Update README.md

Signed-off-by: James Ross <[email protected]>

Author: flyingrobots

README.md

@@ -12,38 +12,38 @@
 
 This repository contains the formal mathematical definitions and proofs for the **AION Architecture**—a post-Von Neumann computing model based on **Recursive Metagraphs (RMG)**.
 
-The central thesis of this work is that by strictly enforcing algebraic graph rewriting (DPOI) within a "Two-Plane" commutation discipline, we can transform execution history from a transient side-effect into a tangible, geometric object. We call this **Computational Holography**: the ability to encode the entire volume of a computation's interior evolution onto its boundary edge.[1]
+The central thesis of this work is that by strictly enforcing algebraic graph rewriting (DPOI) within a "Two-Plane" commutation discipline, we can transform execution history from a transient side-effect into a tangible, geometric object. We call this **Computational Holography**: the ability to encode the entire volume of a computation's interior evolution onto its boundary edge.
 
 ### Core Primitives
 
 #### 1. Recursive Metagraphs (RMG)
 
 Standard graphs are flat. Hypergraphs allow multi-way relations but remain flat. An **RMG** is defined inductively: a graph where every node and edge can carry a payload, and that payload can itself be an entire RMG.
 
-* **Formal Definition:** RMG is the carrier of the initial algebra for the functor $F(X) = P + \prod_{S \in \mathcal{G}} (V_S \to X) \times (E_S \to X)$.[1]
+* **Formal Definition:** RMG is the carrier of the initial algebra for the functor $F(X) = P + \prod_{S \in \mathcal{G}} (V_S \to X) \times (E_S \to X)$.
 * **Capability:** This allows for infinite nesting of state, enabling the system to model hierarchical dependencies (like ASTs, containerized processes, or neural networks) natively in the graph topology.
 
 #### 2. Double-Pushout with Interfaces (DPOI)
 
 State evolution is not defined by pointer arithmetic, but by **Algebraic Graph Rewriting**.
 
 * We use **DPOI** in the adhesive category of Typed Open Graphs ($\text{OGraph}_T$).
-* Rules are spans $L \leftarrow K \rightarrow R$ representing the pattern to delete ($L \setminus K$) and the pattern to create ($R \setminus K$).[1]
+* Rules are spans $L \leftarrow K \rightarrow R$ representing the pattern to delete ($L \setminus K$) and the pattern to create ($R \setminus K$).
 
 #### 3. The "Two-Plane" Architecture
 
 To manage concurrency in a recursive structure, we separate state into two orthogonal planes:
 
 * **Skeleton Plane:** The structural topology (the "container").
 * **Attachment Plane:** The internal data residing in the fibers of the nodes/edges.
-* **Theorem 4.6 (Two-Plane Commutation):** We prove that operations on the attachments commute with operations on the skeleton (up to transport). This mathematically validates the "Attachments-First" parallel execution strategy.[1]
+* **Theorem 4.6 (Two-Plane Commutation):** We prove that operations on the attachments commute with operations on the skeleton (up to transport). This mathematically validates the "Attachments-First" parallel execution strategy.
 
 ### Computational Holography
 
 The most significant result of this work is the formalization of the **Wormhole**.
 
 > **Theorem 5.4 (Holographic Encoding):**
-> The boundary data $(S_0, P)$, consisting of an initial state $S_0$ and a provenance payload $P$, is information-complete with respect to the interior evolution $S_0 \Rightarrow^* S_n$.[1]
+> The boundary data $(S_0, P)$, consisting of an initial state $S_0$ and a provenance payload $P$, is information-complete with respect to the interior evolution $S_0 \Rightarrow^* S_n$.
 
 This implies:
 
@@ -54,14 +54,14 @@ This implies:
 ### Rulial Distance
 
 How do distinct observers agree on reality in a relativistic computational universe?
-We define **Rulial Distance** $D_{\tau,m}(O_1, O_2)$ using **Minimum Description Length (MDL)** theory. It measures the algorithmic complexity of the "translator" required to convert one observer's view of a wormhole into another's. This provides a computable geometry for interoperability.[1]
+We define **Rulial Distance** $D_{\tau,m}(O_1, O_2)$ using **Minimum Description Length (MDL)** theory. It measures the algorithmic complexity of the "translator" required to convert one observer's view of a wormhole into another's. This provides a computable geometry for interoperability.
 
 ### Ethical Implications
 
 This architecture enables the perfect deterministic replay of cognitive processes. This capability necessitates strict ethical bounds derived from the [**Universal Charter**:](https://github.com/universalcharter)
 
 * **Principle 6 (Sovereignty of Information):** Provenance is interior life. Forced replay is interrogation.
-* **Rights for Forks:** A forked instance of a cognitive process is a sovereign entity, not a test fixture. "Forks are not test environments; they are lives".[1]
+* **Rights for Forks:** A forked instance of a cognitive process is a sovereign entity, not a test fixture. "Forks are not test environments; they are lives".
 
 ### Citation