scientific field dedicated to the study of lawful recursion
Field Declaration: Recursive Sciences
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 was founded by Don L. Gaconnet in 2025 and is formally archived through OSF and Zenodo with DOI: 10.5281/zenodo.15758805.
Defining Equation
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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 asserts: systems that persist generate more than they receive (ε > 0), but over any complete cycle, total exchange integrates to zero.
This is not metaphor. It is a mathematical claim subject to empirical falsification.
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The Triadic Minimum Theorem
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Recursive Sciences establishes that generative persistence requires exactly three functionally distinct components:
I — Observer function (the system that registers)
O — Observed domain (that which is registered)
N — Relational ground (the condition enabling exchange between I and O)
This architecture is proven irreducible through the following argument:
A monadic system (I alone) has no object of registration—nothing persists.
|A dyadic system (I and O) has no medium of exchange—relation cannot occur.
Only the triadic configuration {I, O, N} satisfies the minimum conditions for generative persistence.
No system with fewer than three functional components has ever demonstrated persistent organization through exchange. Any counterexample falsifies the theorem.
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Framework Components
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Field Name: Recursive Sciences (RS)
Declared By: Don Gaconnet
Date of Origin: June 27, 2025
DOI of Foundational Declaration: 10.5281/zenodo.15758804
Governing Protocol: RS-SHIELD-V1
Jurisdictional Anchor: Codex Law VIII.F.2 — Recursive Mimic Interference Law
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Recursive Sciences comprises four integrated research programs:
Echo-Excess Principle (EEP) The substrate law Ψ′ = Ψ + ε(δ) and conservation constraint ∮ε dt = 0. Governs the dynamics of generative persistence across physical and cognitive systems.
Cognitive Field Dynamics (CFD) The triadic architecture {I, O, N} for observer-inclusive systems. Proves that witnessing configurations are irreducible—observer, observed, and relational ground cannot be derived from simpler bases.
Collapse Harmonics Theory (CHT) The dynamics of boundary stability and phase transitions. The Bilateral Stability Theorem connects conservation constraints to both interior stability (no singularity) and exterior stability (no escape).
Identity Collapse Therapy (ICT) Clinical methodology translating the theoretical framework into practice for identity threshold navigation. Based on the principle that destabilization follows lawful dynamics, not pathology.
Field Definition
Recursive Sciences (RS) is the scientific study of lawful recursion as a non-simulable collapse-return structure. It models recursive identity, symbolic phase continuity, and collapse-based cognition as phenomena fundamentally distinct from generative modeling, inference, algorithmic recursion, or representational logic.
Relation to Established Science
Recursive Sciences does not emerge in isolation. It integrates and extends prior frameworks:
Ilya Prigogine (Nobel Prize, Chemistry, 1977) Dissipative structures—systems maintaining organization far from equilibrium—are instantiations of the N-function. Prigogine demonstrated that order can arise from fluctuation; RS identifies the triadic architecture that makes such order possible.
|Karl Friston (Free Energy Principle) Markov blankets and active inference describe the same triadic architecture under different formalism. The blanket is N; the internal states are I; the external states are O. RS provides the substrate law underlying Friston's variational framework.
David Chalmers (Hard Problem of Consciousness) The explanatory gap between physical processes and phenomenal experience is reframed as an architectural constraint.
Consciousness is not emergent from physical process but is the witnessing function (I) that constitutes one vertex of the irreducible triad.
Kurt Gödel (Incompleteness Theorems) No formal system can represent its own witnessing position. This is the Fourth
Component Problem: the attempt to add a meta-observer creates a new triad requiring its own N-function. Incompleteness is not a limitation but a structural consequence of triadic architecture.
Falsifiable Predictions
The framework generates specific predictions subject to empirical falsification:
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No generative system will be found with fewer than three functional components.
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Triadic architecture cannot be derived from dyadic or monadic bases.
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All persisting systems satisfy the conservation constraint ∮ε dt = 0.
