The actuality of change is Cartesian-certain ([§2.2.1](<2.2.1 Change Is Actual.md>)): the act of reading is itself a change, and that experienced change exhibits causally structured succession, relational extension, and causal persistence. What remains is whether those Conditions belong only to experience, or to whatever constitutes its ground.

One distinction governs the extension. At the first pass, T, S, and Φ name roles: directed priority, real differentiation, and a real bearer or realizer. Those roles must not be silently upgraded into clock time, metric extension, or material causation. The general grounding argument establishes the roles. Concrete grounds such as computational substrates may instantiate richer temporal, spatial, and causal types, but that is a further realization claim.

The extension runs through three lines with different scopes: level-invariance establishes the roles any ground must realize; the Triconditional Cross-Entailment governs full Condition-instantiation within change-realizers; and the Encoding Dilemma handles live representational grounds such as simulations. They converge on structured grounding without pretending to be premise-disjoint.

*Level-invariance.* The level-invariance argument is the most fundamental of them. It does not depend on how causal transmission works between levels, or on any particular account of what the ground of experience consists in. It depends only on what any grounding relation structurally requires. For one level of reality to host another (for a substrate to host a simulation, a demon to host a dream, a transcendental subject to host experience) that hosting relation must satisfy three structural Conditions.

A ground must be metaphysically prior to what it grounds. This priority need not be temporal or causal grounding is standardly atemporal; (Fine, Kit, 2012); (Schaffer, Jonathan, 2009), but it must be asymmetric and directed. That establishes the T-role of directed order, not yet temporal succession. Treating metaphysical priority as an instance of clock time would contradict the definition of grounding fixed at [§1.5.5](<1.5.5 Ground and Dependence.md>); the argument needs only the role shared by temporal succession and atemporal dependence.

The ground must also be genuinely distinct from what it grounds. That establishes the S-role of real differentiation, not yet traversable spatial extension. Finally, the grounding fact must obtain: there must be something in which the dependence consists rather than a free-floating description. That establishes the Φ-role of real bearing or realization, not yet persistence across a causal interval. The richer spatial and causal types require their own arguments.

This holds at every level of any possible ontological stack.

> [!argument]
> **The Grounding Conditional** · *The Level-Invariance Line*
>
> 1. Any grounding relation R(x,y) requires asymmetric priority (the T-role), real differentiation of x from y (the S-role), and a real fact or realizer in which R obtains (the Φ-role).
>
> 1. Whenever R holds, at any level of an ontological stack, those three roles are instantiated at the level of the ground.
>
> 1. Therefore any coherent ground of actual change instantiates directed order, differentiation, and bearing: T∧S∧Φ at role-resolution.
>
> 1. The line does not by itself identify their concrete types. Temporal succession, spatial extension, and causal persistence require the separate realizer arguments developed later.

Level-invariance therefore secures a role-level extension from experienced structure to any ground of that experience. The unconditional necessity result is reached later, when Necessary Possibility is combined with the Structural Requirement ([§2.4](<2.4 Structural Requirement.md>)); the ∅ argument removes the purported empty alternative but is not a hidden premise in this extension. What this secures, if the grounding relation is granted, is the extension from certainty within experience to certainty at the level of whatever hosts it. The question is no longer whether change is certain *for us*. Could a ground underwrite that certainty while standing outside the very roles it must exercise to ground anything at all? Level-invariance says no. Nothing here depends on the Triconditional Cross-Entailment or on Constitutive Instantiation. If grounding is real, the Conditions are already in play.

*Causal realization.* Skeptical hypotheses about the ground of experience make the richer, type-level requirement concrete. They also anticipate the Encoding Dilemma below: a substrate that merely *encodes* our world must still instantiate the Conditions in order to host a live experience. Suppose our reality is a simulation running on a computational substrate, the most familiar deflation and the case whose machinery makes the requirement easiest to see. The substrate must execute temporal succession to process the simulation's states (T), differentiate the computational elements that encode distinct positions (S), and contain causally active components whose interactions produce its outputs (Φ). These are what level-invariance requires of any simulation-hosting substrate in any possible world, not only our own. A substrate that lacks them does not run a different kind of simulation; it runs none at all, because simulation is a causal process requiring temporal succession, relational differentiation, and a medium of causal transmission.

