*The realizer move, applied to Φ ↔ (T ∧ S).* Persistent bearing is biconditional with both directed succession and relational extension: Φ ↔ (T ∧ S). If something persists, it persists through temporal order as a bearer situated within relational structure; it need not move across a spatial distance. If directed succession and real relational differentiation are instantiated, the argument asks what bears them. Four lines work the T↔Φ link explicitly (two in each direction, each refuting a distinct deflationary mimic), and each line already deploys S in the work that makes it run. The same four lines deliver the Φ→S half of S↔Φ as what the lines are doing already; the remaining half arrives by triangulation with §[§2.6.2](<2.6.2 Succession's Two Conditions.md>)–2.6.3, gathered at [§2.6.5](<2.6.5 Mutual Containment.md>). The same realizer move is worked from the succession and extension pivots at §[§2.6.2](<2.6.2 Succession's Two Conditions.md>) and 2.6.3; the result is cross-confirmation, not assembly. The mimics on each side must be refuted explicitly.

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

*First, the continuity line.* Think of a relay race. The baton must be carried from one runner to the next: if it vanishes at the handoff and a new baton appears, nothing was relayed. Directed succession works the same way: something must carry influence from before-state to after-state. Without a persistence medium, what produced the before-state leaves nothing behind, and the after-state arrives from nowhere. That is not directed transition. It is replacement. The distinction between transition and replacement is not a matter of degree. It is constitutive. A before-state that transmits nothing forward does not produce an after-state. For succession to be causally structured rather than merely sequential, something must persist across the transition as the vehicle of causal transmission. That persistence medium is Physicality.

*Second, the identity line.* For there to be a subject that changes, something must persist as the same subject through the change. If nothing endures from the before-state into the after-state, there is no subject that underwent the transition; there are two disconnected states with nothing in common. Change requires a thing that was one way and is now another. Remove the thing and you remove the change: what remains is two descriptions with no owner.

Whether one approaches from the continuity of causal influence or from the identity of the changing subject, Temporality without Physicality collapses: either succession has no vehicle, or change has no subject. Persistence is not what survives change. It is what makes change possible: the invariant through which variation has content. Something that cannot stay is not passing through time. It is flashing and vanishing. That is replacement, not succession.

*Direction 2: Φ→T.* Two lines converge from the other direction: Physicality analytically requires Temporality.

*First, the persistence line.* Persistence is not a static property. It is persistence through: through transitions, through changes, through the passage from before to after. A medium that never stands in an earlier/later order is not persisting through anything. It exists at no moment, endures across no interval, and sustains nothing from one state to the next. To persist is to be the same thing at a later time as at an earlier time. Remove the temporal ordering and there is nothing for persistence to consist in. Physicality without Temporality is not a being in a reduced mode. It is the word *being* with no structural content.

*Second, the causation line.* Causal capacity (the ability to affect and be affected) requires asymmetric ordering. The cause precedes the effect. The affecting comes before the being-affected. Without temporal direction, there is no fact distinguishing which is the cause and which is the effect. The causal relation becomes symmetric, and symmetric causation is not causation but mere correlation. The asymmetry is not a feature added to causation from outside. It is what causation consists in: an influence that runs from source to recipient, not a symmetric correlation between co-occurring states. Remove the temporal direction and the influence has no arrow, and an arrow without direction is not an arrow.

Whether one approaches from the persistence of the medium or from the directionality of its causal relations, Physicality without Temporality collapses: either persistence has no succession to persist through, or causation has no direction.

Succession needs a persistence medium. The persistence medium needs temporal direction. They empty together. The argument that derived them ran on both.

*Lifting to the triconditional.* Each of the four lines argues T↔Φ, but each already deploys S in its argument: a baton must be carried across (the continuity line: carrying happens between positions); the subject that endures must endure somewhere (the identity line: there is no placeless subject); causation runs from one position to another (the causation line: the asymmetry of cause-to-effect is asymmetry across positions); persistence persists through an interval (the persistence line: the very phrase requires extension). Strip S from any of these and the line loses what makes it run. The pairwise biconditional T↔Φ arrives already engaging S; that S-deployment delivers half of S↔Φ (Φ→S: any argument that yields Φ here passes through S, so Φ-instantiation requires S-instantiation). The other half (S→Φ) is delivered by triangulation with §[§2.6.2](<2.6.2 Succession's Two Conditions.md>) and [§2.6.3](<2.6.3 Extension's Two Conditions.md>): T↔(S∧Φ) is given at [§2.6.2](<2.6.2 Succession's Two Conditions.md>) and S↔(T∧Φ) at [§2.6.3](<2.6.3 Extension's Two Conditions.md>); the three biconditionals jointly entail Φ↔(T∧S). The four lines here do not need to derive S↔Φ in isolation; they need only deliver T↔Φ in a way that already engages S, which they do, and Φ↔(T∧S) is jointly delivered by triangulation across all three pivots at §[§2.6.2](<2.6.2 Succession's Two Conditions.md>)–2.6.4. The result is Φ ↔ (T ∧ S): persistent bearing cannot stand without both succession and extension, and the conjunction cannot stand without a being.

