This is the most critical question. A framework, no matter how elegant, remains speculation until it can be grounded in formalism and produce testable results. The path from the current conceptual document (v1.9) to a scientific theory is long, but it can be broken down into clear, priority-ordered phases. Here are the priority next steps, structured as a multi-phase research program. --- ### **Phase 1: Foundational Formalism - The "Toy Model"** **Objective:** To move from English descriptions to a working mathematical and computational model. The goal here is **not** to replicate the real universe, but to prove that the core principles can work at all in a simplified, formal system. 1. **Define the Primitives Mathematically.** * **Action:** Represent Distinctions (D) and Relations (R) using a formal structure. The most natural starting point is an **Attributed Dynamic Graph**. * **Distinctions (D)** become **nodes** in the graph. * **Relations (R)** become **directed edges** between nodes. * **Formalize Proto-properties.** Represent them as **attributes** (data) attached to the nodes and edges. For example, a node might have `[ID: 123, ProtoPolarity: +1, ProtoValence: 3]`. An edge might have `[Type: 'strong-link', FlowResistance: 0.5]`. 2. **Formalize a Minimal "Cosmic Algorithm".** * **Action:** Define a small, core set of the proposed rules as **Graph Rewriting Rules**. These are precise, automatable operations that transform the graph. * **Priority Rules to Formalize:** * **`GenesisRule(p)`:** A stochastic rule for adding new D/R pairs to the graph. * **`FormationRule(D1, D2)`:** A rule that creates an R edge between two D nodes if their proto-properties are compatible. * **`AnnihilationRule(R)`:** A rule that removes an R edge and its D nodes if they form a logically inconsistent or unstable pair (e.g., `D(+1)` and `D(-1)` annihilating). 3. **Formalize Ontological Closure (OC).** * **Action:** This is the most crucial step. Define OC as a precise, measurable property of a subgraph. * **Possible Definitions:** * **Fixed Point:** A subgraph is "closed" if, for a certain number of simulation steps, the internal rewrite rules no longer change its structure. It has reached a stable state. * **Limit Cycle:** A subgraph is "closed" if its structure oscillates between a finite set of states (this would be an S₃-type stability). * **Tension Minimization:** Define a "Relational Tension" function for any subgraph (e.g., based on unbalanced proto-polarities or unsatisfied proto-valences). A subgraph achieves OC if it represents a local minimum of this tension function. 4. **Build the *Autaxic Generative Engine (AGE) v0.1*.** * **Action:** Implement the attributed graph, the rewrite rules, and the OC definition in a computer simulation. * **Deliverable:** A running program—a "digital petri dish"—that starts with a random "foam" of D's and R's and applies the rules. The primary research question is: **Does this system spontaneously generate stable, non-trivial subgraphs that satisfy the OC condition?** --- ### **Phase 2: Derivation and Validation - The "Bridge to Physics"** **Objective:** To use the toy model (AGE v0.1) to derive analogues of simple physical phenomena. This phase is about building a bridge between the abstract formalism and recognizable physics. 1. **Derive the AQN Analogues.** * **Action:** For any stable subgraph (a "particle") that emerges in the simulation, formalize the calculation of its AQNs. * **C (Complexity):** The number of nodes and edges in the stable subgraph. * **T (Topology):** A vector of topological invariants of the subgraph (e.g., its cyclomatic number, symmetry group, degree distribution). * **S (Stability):** A measure of the subgraph's resilience. This can be quantified by calculating the "depth" of its attractor basin in the simulation's state space or by "pinging" it with random relational noise and measuring its mean lifetime. * **I_R (Interaction Rules):** The specific set of graph rewrite rules that this stable subgraph can participate in with other stable subgraphs. 2. **Search for Emergent Conservation Laws.** * **Action:** Run the simulation and analyze the interactions between emergent "particles." Check for conserved quantities. * **Example:** If particles interact and transform, is the total `C` of the system conserved? Is the sum of all `ProtoPolarity` attributes conserved? * **Goal:** To demonstrate, for example, that "Charge Conservation" emerges naturally from a symmetry in the `ProtoPolarity` rules, providing a concrete analogue of Noether's Theorem. 3. **Derive a Minimal "Autaxic Table".** * **Action:** Run the simulation many times and catalogue all the types of stable "particles" that emerge. * **Deliverable:** The first-ever derived Autaxic Table, even if it's for a toy universe (e.g., "Our simulation produces three stable particle types: a low-C 'photon-analogue', a medium-C 'electron-analogue', and its 'positron' counterpart."). --- ### **Phase 3: Expansion and Prediction - Towards a Scientific Theory** **Objective:** With a validated formal core, expand the model to approach the complexity of the real world and generate novel, falsifiable predictions. 1. **Scale Up the Model (AGE v1.0).** * **Action:** Systematically add more proto-properties and more complex rules to the simulation, guided by the goal of reproducing the known particle spectrum (leptons, quarks, bosons). The key is to find the *minimal* set of additions that generates the required complexity. * **Research Question:** What is the simplest set of proto-properties and rules that can generate both "fermion-like" (stable, S₂) and "boson-like" (transient, mediating I_R) patterns? 2. **Identify Novel Predictions.** * **Action:** As the model generates analogues of the Standard Model particles, rigorously analyze any other stable patterns that emerge. * **Example:** If the simulation that produces an "electron" and "up quark" also consistently produces a very high-C, neutral, S₆-stable pattern, then the properties of this simulated pattern become the **concrete, quantitative prediction for the *auton*** (its mass from `C`, spin from `T`, lifetime from `S`, and interaction cross-sections from `I_R`). 3. **Engage with Experimentalists.** * **Action:** Translate the quantitative predictions into signatures that can be searched for at colliders (like the LHC) or in astrophysical data (from observatories like JWST, LIGO, or dark matter detectors). * **Example:** "Our model predicts a dark matter candidate (*auton*) that does not annihilate but should subtly alter the local gravitational lensing profile in a frequency-dependent way due to its interconverting states. This is a novel signature that can be searched for in galactic cluster surveys." By completing these three phases, the Autaxic framework would transition from a philosophical proposal into a testable, scientific research program. The speculative ideas would no longer be mere assertions but the direct, verifiable outputs of a self-consistent formal system.