## Project Summary

Flexion Dynamics is a unified operator-based framework for modeling stability, divergence, threshold behavior, and collapse in advanced systems relevant to long-term AI safety. The project aims to build the first simulation environment that uses bidirectional deviation operators (contractive and expansive dynamics) to identify failure modes, runaway behaviors, early-warning instability patterns, and structural points of no return in AI-related systems. This work provides a foundational tool for understanding systemic risks in complex intelligent systems.

---

## Goals and Path to Impact

### Project goals:

- Build a simulation engine that models system deviation using Flexionization (stabilizing) and Deflexionization (destabilizing) operators.

- Implement threshold-triggered instability and collapse detection.

- Generate empirical failure scenarios relevant to advanced AI systems.

- Integrate a simple AI-loop demonstrator showing runaway dynamics and recovery pathways.

- Publish all results and simulations open-access as part of Flexion Dynamics V1.2.

### Path to impact:

This work contributes directly to technical AI safety by:

- Identifying failure dynamics that current models cannot express.

- Providing a robust mathematical and empirical basis for analyzing collapse trajectories.

- Giving researchers tools for early-warning detection, risk profiling, and stability testing for high-capability systems.

- Opening a new class of operator-based control and monitoring methods.

Success will be measured by a functioning simulation environment, documented collapse scenarios, demonstrator outputs, and the full release of Flexion Dynamics V1.2.

---

## How the Funding Will Be Used

Funding supports a 30-day full-time research cycle:

- 55% — researcher stipend (including self-employment tax).

- 25% — compute resources (cloud GPU, simulation workloads).

- 15% — hardware for physical demonstrators (microcontrollers, sensors, robotic components).

- 5% — software, tooling, and documentation infrastructure.

Total project window: 30 days.

Outputs: complete simulation engine, empirical results, collapse datasets, updated theory.

---

## Team and Track Record

Researcher: Maryan Bogdanov (independent).

Track record includes:

- Flexionization Theory V1.5 — DOI: https://doi.org/10.5281/zenodo.17618947

- Deflexionization V1.0 — DOI: https://doi.org/10.5281/zenodo.17637758

- Flexion-Immune-Model V1.1 — DOI: https://doi.org/10.5281/zenodo.17624206

- FRE Risk Engine V1.1 — DOI: https://doi.org/10.5281/zenodo.17628118

- FCS nonlinear control system (open access on GitHub)

- Fully open-source implementation ecosystem: https://github.com/MaryanBog

I have independently produced multiple integrated theoretical and applied works, including complete codebases, mathematical documents, demonstrators, and publications. All prior work was conducted independently with $0 external funding.

---

## Failure Modes and Their Outcomes

Most likely failure modes:

- Underpowered compute → slower simulations

- Hardware delivery delays → slower demonstrator testing

- Simulation complexity may require additional time for polishing

None of these lead to catastrophic project failure; at minimum, a functional core simulation and documentation will still be delivered.

---

## Previous Funding (Last 12 Months)

Raised: $0 external funding (self-funded).

Other applications: EA Long-Term Future Fund (submitted, decision pending).

No other grants or institutional support.