*Interaction* presents as causal vocabulary: things affecting one another. But the result reached above runs in ordinary language before any formal analysis arrives. Interaction requires relational extension (S): without distinct positions, there is no between, and without a between, what appears to be exchange is a single event described twice. It requires directed succession (T): causal influence runs from before-state to after-state; without that direction, what appears to be affecting is correlation, not causation. Strip either Condition and the word stops applying. Interaction is not a causal word that happens to imply the others. It is a triconditional word built around the persistence pivot: Φ ↔ (T ∧ S) embedded in a single noun.

*A dynamic supplement.* The realizer lines establish Φ↔(T∧S) conceptually: persistence cannot stand without succession and extension, and the conjunction cannot stand without a being. That derivation is the load-bearing argument for the biconditional; what follows is characterization of Φ's further texture, not additional derivation. The same persistence is available as first-person datum, and three further observations sharpen what kind of host Φ is.

*Persistence hosts change.* A thought held in attention spans changes that proceed around it: the room's air exchanging, the page's light scattering, the body's blood circulating. The thought spans the changes; the changes do not erase it. This does not require an unchanged host. A process may alter its own bearer while enough continuity remains to carry the process and its effects. Φ is the bearing continuity through which change occurs, not an invariant configuration that change can never affect.

*Persistence admits hold-and-proceed.* Breath suspended, heartbeat continuing, neural firing continuing, manuscript resting on the desk: one change-process is held while sibling processes proceed at their own rates. The temporal order of change is not totally serial. There is no master succession running the world with everything else as derived sub-steps. Φ is the condition under which many change-processes can run concurrently and one can be suspended without arresting the others.

*Persistence is grain-independent: it admits processes at different temporal grains.* A held thought spanning an interval and blinks occurring periodically across the same interval are persistence-bearing processes at different temporal grains within the same Φ. The observation is not that the cadences are mathematically incommensurable, but that no master cadence is given in the data as constitutively fixing both. Their temporal relation is contingent; their co-occurrence within one persistence-bearing structure is the point. Φ is the condition under which processes at different grains are co-hosted at all.

*What the supplement adds.* The realizer lines establish Φ↔(T∧S); these three observations characterize what Φ further is. Φ is hosting, plural, and grain-independent: a host that change operates within rather than upon, a manifold that admits concurrent suspension, a condition that does not impose a master cadence on what it hosts. *Cogito ergo muto* ([§2.8.2](<2.8.2 Nature Cannot Be Denied.md>)) catches the denier of change at the token level; the supplement characterizes what the catch is catching the denier inside of. The denial is hosted, runs alongside sibling processes, and proceeds at a cadence the denier did not select.

*Where the three triconditionals stand.* Each pivot has been worked in both directions: T ↔ (S ∧ Φ) in [§2.6.2](<2.6.2 Succession's Two Conditions.md>), S ↔ (T ∧ Φ) in [§2.6.3](<2.6.3 Extension's Two Conditions.md>), Φ ↔ (T ∧ S) here. Three pivots on one fact, twelve lines in total, every pair of Conditions covered twice from the vantage of each pivot. The full instantiation of any one Condition, when unpacked, reveals the other two as internal requirements rather than external correlates.

*What converges.* Three Conditions, three triconditionals, and one structure read through all three. What that structure amounts to (as one fact rather than three) is what follows.[^2-6-4-persistence-pivot-ch4]

[^2-6-4-persistence-pivot-ch4]: The Φ pivot, Φ ↔ (T ∧ S) and the four realizer lines (continuity, identity, persistence, causation), plus the hosting/plural/grain-independent supplement, is engaged in Chapter 4. The strongest opponent of the identity line is eliminativism and illusionism about persistence ([§4.3.2](<4.3.2 Eliminativism and Illusionism.md>)). Sider's stage theory reads persistence as concatenation of stages rather than endurance ([§4.2.8](<4.2.8 Stage Theory.md>)), bundle theory and tropes ask whether there is a persistent subject beyond the bundle ([§4.3.10](<4.3.10 Bundle and Trope Theory.md>)), idealism accepts persistence but reads it as mental rather than as Φ ([§4.3.5](<4.3.5 Idealism.md>)), Russellian monism posits intrinsic categorical natures behind the persistence-medium ([§4.3.3](<4.3.3 Russellian Monism.md>)), and the Humean denial of necessary connection presses at the persistence-vehicle for causal transmission ([§4.1.4](<4.1.4 Humean Contingency.md>)).


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← [2.6.3 Extension's Two Conditions](<2.6.3 Extension's Two Conditions.md>) | [2.6.5 Mutual Containment](<2.6.5 Mutual Containment.md>) →
