1. The unresolved question inside “sustaining”
Sustenesis Theory asks how an identifiable structure becomes possible and how it remains sufficiently coherent to continue existing and operating through change, rather than beginning with an entity considered in isolation. Its formulation names three foundational concepts—Difference, Constraint, and Sustained Coherence (Chen, 2026).
Difference is required because a structure without distinguishable terms, states, or relations cannot have articulated form. Constraint is required because unrestricted difference does not by itself produce a stable structure; some relations must be permitted, limited, repeated, excluded, or preserved. Sustained Coherence is required because a structure that cannot retain sufficient organization across variation does not remain identifiable as that structure.
This formulation leaves a question about the meaning of “sustained”. The word readily suggests a temporal account in which something exists at one moment and continues to exist at a later moment. If this account is used as the general definition of sustaining, time is already assumed before Sustained Coherence has been explained. The same issue arises with space. Describing preservation through remaining “in the same place”, “within a boundary”, or “across a distance” already presupposes spatial relations.
The question concerns both language and the explanatory architecture of the theory. If Sustenesis uses time to define Sustained Coherence and subsequently uses Sustained Coherence to explain time, the account risks circularity. To examine the status of spacetime within the theory, the reference background of maintenance therefore needs to be stated without relying exclusively on temporal or spatial relations.
The State Domain names this reference background. It does not introduce another metaphysical substance, but makes explicit the relations involved in state variation, structural comparison, and the preservation of constitutive relations.
2. State Domain as a structural presentation
In this paper, the State Domain is defined as follows.
A State Domain is the structured domain of all states that are admissible for a given Sustenetic structure, together with the relations among those states, as jointly determined and presented through Difference, Constraint, and Sustained Coherence.
The definition has the following scope.
First, the State Domain is not a fourth foundational element. Difference, Constraint, and Sustained Coherence remain the foundational conceptual triad. The State Domain does not stand beside them as another primitive. It names the structured presentation in which their joint operation becomes describable.
Second, the State Domain is not a prior container. It is not an empty domain that exists before structures arise and subsequently receives them. Such an account would replace spacetime with another independently presupposed background. A State Domain is inseparable from the structure whose admissible states and relations it expresses.
Third, the State Domain is not a later result in a temporal or causal sequence. A sequence in which Difference occurs first, Constraint second, Sustained Coherence third, and the State Domain fourth would already presuppose temporal order. Difference, Constraint, and Sustained Coherence are understood here as mutually conditioning aspects of one structure. Difference permits distinctions, Constraint organizes relations and their limits, and Sustained Coherence concerns the structure’s preservation through admissible variation. The State Domain is the presentation of their joint constitution, not a fourth entity produced afterwards.
Fourth, “all possible states” does not mean every logically imaginable condition in an unrestricted universe. It means the states that count as admissible relative to a particular structure and its constitutive constraints. The State Domain of a cell, a legal institution, a language model, a molecule, or a social relation need not have the same content or the same relations.
For a descriptive representation, let ΣX denote the states distinguishable with respect to a structure X, and let RX denote the admissible relations or transformations among those states under the relevant constraints. The State Domain of X can then be represented schematically as follows.
DX = <ΣX, RX>
This notation is descriptive rather than ontologically additive. Difference makes distinctions within ΣX possible. Constraint restricts admissible states and organizes RX. Sustained Coherence concerns whether sufficient constitutive relations are preserved across relevant relations or transformations for X to remain identifiable and operational. The admissibility of a variation does not by itself guarantee this preservation.
The relations in RX need not be defined in advance as temporal relations. They may be temporal, causal, logical, conditional, computational, modal, topological, or otherwise structural. Physical time is therefore not included as a necessary starting point in the most general formulation of sustaining.
3. Reconstructing Sustained Coherence
Within the State Domain, Sustained Coherence can be formulated as follows.
Sustained Coherence is the capacity or condition by which a structure preserves sufficient constitutive relation across admissible state variation to remain identifiable and operational within its State Domain.
Preservation here does not mean static sameness. A structure can change while retaining the relations through which it remains identifiable. An organism may exchange matter and energy; a language may change its vocabulary; an institution may revise its rules; a software system may change its internal variables; a model may produce different outputs under different prompts. These examples concern the preservation of constitutive relations rather than the complete identity of materials or states.
