/ # reversible narrative compiler (Wave‑C) ├── runtime/ # server + client scaffolds (Wave‑C) ├── ui/ # documentation-only placeholders (Wave‑C) ├── docs/ # architecture, provenance, explainers, notes └── preprint/ # Phase‑D mathematical spine (preprint.md + appendices) `
🚀 Getting Started
bash python3 runtime/server.py python3 runtime/client.py
These scripts provide minimal state scaffolding.
Full UI/HUD rendering will occur in the Fun‑Sphere Fantasy Engine (Godot Mobile).
📚 Citation
If you use Fun‑Sphere in research:
Hedling, B. (2026). Fun‑Sphere: A Holonomy‑Induced Submanifold for Reversible Narrative Ecologies. Zenodo.
https://zenodo.org/records/23635844
Hedling, B. S. (2026). Fun‑Sphere Engine: Geometric Foundations Preprint (v1.0). Zenodo.
https://doi.org/10.5281/zenodo.23653405
🧬 Provenance
🟦 Wave‑A — Geometric Substrate Introduced ND state, reversible operators, Laplacian geometry, holonomy, and structural physics primitives.
🟧 Wave‑C — World + Runtime + UI Documentation Introduced world containers, spectral ecology scaffolds, reversible quests, runtime stubs, architecture overview, and UI documentation placeholders.
🟫 Phase‑D — Mathematical Spine (Complete) Introduced the full geometric foundation:
- operator algebra
- holonomy + curvature
- Laplacian geometry
- spectral ecology
- quest‑path geometry
- appendices + glossary
- references + provenance
Documented in:
📄 preprint/preprint.md
🎮 Downstream: Fun‑Sphere Fantasy Engine (Godot Mobile)
A separate repository will implement:
- glyph atlas + visual grammar
- HUD routing
- emotional physics visualization
- adapter firewall indicators
- spectral ecology overlays
- VR/XR rendering surfaces
- full Godot Mobile UI
This engine will consume the geometric substrate defined here.
🟪 License
MIT License `