primefoldtheory

Prime Fold Theory — Research Modules

Author: Sean Sowden
Website: primefoldtheory.org

Prime Fold Theory (PFT) is a structural ontology for physics that builds the universe from an information-zero baseline, rather than assuming spacetime, fields, or energy.

The hierarchy is:

• 0D — Prime Substrate
  Information-zero, no geometry, no time, no energy, no fields, no metrics.

• 1D — Prime Fold
  The first informational event (“power-on”), creating the arrow of time and activating three primitives:
  • Fold-Time τ̄ — tension-like accumulation with reset at collapse,
  • Fold-Density Φ — informational/structural loading,
  • Threshold κ — local collapse bound.

• 2D — Fold Field
  A discrete relational surface where geometry emerges as a behavior of the network (adjacency, distance, curvature-like patterns), not as a substance.

• 3D — Shells and Skew (Gravity)
  3D volume appears when regions of the Fold Field wrap or layer into shells. Imperfect layering produces skew — a structural imbalance that radiates outward with a natural (1/r^2) pattern. Gravity is interpreted as skew from shells, rather than curvature of a fundamental spacetime.

The traditional law-of-invariance program (Φτ̄ conservation between events with threshold resets) is preserved and developed in later modules, but now sits on top of this deeper ontological ladder.

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📖 Modules

Module 1 — The Prime Substrate (2025 Ontology Rewrite)

Status: Current canonical foundation (see module1/).

Defines:

• the Prime Substrate (0D, information-zero),
• the Prime Fold as the unique first event (1D),
• the Fold Field as the first geometric layer (2D),
• shells and skew as the origin of 3D volume and gravity.

Goals:

• Show that geometry is emergent, not assumed.
• Show that curvature is optional; skew from shells is sufficient for gravitational behavior.
• Place GR and QM as effective descriptions on top of the Fold hierarchy (rather than competing foundations).

Type: Ontology-first, theory foundation.

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Module 2.1 — Cross-System Simulation

Status: Simulation study (see module2.1/ or paper/ subtree if legacy).

Stress-tests Fold-Time invariance and threshold dynamics across multiple toy systems (e.g. SRF-like lattices, quake toys), dimensions, and parameter sweeps.

Key results:

• Normalized Fold-Time cycles (τ̄ with reset at κ) show structural invariance across different systems and conditions.
• Supports the idea that the Φ–τ̄–κ primitives behave consistently across heterogeneous substrates once mapped into the Fold framework.

Type: Simulation / numerical experiment.

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Module 2.2 — Mathematical Well-Posedness

Status: Math foundation module (see module2.2/ or paper/).

Establishes a rigorous backbone for Fold dynamics via the “Big Five” theorems:

1. Positivity
2. Existence & Uniqueness
3. Budget Closure
4. Reset Locality
5. Anti-Zeno

Includes:

• a minimal reference solver (fold_solver_1d.py),
• plotting / demo scripts,
• notes on verification and audit structure.

Type: Mathematical foundation and reference implementation.

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Module 5 — Quaoar: First Observable Fold-Shell Anomaly

Status: Empirical application (see paper/ subtree).

Applies Fold gravity / shell-skew interpretation to Quaoar’s ring system beyond the Roche limit.

Results:

• The ring location matches a predicted Fold-shell boundary rather than a classical Roche limit constraint.
• Extension of the same reasoning to Haumea and Chariklo suggests a wider class of ring–shell anomalies.

Type: Observational test / case study.

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Legacy / SRF-Era Drafts

Earlier drafts and SRF-centric formulations (e.g. the original Module 1 focused on the “Structural Recursive Field”) are preserved under the paper/ directory for historical and comparison purposes. These represent the 2024-era framing prior to the Prime Substrate / Prime Fold / Fold Field ontology rewrite.

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🔗 Resources

• Website: primefoldtheory.org
• Contact: Sean@PrimeFoldTheory.org

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📌 License

Copyright © 2025 Sean Sowden — All rights reserved.

This repository contains original theoretical work in progress under the Prime Fold framework, including terminology, structural models, symbolic definitions, and recursive formulations.

Redistribution is permitted for:

• Academic review
• Citation with attribution
• Endorsement requests

The following restrictions apply until formal release:

• Public reuse of equations, terminology, or structural models is not permitted
• Derivative works, translations, or republishing are not allowed
• Commercial use is strictly prohibited

For full terms, see the LICENSE file in this repository.
To cite this work or request collaboration, visit
https://primefoldtheory.org or contact
Sean@PrimeFoldTheory.org.

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