The empirical particulars of *our* computational substrates instantiate those structural Conditions; they are not the Conditions themselves. Hardware has locational structure (chips, memory, buses, racks); energy cycles; processors obey conservation constraints; cooling systems manage waste heat. A substrate sustaining N joules of simulated activity must supply the corresponding computational throughput. The particulars only make the requirement legible: when one tries to imagine a substrate stripped of T, S, and Φ, one finds oneself imagining no substrate at all. The very features that would make it a hosting substrate are the ones being stripped.

So the substrate is not ontologically lighter than the simulated world but an additional extended manifold stacked behind it, running on its own structural cycle. The hypothesis multiplies T-S-Φ instantiation rather than reducing it, and relocates the structural cost rather than eliminating it. The appeal of simulation (that we get to keep the phenomenology without paying the structural cost) terminates where it began, with another T-S-Φ-instantiating system doing the hosting.

The same requirement bites on the other classic hypotheses. If our reality is a dream in the mind of a Cartesian demon, the demon's cognitive architecture must undergo causally structured transitions to produce the dream's content (T), differentiate the elements of its cognitive states to produce the dream's variety (S), and possess a medium of cognitive persistence connecting one dream-state to the next (Φ). And if we are Boltzmann brains, fleeting fluctuations in an entropic void, even the fluctuation must be an event in Physicality (Φ), occurring in temporal succession (T), at a position differentiated from its surroundings (S).

The concrete pattern generalizes to any **causal hosting** hierarchy. If reality₁ is produced or processed by reality₂, then reality₂ must instantiate temporal succession, differentiated vehicle-elements, and a persistent causal realizer. If reality₂ is causally hosted by reality₃, the same typed requirement applies. This is stronger than the general grounding claim because causal hosting supplies the type-upgrades directly. A purely atemporal grounding relation remains governed by the thinner role-level conclusion above.

*The Triconditional Cross-Entailment.* This line (developed at [§2.6](<2.6 Triconditionality of Nature.md>)) works inside the domain of full change-realizers. It does not claim that every abstract order, geometry, or bearer carries all three Conditions; it claims that where one Condition is fully instantiated as part of genuine change, the other two are co-instantiated.

T, S, and Φ are analytically interdependent: the full instantiation of any one structurally requires the others. The claim is used here in advance of its derivation and stands or falls with it. Temporal succession without a persistence medium (Φ) is not a transition through which anything survives or occurs but a list of unrelated snapshots; temporal succession without a relational structure (S) is a bare ordering with no differentiated positions, and so not an order of anything at all. If these entailments hold, then the Cartesian certainty of T alone analytically carries S and Φ with it; the extension from the Cartesian premise to the full structure requires no further empirical premise. The *Cogito*, which establishes T with unconditional force, already contains S and Φ analytically. It survives even if one brackets hosts, substrates, and all appeal to output-constraints. The argument asks only whether Temporality can be fully instantiated without the other two, and if not, the extension is already complete.

*The Encoding Dilemma.* If the first works by the structure of grounding and the second by the internal entailment of the Conditions, the third works by turning the deflationist's own escape against it, and needs neither the grounding-priority premise of the first nor the cross-entailment of the second. It is stated and proved as the Constitutive Instantiation result at [§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>), and it carries no premise about what production transmits. Its force is a dilemma. A candidate ground of an actually structured experience either instantiates the experienced Conditions outright or merely *encodes* them, and an encoding that grounds a live experience is itself a tokened structure, so either horn delivers a structured ground. This is why the simulation, demon, and Boltzmann-brain cases above press as hard as they do: each is the encoding horn made concrete, a substrate that must *process* states (T), *differentiate* elements (S), and *sustain* a medium (Φ) to encode the experience it grounds.

