THE RECURSIVE FUNCTIONAL CONVERSION PRINCIPLE (RFCP): A Domain-Independent Candidate Framework for System-Generated Operations, Generalization, Re-Entry, and Functional Conversion
- 1Independent Researcher
Abstract
This paper proposes the Recursive Functional Conversion Principle (RFCP), a generalized systemic principle intended to formalize a recurring structural possibility: an operation generated within a system may be generalized across a system-set, re-enter the system-set or an originating system, and thereby acquire a functionally transformed state. The primary case study is the Self-Confidence Paradox (SCP), in which self-assessment can participate in the subsequent systemic attribution of confidence. The paper deliberately separates this confidence-specific phenomenon from the generalized mechanism. Projection, signaling, labeling, classification, measurement, evaluation, processing, communication, prediction, control, optimization, verification, coordination, representation, and other operations are treated as operation classes rather than as the primitive of the theory.
The formal architecture represents each system by a generated operation \mathcal{O}_{i} a generalized operation \mathcal{G}_{N}, a generalized systemic state \mathcal{R}_{N}, a re-application operator \mathcal{A}_{i} and an observable conversion or divergence quantity \Delta_{i} Criterion, metric, standard, and enabling medium are represented jointly by a context vector . The model is parameterized for arbitrary finite system number N>2 and is explicitly designed so that conversion is not automatically equated with paradox. Invariance, variation, conversion, divergence, feedback amplification, functional reversal, and paradox are treated as distinct regimes. Thirty analytical case instances are supplied across three layers: philosophical-ontological, epistemological-functional, and systemic-mathematical- operational.
The paper does not establish RFCP as a universal law. It instead specifies a falsifiable candidate principle, an operationalization strategy, boundary conditions, counterexample requirements, synthetic simulation design, and a literature-grounded distinction between established concepts and the proposed synthesis. Mathematical notation is used only where variables, mappings, domains, and testable relations can be defined. Consequently, the central contribution claimed here is a formalizable research program rather than a proof of universal empirical truth.
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BibTeX
@misc{shan2026recursive,
title = {{THE RECURSIVE FUNCTIONAL CONVERSION PRINCIPLE (RFCP): A Domain-Independent Candidate Framework for System-Generated Operations, Generalization, Re-Entry, and Functional Conversion}},
author = {Shamiul Hoque Shan},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23441333},
url = {https://zenodo.org/records/23441333},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - THE RECURSIVE FUNCTIONAL CONVERSION PRINCIPLE (RFCP): A Domain-Independent Candidate Framework for System-Generated Operations, Generalization, Re-Entry, and Functional Conversion
AU - Shamiul Hoque Shan
PY - 2026
DA - 2026/10/17
PB - Zenodo
DO - 10.5281/zenodo.23441333
UR - https://zenodo.org/records/23441333
AB - This paper proposes the Recursive Functional Conversion Principle (RFCP), a generalized systemic principle intended to formalize a recurring structural possibility: an operation generated within a system may be generalized across a system-set, re-enter the system-set or an originating system, and thereby acquire a functionally transformed state. The primary case study is the Self-Confidence Paradox (SCP), in which self-assessment can participate in the subsequent systemic attribution of confidence. The paper deliberately separates this confidence-specific phenomenon from the generalized mechanism. Projection, signaling, labeling, classification, measurement, evaluation, processing, communication, prediction, control, optimization, verification, coordination, representation, and other operations are treated as operation classes rather than as the primitive of the theory. The formal architecture represents each system by a generated operation \mathcal{O}_{i} a generalized operation \mathcal{G}_{N}, a generalized systemic state \mathcal{R}_{N}, a re-application operator \mathcal{A}_{i} and an observable conversion or divergence quantity \Delta_{i} Criterion, metric, standard, and enabling medium are represented jointly by a context vector . The model is parameterized for arbitrary finite system number N>2 and is explicitly designed so that conversion is not automatically equated with paradox. Invariance, variation, conversion, divergence, feedback amplification, functional reversal, and paradox are treated as distinct regimes. Thirty analytical case instances are supplied across three layers: philosophical-ontological, epistemological-functional, and systemic-mathematical- operational. The paper does not establish RFCP as a universal law. It instead specifies a falsifiable candidate principle, an operationalization strategy, boundary conditions, counterexample requirements, synthetic simulation design, and a literature-grounded distinction between established concepts and the proposed synthesis. Mathematical notation is used only where variables, mappings, domains, and testable relations can be defined. Consequently, the central contribution claimed here is a formalizable research program rather than a proof of universal empirical truth.
ER -