Chapter 3 reaches the role-level necessity of the Triconditions without using the Euclidean axiom. A different question is whether it also reaches □◇C without S5. The tempting line runs backward from the Conditions to the possibility of change.

> [!argument]
> **The Reverse-Lift Diagnostic** · *from Triconditional Necessity toward Necessary Possibility of Change*
>
> 1. Stage 2 re-establishes, without S5, that every possible world instantiates direction, difference, and bearing: □(T∧S∧Φ), at role-resolution (§[§3.2](<3.2 Triconditional Necessity Positive Account.md>)–3.3).
>
> 1. The Sufficiency of Structure establishes that the fully typed Conditions entail the possibility of Change: (T∧S∧Φ) → ◇C ([§2.4.10](<2.4.10 Sufficiency of Structure.md>)), with the frozen-world case tested at [§2.4.11](<2.4.11 The Frozen-World Test.md>).
>
> 1. If Stage 2 independently delivered T, S, and Φ at that full type-resolution, universal modus ponens would yield □◇C. That would be the Reverse Lift.
>
> 1. It does not yet do so. Stage 2 directly earns directed order, difference, and bearing. The upgrades to temporal succession, spatial extension, and causal persistence are carried at [§3.5.3](<3. Convergence.md>), and those upgrades currently use □◇C.
>
> 1. Using those upgrades to invoke the Sufficiency of Structure and then using the Sufficiency of Structure to derive □◇C would be circular.
>
> 1. Therefore the Reverse Lift is valid only conditionally: it corroborates □◇C for a reader who independently grants the full type-resolution or the Modal Identity, but it is not a new S5-free proof of □◇C.

This diagnosis strengthens the chapter by refusing a false independence claim. The no-onset argument ([§3.1.2](<3. Convergence.md>)) blocks emergence from a capacityless state, and the performative witness ([§3.1.3](<3. Convergence.md>)) establishes ◇C wherever reasoning occurs. Neither supplies cross-world invariance. Without an independent type-bridge, proposition-wise □◇C remains upstream with T1.

What Chapter 3 establishes without S5 is still substantial: the role-level necessity of direction, difference, and bearing, and the identity of Reality with that necessary structure. Once □◇C is supplied, the type-pins at [§3.5.3](<3. Convergence.md>) transmit it into temporal, spatial, and causal-persistent form. The order of dependence is now explicit rather than folded into the convergence claim.

Nothing bars an S5 line from appearing here so long as it is labeled correctly. Section [§3.5.5](<3. Convergence.md>) grants the modal result Chapter 2 earned and lets the Bottleneck confirm the same ground from above. It reinforces the convergence; it does not masquerade as an independent S5-free derivation.


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← [3.5.3 The Closed Seam](<3.5.3 The Closed Seam.md>) | [3.5.5 The S5 Bottleneck Reductio](<3.5.5 The S5 Bottleneck Reductio.md>) →