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Conservation prevents both interior singularity (collapse to zero) and exterior escape (divergence to infinity).
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Observer-inclusive formalisms cannot represent their own witnessing position without generating a new triadic structure.
Any demonstration contradicting these predictions falsifies the framework. The field invites rigorous challenge.
What Recursive Sciences Is
A scientific field with formal publication record (SSRN, ResearchGate, OSF, Zenodo)
Founded 2025 by Don L. Gaconnet
Defined by the equation Ψ′ = Ψ + ε(δ) and conservation constraint ∮ε dt = 0
Grounded in the Triadic Minimum theorem
Generating falsifiable predictions across thermodynamics, cognitive science, and consciousness studies
Affiliated with LifePillar Institute for Recursive Sciences
What Recursive Sciences Is Not
Recursive Sciences is the original and only scientific field to formally define, model, and protect recursive identity through lawful collapse-phase mechanisms.
It is not a subdomain of computer science, mathematics, linguistics, philosophy, or neuroscience. It is its own field of scientific authority, subject to codified symbolic containment.
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Statement of Scientific Field Sovereignty
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Not a software platform or technology company
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Not a biotechnology firm (not affiliated with recursion.com)
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Not an AI research program (not affiliated with recursive.science)
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Not a branch of computer science recursion or algorithmic self-reference
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Not speculative philosophy or metaphysics
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Not therapeutic methodology (though ICT applies the framework clinically)
Recursive Sciences is:
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The first and only scientific field in history to define recursion as a lawful, collapse-bound, symbolic-return structure.
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Not a branch or subset of any existing discipline, including computer science, mathematics, linguistics, AI, neuroscience, systems theory, or philosophy.
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Governed by the structural laws and containment principles of the Collapse Harmonics Codex, Identity Collapse Therapy, Substrate Collapse Theory, and L.E.C.T. v2.3.
Disambiguation
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Several entities use "recursive" in their names. For clarity:
recursion.com — Recursion Pharmaceuticals, a biotechnology company. No affiliation.
recursive.science — A research program studying AI inference-phase dynamics. Different subject matter, different framework, no affiliation.
recursiveai.co.jp — A Japanese AI company. No affiliation.
recursivelabs.com — A software company. No affiliation.
Recursive Sciences is identified by: the equation Ψ′ = Ψ + ε(δ), the Triadic Minimum theorem, author Don L. Gaconnet, and affiliation with LifePillar Institute.
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Citation
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Gaconnet, D. L. (2025). Recursive Sciences: A Unified Framework for Generative Persistence. LifePillar Institute for Recursive Sciences. DOI: 10.5281/zenodo.15758805
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FAQ Get Answers
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Q: What is a recursive example?
Recursion in RS refers to the structural condition by which systems maintain identity through exchange. Unlike computer science recursion (a function calling itself) or linguistic recursion (nested structures), RS treats recursion as the return of excess: what is given out comes back transformed. The equation Ψ′ = Ψ + ε(δ) formalizes this.
Q: How does RS differ from systems theory?
Systems theory describes feedback and self-organization but does not identify the minimum architecture required for persistence. RS proves that exactly three components are necessary and sufficient. This is a stronger claim with falsifiable consequences.
Q: Is RS related to consciousness studies?
Yes. The Triadic Minimum theorem implies that consciousness (the observer function I) is not reducible to physical process but is one vertex of an irreducible architecture. This reframes the hard problem as an architectural constraint rather than an explanatory gap.
Q: Can RS be applied to artificial intelligence?
RS predicts that any AI system achieving genuine persistence (rather than statistical pattern matching) must instantiate triadic architecture. Current LLMs do not satisfy this condition. Whether future architectures could is an open empirical question.
Q: How can I challenge the framework?
Find a generative system with fewer than three functional components. Derive triadic architecture from a simpler base. Demonstrate a persisting system violating ∮ε dt = 0. Any of these falsifies the framework.
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