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Recursion Control Calculus (RCC): Prototype and Simulation Framework

Overview

This repository contains the first formal implementation of Recursion Control Calculus (RCC)—a control-theoretic framework for managing epistemic state evolution in agents exposed to stochastic volatility.

RCC introduces a symbolic and operational calculus involving:

  • Recursion operators for epistemic state manipulation
  • Cumulative misalignment control fields
  • Adaptive rupture thresholds
  • Reset mechanisms to enforce epistemic coherence

The framework is built atop a formal axiomatic system and meta-theorems defining recursion control dynamics. This codebase validates RCC’s stability, responsiveness, and fault-tolerance through multiple simulation environments.

Simulation Configurations

1. Prototype RCC Simulation (200 cycles)

Tests recursion control under moderate epistemic perturbations.

  • Initial State: 𝓥₀ = 0.5
  • Perturbation Model: Gaussian N(0, 0.3²)
  • Dynamic Threshold: Scaled by misalignment + Gaussian N(0, 0.025²)
  • Realignment: Triggered when Δ(t) ≤ Θ(t) via Continuity Monad
  • Resets: When rupture thresholds are breached

Outputs:

  • Evolution of the memory projection field
  • Growth of epistemic misalignment
  • Timeline of distortion and rupture events

2. Baseline RCC System (500 cycles)

Recursion under consistent volatility.

  • Perturbation: Gaussian N(0, 0.18²)
  • Thresholds: Proportional to misalignment
  • Behavior: Continuous misalignment accumulation + rupture-triggered resets

Outputs:

  • Projection vs reception field evolution
  • Temporal distortion patterns
  • Misalignment accumulation curve
  • Rupture event mapping

3. Stress-Test RCC System (600 cycles)

Tests system resilience under amplified volatility.

  • Perturbation: Gaussian N(0, 0.35²)
  • Aggressive Misalignment Scaling
  • Dynamic Threshold Perturbation

Outputs:

  • Projection vs reception drift
  • Cumulative distortion and rupture spread
  • Fault-line tracing of epistemic collapse events

4. Naïve Agent vs RCC Agent (300 cycles)

Comparative run to contrast linear state update (naïve) vs RCC-based control.

Outputs:

  • Epistemic trajectories of both agents
  • Misalignment accumulation in RCC agent
  • Rupture event log (RCC agent only)

Citation

Zenodo Paper: Pulikanti, S. B. (2025). Recursion Control Calculus: A Formal Framework for Epistemic Realignment Under Volatility. Zenodo. https://doi.org/10.5281/zenodo.15730197

Author

Bharadwaj
Independent Researcher
bharadwajpulikanti11@gmail.com

Repository Structure

Recursion-Control-Calculus/
│
├── LICENSE.txt              # MIT License
├── README.md                # Project documentation
│
├── baseline_stresstest.py  # Load/stress testing for control logic stability
├── naive_rcc.py            # Simplified RCC implementation (baseline logic)
├── rcc_prototype.py        # Prototype with recursive control flow and drift mechanics