*The realizer move, applied to S ↔ (T ∧ Φ).* Real relational extension is biconditional with both directed succession and persistent bearing: S ↔ (T ∧ Φ). If positions are real, something must occupy them, something must distinguish them through ordered relation, and crossings between them must run in time. Four lines work the S↔Φ link explicitly (two in each direction, each refuting a distinct deflationary mimic), and each line already deploys T in the work that makes it run. The same four lines deliver S↔T: not as a separate step, but as what the lines are doing already. The same realizer move is worked from the succession and persistence pivots at §[§2.6.2](<2.6.2 Succession's Two Conditions.md>) and 2.6.4; the result is cross-confirmation, not assembly. The extension pivot alone already delivers the full triconditional; the three vantages are gathered at [§2.6.5](<2.6.5 Mutual Containment.md>).

*Direction 1: Φ→S.* Two lines converge on the same result: Physicality analytically requires Spatiality.

*First, the distinctness line.* For causation to be real, its source and uptake terms must be genuinely distinguishable, not merely two names for one undifferentiated state. This need not require two numerically distinct beings: one persisting system may occupy the causal roles at different stages. Intrinsic difference alone is not enough to order those roles. For the causal terms to be structurally distinct, they must occupy distinguishable positions or states within a relational structure. That is the Spatiality-role of relational differentiation. The constitutive claim (that the genuine non-identity of causal relata is relational non-identity) receives the haecceitist's primitive-thisness counter (set out at strength in [§2.4.7](<2.4.7 Distinction Requires Spatiality.md>)) in the same form, and survives by the same articulability bridge. Even a primitive haecceity that distinguishes one causal relatum from another must remain articulable as *this-cause* rather than *that-effect* in the very specification of what it distinguishes. A haecceity that distinguishes one causal relatum from another is itself a relation between the haecceity and what it is the haecceity of, and the *this-cause / that-effect* contrast that haecceities pick out is the very relational non-identity Spatiality names, carried at the level of the thisness rather than at the level of qualitative properties. Haecceitism about causal relata either reads relational structure into its haecceities (confirming Spatiality's contribution under different vocabulary) or strips it out and loses the explanatory work the haecceities were posited to do.

*Second, the interaction line.* Causal exchange is not a bare relation between two labels. It requires transmission from a source-state or role to an uptake-state or role. The interval need not be a distance between two beings; internal causation may run between distinguishable states of one persisting system. What cannot be removed is relational separation between the causal terms: without any distinction between source and uptake, there is no path or articulation by which influence could run, only one undifferentiated event described twice. The relational interval that distinguishes the causal terms is the Spatiality-role invoked here.

Whether one approaches from the distinctness of the relata or from the interaction between them, Physicality without Spatiality collapses: either the relata are not genuinely distinct, or the causation has no path. A being that carries influence needs somewhere to carry it. The interval does not merely lie between them; it is what makes them two things at all.

*Direction 2: S→Φ.* Now the reverse. Two lines converge from the other direction: Spatiality analytically requires Physicality.

*First, the occupancy line.* A load-bearing structural feature of Spatiality is exclusive occupancy — the fact that two things cannot occupy the same position — the point where Spatiality's positions meet Physicality's work. But exclusion is a causal act in the broad sense: to exclude is to prevent, to resist, to block, and preventing, resisting, and blocking are things only a causally active medium can do. A primitivist about exclusion who reads exclusion as a primitive structural fact rather than a canonical-causal one inherits the same medium-work under different vocabulary, by the argument of [§2.4.8](<2.4.8 Exchange Requires Physicality.md>): whatever makes a primitive exclusion *do* exclusion-work must operate across the foreclosure interval, and that cross-interval operation is what Φ names, whether read as canonical causation or as primitive foreclosure performing the same structural function.

A position that nothing *could* occupy functions as an abstract coordinate label, not a spatial position. The reality of spatial positions (what makes them positions rather than mathematical indices) is that they are occupiable. The argument does not deny that *empty* regions of physical space are real: empty regions are real precisely because they are occupiable; something *could* occupy them, even when nothing currently does. The reality of an empty region rests on the occupiability of its positions, not on the presence of actual occupants at every position. What collapses into a coordinate label is not the empty region but the would-be position that nothing could ever occupy. And occupiability requires something capable of occupying: a medium with the causal capacity to occupy and to exclude other occupants. That medium is Physicality. Exclusive occupancy without a being is exclusion with nothing doing the excluding.

*Second, the interval line.* A relational interval between two positions is real only if something can traverse it. An interval that nothing crosses, nothing bridges, nothing moves through is a notation, not a distance. The reality of the interval consists in its traversability, and traversability requires a medium that persists through the crossing. The medium that makes spatial intervals real rather than abstract (by being what crosses them and persists through them) is Physicality.

Whether one approaches from the occupancy of positions or from the reality of intervals, Spatiality without Physicality collapses: either exclusion has no excluder, or intervals have no medium to make them real. The pressure is symmetric: just as Physicality without Spatiality had no path for its causation, Spatiality without Physicality has no medium to make its positions real. Each is the other's internal requirement, not its external correlate.

*Lifting to the triconditional.* Each of the four lines runs on more than the pair it names. Causal exchange (the interaction line) requires transmission, and transmission across an interval is travel, already temporal. Exclusive occupancy (the occupancy line) is exclusion, and exclusion is a causal act that runs in time. Distinctness (the distinctness line) presupposes positions whose differentiation cannot be static: a being that excludes another at a position must endure long enough to do so. The pairwise biconditional S↔Φ arrives already engaging T; the four lines deliver S↔T as part of the same argument. The result is S ↔ (T ∧ Φ): extension cannot stand without both succession and being, and the conjunction cannot stand without extension.

*Movement* presents as spatial vocabulary: traversal of distance. But the result reached above runs in ordinary language before any formal analysis arrives. Movement requires directed succession (T): without before and after, there is no moving, only occupying: being at a position rather than arriving at it. It requires a persistent being (Φ): without something that moves, there is no movement, only position change: a difference between two states with no owner of the difference. Strip either Condition and the word stops applying. Movement is not a spatial word that happens to imply the others. It is a triconditional word built around the extension pivot: S ↔ (T ∧ Φ) embedded in a single noun.

*What converges.* Extension without a being is empty. A being without extension has no positions to occupy. Neither has its work to do without succession to do it through. Three sides of one structural fact: the same fact read from the extension pivot. The remaining link is the one that feels obvious, which is precisely why it must be proved.[^2-6-3-extension-pivot-ch4]

[^2-6-3-extension-pivot-ch4]: The S pivot, S ↔ (T ∧ Φ) and the four realizer lines (distinctness, interaction, occupancy, interval), is engaged in Chapter 4. The canonical anti-S opponent is mereological nihilism: no composites, hence no relational structure beyond simples ([§4.3.11](<4.3.11 Mereological Nihilism.md>)). Structural realism (Ladyman, French) is the closest ally on relational fabric, diverging on what the relations consist in ([§4.3.9](<4.3.9 Structural Realism.md>)), Sider's structuralism takes up spatial structure ([§4.4.7](<4.4.7 Sider's Structuralism.md>)), bundle theory and tropes ask whether positions are anything beyond their occupants ([§4.3.10](<4.3.10 Bundle and Trope Theory.md>)), and Tegmark asks whether relational extension is mathematical rather than substantive ([§4.3.7](<4.3.7 Mathematical Universe Hypothesis.md>)).


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← [2.6.2 Succession's Two Conditions](<2.6.2 Succession's Two Conditions.md>) | [2.6.4 Persistence's Two Conditions](<2.6.4 Persistence's Two Conditions.md>) →
