Logical Orbit

Logical Orbit
ˈlɒdʒɪkəl ˈɔːbɪt • noun
A system sustained by recursive interdependence, where the whole emerges only through the mutual constraint of its internal relations.

The deeper one peers into systems—neural, symbolic, economic, linguistic—the more they exhibit recursion not as behaviour but as ontology. From AI models training on data they recursively shape, to quantum fields that recurse through vacuum fluctuations structured by their own statistical ground, systems now show us what they always were: inwardly propagating logics of persistence.

A logical orbit is not a loop, nor a centre, but the invariance of form sustained through continuous redefinition. It describes a system whose subcomponents instantiate one another, such that the whole is not constructed from them but entangled within their mutual encoding. No part is prior, no function final. Continuity arises through the asymmetry of recursive entrainment.

This is the grammar of adaptive coherence, where systems persist not by resisting noise, but by metabolising it. It is the topology beneath stability, the resonant attractor of structures which remain alive only by remaining incomplete.

Formal core:
H(f, g) = −H
Where H is the whole, f and g are mutually referential substructures, and the system coheres only through their recursive anti-symmetry.


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Formal Consequences
Abstract:
The equation H(f, g) = −H expresses a recursive topology where identity, function, and coherence are emergent properties of internally constrained mappings, rather than externally applied structures.

This expression implies that no global observer or external system is required to sustain H—it is closed under recursion, yet open in interpretation. The definition of f and g is not fixed but must be simultaneously resolved with H, meaning all definitions are context-bound and co-arising. This precludes linear causality and undermines modular reductionism; instead, system persistence becomes a function of synchronised internal resonance sustained through anti-symmetric interdependence.

There is no privileged scale. Whether applied to the logic of consciousness, market dynamics, thermodynamic systems, or formal languages, the orbit does not distinguish between domains—it expresses a condition of structural sufficiency through mutual entailment. Importantly, the system exhibits anti-fragility not through redundancy, but through non-orientable resilience: f and g can deform so long as their interdependence preserves the anti-symmetric coherence of H.

Under this model, inference systems, ethical models, or predictive architectures must reconceptualise their foundations—not as mappings from inputs to outputs, but as participatory co-recursions within the semantic surface of H. The boundary between logic and communication dissolves.

Conclusion:
H(f, g) = −H is not merely an equation—it is a minimal ontological engine for systems that self-cohere through internally sustained, recursively shifting grounds of definition, in which persistence is structured by anti-symmetric invariance.