Maintenance can therefore be understood not only as a fixed object’s continuation over a period of time, but more generally as the preservation of sufficient constitutive relations across admissible variation. What is maintained is the organization through which the structure remains identifiable.
Ordinary uses of “maintain”, “continue”, and “sustain” usually carry temporal meaning. Here these words are used more generally for the preservation of structural coherence across relevant state relations, without requiring those relations to be defined first in terms of physical time. This use distinguishes the abstract account from its temporal instances; it does not imply that an actual physical process takes place outside time.
Structural identity is understood here through the relation between variation and what is preserved, rather than through absolute sameness of substance. A structure can undergo change while remaining itself when the relevant constraints preserve sufficient constitutive relations. Difference, Constraint, and Sustained Coherence thus describe related aspects of the same maintenance process.
4. Spacetime as a specific form of State Domain
This account also specifies the place of time and space within Sustenesis Theory.
In descriptions of human experience and physical processes, change is commonly organized through time and coexistence through space. The State Domain account does not take the stability of these forms as a reason to leave them outside explanation. It asks how distinguishable states, constraints, and sustained relations can be expressed in particular stable forms, including time and space.
At the level of human experience, time can be defined as a comparative encoding of order, interval, and relative rhythm among changes. We identify that one change precedes another, that two changes are separated by an interval, or that a process repeats with a certain rhythm. Time is understood here as the stable relational form through which changes can be ordered, compared, and measured. This is an account of experienced time, not a derivation of physical time from an unordered collection of states.
Space can be defined as the organization of coexistence and extension among differences within a common State Domain. Here coexistence means that the differences can jointly belong to one state structure. Space becomes experientially concrete through relations such as here and there, position, adjacency, distance, orientation, scale, containment, and separation.
Coexistence is distinguished here from temporal simultaneity. Defining space by saying that here and there exist “at the same time” would already introduce time into the definition. At the more abstract level, the relevant relation is that differences jointly belong to one state structure. Temporal description can express their coexistence as simultaneity, but simultaneity is not taken as the starting point of this definition.
This account does not take the following order as its basic explanatory arrangement.
spacetime → states → structure.
The proposed relation can instead be represented as follows.
The arrows indicate levels of description, not temporal succession or a causal chain. Spacetime is a specific stable form of state organization in human experience and physical description. The State Domain is more abstract because it does not require admissible relations to be defined exclusively in spatial or temporal terms.
This is a philosophical account, not a new physical theory of spacetime. It does not derive the metric of general relativity, determine the dimensionality of physical spacetime, or replace empirical physics. The claim is that structural maintenance can be formulated without treating spacetime as its unexplained final background.
5. Layered compatibility with Kant
The relation to Kant concerns the distinction between human experience and the more general structural account proposed here.
Kant treats space and time as a priori forms of sensibility through which objects can be given in human experience. His analysis concerns the conditions of possible experience; it does not establish space and time as properties of things considered independently of those conditions (Kant, 1781/1787, Transcendental Aesthetic, §§2–7). The State Domain account retains this distinction between the forms of human experience and claims about existence in general.
The State Domain introduces a more abstract level. It asks not only how human experience is organized, but how the background forms through which structures become describable might themselves be understood as specific organizations of more general state relations. At that level, spacetime need not be granted final ontological priority.
The proposed compatibility concerns levels of explanation. Space and time can retain their role as forms of human experience while being considered, within Sustenesis Theory, as particular expressions of more general state relations. This does not establish compatibility with every claim in Kant’s philosophical system.
Abstraction and instantiation in software design provide an illustrative analogy. An abstract type can specify relations that are realized differently in particular implementations. In this limited sense, the State Domain corresponds to the more abstract level, while humanly experienced spacetime is one concrete realization. The analogy illustrates a relation between levels; it does not establish a formal isomorphism between software architecture and ontology.
A further analogy concerns the relation between a more general theory and a more restricted framework retained within its domain of application. The relation between relativity and classical mechanics serves here only as an illustration of layered compatibility. It is not evidence that Sustenesis contains Kant’s philosophy in the same way, nor does it confer the empirical standing of a physical theory on the present account.
The question is therefore not whether Kant is simply correct or obsolete, but which aspects of his account are retained and at what level. The proposed framework retains the role of space and time in human experience while allowing their structural status to be examined within a more general account of sustaining.
