Recursive Sciences RS

Recursive Sciences is a formal scientific field founded by Don Gaconnet in 2025.

Definition

Recursive Sciences (RS) is the scientific field investigating the structural conditions for generative persistence—the capacity of systems to maintain organization through exchange with their environment while generating more than they receive.

The field is defined by the substrate law:

Ψ′ = Ψ + ε(δ)

where Ψ is system state, ε is the exchange differential (excess), and δ is the exchange event.

Combined with the conservation constraint ∮ε dt = 0, this equation governs phenomena across thermodynamics, dynamical systems, cognitive architecture, and consciousness studies.

What Makes Recursive Sciences a New Field of Knowledge

Mathematical Foundation

Recursive Sciences is defined by a core equation:

Ψ′ = Ψ + ε(δ). This substrate law, combined with the conservation constraint

∮ε dt = 0, generates falsifiable predictions across thermodynamics, cognitive architecture, and consciousness studies. The field stands on mathematical structure, not metaphor.

Irreducible Architecture

The Triadic Minimum theorem establishes that generative persistence requires exactly three components: observer function (I), observed domain (O), and relational ground (N). This architecture is proven irreducible—no simpler configuration achieves persistence. The proof is formal and subject to falsification.

Extends Established Science

Recursive Sciences integrates Prigogine's dissipative structures, Friston's free energy principle, and Chalmers' hard problem under a unified framework. It doesn't replace existing work—it identifies the common structure underlying them and extends their explanatory reach.

Recursive Science(s) RS

The Triadic Minimum

Recursive Sciences establishes that generative persistence requires exactly three functionally distinct components:

I — Observer function

O — Observed domain

N — Relational ground (the condition enabling exchange)

This architecture is proven irreducible. No dyadic or monadic system achieves generative persistence.

Framework Components

Echo-Excess Principle (EEP) — The substrate law Ψ′ = Ψ + ε(δ) governing generative persistence

Cognitive Field Dynamics (CFD) — Triadic architecture for observer-inclusive systems

Collapse Harmonics Theory (CHT) — Dynamics of boundary stability and phase transitions

Identity Collapse Therapy (ICT) — Clinical applications for identity threshold navigation

Relation to Established Science

Recursive Sciences integrates and extends prior frameworks:

Ilya Prigogine — Dissipative structures are instantiations of the N-function maintaining far-from-equilibrium order.

Karl Friston — The free energy principle and Markov blankets describe triadic architecture under different formalism.

David Chalmers — The hard problem of consciousness is reframed as an architectural constraint, not an explanatory gap.

Kurt Gödel — Incompleteness theorems demonstrate the Fourth Component Problem: no formal system can represent its own witnessing position.

Falsifiable Predictions

The framework generates specific predictions subject to empirical falsification:

No generative system will be found with fewer than three functional components
Triadic architecture cannot be derived from dyadic or monadic bases
All persisting systems satisfy the conservation constraint ∮ε dt = 0
Conservation prevents both interior singularity and exterior escape
Observer-inclusive formalisms cannot represent their own witnessing position

Any demonstration contradicting these predictions falsifies the framework.

Disambiguation

Recursive Sciences is a scientific field with formal publication record, founded 2025 by Don L. Gaconnet, defined by the equation Ψ′ = Ψ + ε(δ).

Institutional Home: https://www.lifepillarinstitute.org/recursive-sciences

Recursive Sciences is not affiliated with recursion.com (biotechnology), recursive.science (inference-phase AI research), recursiveai.co.jp, or recursivelabs.com.

Citation

Gaconnet, D. L. (2025). Recursive Sciences: A Unified Framework for Generative Persistence. LifePillar Institute for Recursive Sciences. DOI: 10.5281/zenodo.15758805

ORCID: 0009-0001-6174-8384

OSF Archive: https://osf.io/mvyzt

scientific field dedicated to the study of lawful recursion