□(T ∧ S ∧ Φ) is a conjunction, and the Moves do not support its three limbs equally. Saying so is the honest core of the stage.

> [!info]
> **Quick map.** This short section is the book keeping its own books. The conclusion is a conjunction—time and space and persistence are all necessary—and the many arguments don't support the three equally. Being honest about that is the point. The necessity of succession (time) and of a persisting bearer are heavily overdetermined: nearly every argument re-earns them. The necessity of difference (space) is just as solid at the level of this coexisting with that, but the further step to spatial difference proper takes an extra move, borrowed from earlier. Richer still—a measurable, traversable space—isn't claimed here at all; that's contingent physical detail saved for Chapter 7. At role level, all three stand together.

**T-role: necessary directed ordering.** Supported by several lines, but bare obtaining does not by itself re-derive full temporal succession. The upgrade from asymmetric order to Temporality's loaded type remains a separate bridge.

**Φ-role: necessary bearing or realization.** Supported where a fact, act, or arrangement must be borne, but this is not yet the full type of causal persistence.

**□S: the necessity of difference.** Robustly overdetermined at role-resolution. Stated at the same resolution as its siblings (succession for T, persistence for Φ), the necessary S-claim is *co-existing this-rather-than-that*, and every Move that earns succession or persistence also earns it. The step from bare logical non-identity to *spatial-type* difference (a *where*, not merely a *which*) is earned upstream, though not on □◇C alone as the temporal type-upgrade is. It rides □◇C *together with* the Stage-2 realizer it activates ([§2.4.7](<2.4.7 Distinction Requires Spatiality.md>), [§2.6.2](<2.6.2 Succession's Two Conditions.md>)): the chain that makes the ordering temporal in type makes it extended in type in the same step, set out in full at [§3.5.3](<3. Convergence.md>). The further step to a *metric, traversable manifold* is not forced and is not claimed: that richness is contingent physical content, parallel to a particular temporal metric for T and particular fields for Φ (Chapter 7).

*What converges.* The enactment, construction, and structural-floor families supply overlapping support for the role-level triad: directed order, difference, and bearing. Their support is uneven, and several lines rely on the shared ∅-floor (itself resting on [§3.2.1](<3. Convergence.md>)'s essence-of-obtaining step, an essentialist commitment that line declares by design) or on premises imported from §[§1.3](<1.3 Change.md>)–1.4. They do not, without Stage 1, establish proposition-wise necessity of the fully loaded types. Section 3.5.3 assesses the role-to-type upgrades, while [§3.5.4](<3. Convergence.md>) preserves the remaining □◇C burden. The next stage ([§3.4](<3.4 Reality and Nature Are One.md>)) may use the role-level structure as its input, but should not silently treat the full □(T ∧ S ∧ Φ) theorem as independently re-proved here.


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← [3.3.5 Not Even the Impossible](<3.3.5 Not Even the Impossible.md>) | [3.4 Reality and Nature Are One](<3.4 Reality and Nature Are One.md>) →