> [!corollary]
> **Constitutive Instantiation** · **R8** · *Result of T3*
>
> Where one of the Conditions (Temporality, Spatiality, or Physicality, or a determinate of one) is actually present in an experiencing, instantiated and not merely represented in content, all three are co-instantiated in that experiencing; and because the experiencing is a state its ground is in rather than a content the ground merely represents, the ground itself instantiates all three. And a ground reaches the same conclusion on either horn of a dilemma: if it instantiates the experienced Condition outright, directly; if it merely encodes it, then by tokening that encoding (borne in a medium, across distinct elements, processed across steps) it instantiates the Conditions all the same. A system can encode a Condition in the abstract without instantiating it, but it cannot ground a live experience in which that Condition is actually present without instantiating Temporality, Spatiality, and Physicality. ([§2.6.7](<2.6.7 Triconditional Cross-Entailment.md>))

A two-dimensional game engine can *encode* a three-dimensional world by projection, but the encoding itself runs on a substrate with the spatial structure required to compute and store it; the engine's hardware is three-dimensional even when its rendered output is displayed on a two-dimensional surface. Constitutive Instantiation does not deny that lower-dimensional encodings of higher-dimensional structures exist; it requires that whatever *instantiates* the higher-dimensional structure as such (not as encoded representation but as the feature actually present in experience) must itself instantiate the Conditions that make that feature coherent. A system that lacks the structural Conditions can encode them in a representation but cannot host an experience in which those Conditions are actually present rather than merely represented. The result needs no premise about what causation transmits: on either horn of the dilemma, the actual presence of a structured Condition in the experience a ground sustains is instantiated in that ground; and the encoding/instantiation distinction marks where the result bites and where it does not.

*Applied to the ground of experience.* Our experience exhibits causally structured succession, relational extension, and causal persistence. Whatever constitutes the ground of this experience (physical medium, divine mind, Kantian transcendental subject, simulation substrate) must itself instantiate these three structural features for them to be actually present in the experience it hosts. The result thereby closes the extension from the Cartesian certainty of experience to the structural character of its ground: a Condition actually present in an experiencing co-instantiates all three within that experiencing by the cross-entailment, and because the experiencing is a state its ground is in rather than a content the ground merely represents (the realizer reading of [§2.6.1](<2.6.1 Three Conditions, One Nature.md>)), those Conditions are the ground's own.

*The emergence objection.* Liquidity emerges from molecules that are not liquid; life emerges from chemistry that is not alive. The pattern is real, and its credentials are honest. The objection (that novel structural properties can arise from substrates that do not individually possess them) does not defeat the result, because the result is not a claim about what individual components can produce but about what the system as a whole must instantiate once the feature is actually present. Whether the emergence is weak (macro-properties deducible from micro-dynamics) or strong (genuinely novel causal powers), the system in which those powers are actually instantiated must itself instantiate temporal succession, spatial distinctness, and a causal medium; emergence may relocate where a structural feature is first instantiated, but it cannot convert actual instantiation into mere encoding. Emergence moves the argument; it does not escape it.

*Weight of the three.* Level-invariance is the general line, but its conclusion is role-level. The Cross-Entailment is stronger in content and narrower in domain: it applies to full change-realizers. The Encoding Dilemma is narrower still, applying to tokened grounds of actual, ongoing experience. Its temporal step does not cover a frozen, never-read encoding. The lines therefore reinforce one another by covering different escape strategies, not by independently proving one unrestricted conclusion.

*What converges.* Any ground of actual structured experience must at minimum realize directed priority, differentiation, and bearing. Concrete causal or computational grounds instantiate richer temporal, spatial, and persistent types. Full change-realizers fall under the restricted Cross-Entailment, while tokened encodings fall under the Encoding Dilemma. A critic may resist one line without thereby defeating the others, but the conclusion carried forward must remain at the resolution and within the domain of the line that earned it.


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← [2.2.1 Change Is Actual](<2.2.1 Change Is Actual.md>) | [2.2.3 Witness's Reach](<2.2.3 Witness's Reach.md>) →
