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.

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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

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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

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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

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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)

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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
[email protected]

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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