6. Large language models and the structural meaning of emergence
The State Domain framework can also be applied to higher-order functions in large language models.
An account of a language model’s higher-order capabilities does not end with identifying a single neuron, parameter, token, or layer. In Transformer models, computation involves relations among representations, attention, and successive transformations (Vaswani et al., 2017). Model behaviour also depends on the current input and context (Brown et al., 2020). In applications, system instructions, decoding procedures, and available tools introduce further operating conditions. These factors do not exclude causal contributions from particular components; they place those contributions within the organization of the system.
From a Sustenetic perspective, the object of analysis is the structured domain of model states and relations under specified constraints. A prompt changes the active context; system instructions specify requirements that influence generation; fine-tuning changes parameter relations; tool access changes the operations available to the application; decoding determines how internal output distributions are used to produce sequences. These changes concern different aspects of the system. The resulting behaviour is considered in relation to their organization rather than attributed solely to an isolated component.
Wei et al. (2022) describe certain abilities as emergent when they are absent from smaller models but present in larger models and cannot be predicted simply by extrapolating smaller-model performance. Schaeffer et al. (2023) show that some apparent discontinuities depend on evaluation metrics rather than corresponding discontinuities in underlying performance. These findings distinguish the question of how a function is organized from the question of how its appearance is measured.
Within the present framework, whether a capability appears sharply or gradually, higher-order function can be understood through relations among constrained states rather than through an additional entity introduced into the system. A new functional pattern may become expressible when the system’s organization makes previously unavailable or unstable relations sufficiently accessible and coherent. This is a structural interpretation of functional formation, not a conclusion about how every particular capability emerges.
The State Domain account does not identify every unexpected model behaviour with a phase transition, nor does it replace mechanistic interpretability, scaling analysis, training research, or empirical measurement. It treats capability as a feature of an organized relational system, without assuming that a complete account must be located in a single component.
Context-dependent behaviour can be considered in the same terms. A model can respond differently to instructions and examples while its parameters remain unchanged, as in the evaluations reported by Brown et al. (2020). In State Domain terms, changed contextual conditions affect which relations are brought into operation and how they are expressed. This differs from changes to the model’s parameters through training or fine-tuning.
7. Quantum theory as a heuristic boundary case
The quantum discussion concerns philosophical interpretation rather than physical derivation.
Quantum descriptions of composite systems involve relations that are not captured by first assigning complete independent states to spatially separated parts. This issue is central to the problem examined by Einstein, Podolsky, and Rosen (1935). Quantum states are described through the mathematical framework of Hilbert space; in the pure-state case, an entangled joint state cannot be written as a product of pure states of its parts (Horodecki et al., 2009, §II). Bell’s theorem shows that, under its assumptions, local hidden-variable theories cannot reproduce certain correlations predicted by quantum mechanics (Bell, 1964).
These results do not prove Sustenesis Theory. The present account provides no new equation or probability rule, no derivation of the Born rule, no solution to the measurement problem, and no experimentally distinguishable prediction. Its discussion of quantum theory is limited to the structural starting point from which states and relations are understood.
The relevant point is that classical spatial separation does not exhaust the organization of a joint quantum state. An entangled system is not described completely by assigning independent states to its parts and then adding an external connection. The joint state is part of the account of the system’s correlations (Horodecki et al., 2009, §II).
A State Domain approach begins with the admissible relations of the overall state and then considers the place of local descriptions within that structure. The question becomes how the joint state is organized and under what measurement conditions local outcomes are described, rather than how two states already assumed to be independent acquire a connection across space. This changes the starting point of the philosophical description, not the mathematical predictions of quantum mechanics.
The State Domain is not identified with Hilbert space. Hilbert space has a mathematical definition and a specific role in quantum theory, whereas the State Domain is used here to describe admissible states and relations within Sustenesis Theory. Their relation in this discussion is an analogy at the level of structural description, not an equivalence between concepts.
Quantum correlations alone do not permit controllable faster-than-light signalling (Horodecki et al., 2009, §IV.6). They therefore do not establish that causality can be discarded or that distance is unreal. The point retained here is that spatial separation is not sufficient to determine all relations within a quantum state. The philosophical account begins with those relations rather than presupposing complete independence of the parts.
8. State Domain and the internal relations of the three foundational concepts
The State Domain specifies the reference background of sustaining within Sustenesis Theory.
When sustaining is described only as continuation from one physical moment to another, its reference background remains temporal. The State Domain account instead states that background in terms of admissible states and relations. Temporal continuation can then be considered within this account without being the sole meaning of sustaining.
The State Domain makes that reference explicit. A structure is sustained relative to its own admissible state relations and constitutive constraints. Physical time may be one way those relations are organized, but it is not the only possible form that must be presupposed in the definition.
This also clarifies that the three foundational concepts are not three events occurring one after another. Difference, Constraint, and Sustained Coherence are three relational aspects that jointly define what it means for a structure to be what it is. The State Domain is the structured presentation of that joint constitution.
These relations can be summarized as follows.
Difference provides distinguishability.
Constraint provides selective relational organization.
Sustained Coherence provides structural persistence across admissible variation.
The State Domain is the structured range in which these three are jointly expressed.
Spacetime is one specific stable form through which such relations can be organized and experienced.
Applying the framework to a specific structure requires an account of the relevant differences, the constraints that organize them, the admissible states and relations, and the constitutive relations preserved through variation. Naming a State Domain does not by itself supply that account. Its content depends on the relations and conditions specified in the application.
A retrospective description using the three foundational concepts is not sufficient by itself to explain a particular structure’s maintenance. The analysis also concerns how the relevant constraints support the preservation of relations and under what changes that preservation ceases. This is the connection between the general framework and domain-specific explanation.
9. Theoretical boundaries and next steps
This paper presents a conceptual framework rather than a completed formal theory.
Its scope is limited in the following respects.
First, the State Domain is not automatically identified with a state space in physics, mathematics, control theory, or computer science. A state-space model is specified for a particular analytical purpose. The State Domain is used here for the more general relation between states, constraints, and sustaining. Their connections require comparison rather than an inference from similarity of terminology.
Second, the account does not derive the physical generation of spacetime from the three foundational concepts. It formulates structural maintenance without presupposing spacetime as its final background. A physical theory of spacetime generation would require additional mathematical and empirical arguments beyond those given here.
Third, the discussions of language models and quantum states are applications of the framework’s structural vocabulary, not independent proofs of the framework. The language-model discussion concerns the organization of functions under different conditions; the quantum discussion concerns the relation between joint states and spatially separated parts. Neither discussion replaces the corresponding scientific explanations.
Fourth, the relation to Kant is a proposal for layered compatibility concerning the forms of human experience, not a claim that Sustenesis Theory has superseded transcendental philosophy. It retains that level of analysis while examining spacetime within a more general structural account.
Further work concerns the specification of admissible states, relations, constraints, and the constitutive relations preserved through variation. It also concerns comparison with existing accounts of state spaces, possible-world structures, dynamical states, processes, fields, and structural realism. Such comparisons would clarify where the State Domain account coincides with those approaches and where its explanation of sustaining differs.
10. Conclusion
The central question of this paper is the reference background relative to which a structure is sustained.
The answer proposed here is the State Domain.
The State Domain is not an additional substance, not an empty background, and not a fourth element beside Difference, Constraint, and Sustained Coherence. It is the structured domain of admissible states and relations presented by their joint constitution. Once this concept is made explicit, “sustaining” no longer has to presuppose ordinary physical time. It means that sufficient constitutive relation is preserved across admissible state variation for a structure to remain identifiable and operational.
This reconstruction also changes the status of spacetime. Time and space can be treated as specific stable organizations of state relations rather than the unquestioned final background of all existence. Human time encodes order, interval, and rhythm among changes; human space organizes coexistence and extension among differences. At a more abstract level, both can be understood as concrete forms of a wider State Domain.
The account provides a basis for the proposed layered relation to Kant, the structural interpretation of context-dependent functions in language models, and the philosophical discussion of joint quantum states. These applications remain distinct from a derivation or empirical validation of the framework.
The internal claim is that sustaining concerns the preservation of constitutive relations within a State Domain, rather than merely continuation within an unexplained temporal background.
Difference, Constraint, and Sustained Coherence describe the related conditions of that preservation, while the State Domain names their structured presentation.
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