The cycle entails specific consequences for cosmology and hands off cleanly to history.

> [!corollary]
> **Big Bang Within the Cycle** · **R19** · *Result of R17*
>
> The Big Bang is the local inflection of compression into expansion at the start of the present cycle, not the first moment of Temporality. Follows from the structural closure of Temporality established across Modal Constitution and Cartesian Certainty (§[§2.1.3](<2.1.3 Modal Constitution.md>), 2.2) and the Singularity Preclusion Result ([§7.6](<7.6 Singularity.md>)) jointly: the first result forecloses any "before" or "outside" Temporality (so the bang cannot be an absolute beginning) and the second rules out the inflection itself being a state Nature could occupy.

*The Big Bang begins this cycle, not Temporality.* The structural closure of Temporality (§[§2.1.3](<2.1.3 Modal Constitution.md>), 2.2, [§7.6](<7.6 Singularity.md>)) and the preclusion of a stable zero-extension state ([§2.7](<2.7 Nothing to Consider.md>), [§7.6.1](<7.6.1 What is Disputed.md>)) jointly locate the bang inside the cycle, not at the inception of Nature. The bang is the local inflection of compression into expansion at the start of the present arc. It is not the first moment of Temporality. *No change* is not a coherent prior state; difference itself is what change tracks. Cosmological "first cause" arguments that read the bang as the origin of Nature engage the wrong object: the bang has a before; what it does not have is a creation event prior to all changes whatsoever. The closure that runs in [§4.3](<4.3 Physics and Mind.md>) against a creator standing outside structure runs here, at cosmological scale, against a creator standing prior to it. The implication is strictly modal: it depends on past-eternity and singularity-preclusion, not on any specific physics of the bounce.

Craig's personal-cause disjunction fails at the same point. The disjunction says that an impersonal necessary cause would produce its effect eternally if it were sufficient, or would never produce it if it were insufficient; only a free personal agent could initiate a temporally finite universe without prior temporal conditions. The Necessity of Nature denies the shared premise. Nature is not a sufficient cause standing before a temporally finite cosmos and deciding whether to produce it. Nature is the necessary structure within which the cycle is already past-unbounded, and the bang is a local transition internal to that structure. Once the effect is not a temporally finite universe needing a first-producing act, the disjunction has no object.

Locating the bang in the quantum-cosmology landscape sharpens what the structural claim does and does not adjudicate. Loop quantum cosmology (Bojowald, *Once Before Time* -(Martin Bojowald, 2010); Ashtekar and Singh -(Ashtekar, A., and P. Singh, 2011)) replaces the singular point with a quantum-gravitational bounce (directly compatible with the cyclic reading). Hartle and Hawking's no-boundary proposal (James B. Hartle and Stephen W. Hawking, 1983) takes the early universe to have a smooth, geometry-stripped lower boundary in which temporal direction emerges from the geometry rather than pre-existing it; cyclic and no-boundary both reject a singular first moment of Temporality, and disagree on whether what lies below the bang is a prior cycle or a smooth geometric bottom. Vilenkin's tunneling-from-nothing -(Alexander Vilenkin, 1982) sits more uncomfortably: it nucleates the universe from a zero-extension state, and the structural argument forecloses any reading in which the pre-tunneling state is itself a state Nature occupies ([§2.7](<2.7 Nothing to Consider.md>) Null State preclusion). Tunneling is compatible with the Necessity of Nature only if the pre-tunneling 'nothing' is treated as a calculational artifact rather than a metaphysical state. Across all three programs, none lets a stable zero-extension state obtain in Nature: ¬◇(permanent ¬S) is the constraint they jointly respect at the structural layer, even where they disagree empirically on which mechanism realizes the resolution.

*Heat death is a phase, not a terminus (on the abductive cycle layer).* The dilute, low-energy far future of the present cycle is not the end of Nature on the cycle reading; it is the configuration from which the next cycle proceeds, under whichever resolution mechanism the bounce turns out to follow ([§7.6.2](<7.6.2 What is Required.md>)). What each cycle's bounce-region must deliver to license the thermodynamic arrow of the next is what the *Past Hypothesis* names in the standard literature (Albert, *Time and Chance* -(Albert, David Z., 2000); Loewer, 'Counterfactuals and the Second Law' -(Barry Loewer, 2007)); the framework's commitment is that structural argument requires *something* deliver such a state at each recurrence, while *which* mechanism realizes the delivery is for physics to settle ([§7.6](<7.6 Singularity.md>)). The popular eschatology that reads heat death as a final state mistakes one cycle's late phase for the whole. Penrose's CCC, Conformal Cyclic Cosmology, the proposal that the very late, geometry-stripped state of one cosmic aeon is conformally identical to (i.e., agrees with up to overall scaling) the very early, geometry-stripped state of the next, makes the conformal indistinguishability (the equivalence of two geometries up to a smooth pointwise rescaling of distances, when the absolute distance scale ceases to register physically) explicit; ekpyrotic and torsion-bounce variants reach the same destination by other lines. The structural account commits to the destination (that the apparent terminus is a phase) without committing to any specific resolution program. The implication depends on the modal preclusion (strict) plus the cyclic prediction (abductive, [§7.6.2](<7.6.2 What is Required.md>)).

> [!lemma]
> **No Changeless Duration** · **L10** · *Lemma toward the Cyclic Reading*
>
> No interval of positive duration is changeless. A stretch of time has positive duration only if it contains two distinct moments; and where moments are individuated by some discerning difference in the T∧S∧Φ state they index (relationalism about instants), distinct moments require that difference to obtain, so positive duration entails differentiation across the stretch. The dilute far future then faces two horns: if it genuinely elapses it is differentiated, hence not changeless and no terminus; if it does not elapse it has zero duration, collapsing to a single moment, not a changeless *stretch* at all, and so not the infinite changeless duration the lemma denies. (Whether that single moment could stand as a bare terminus, a last instant with no successor individuated, is the order-type question [§7.6](<7.6 Singularity.md>) leaves open: □◇C keeps change *possible* there but does not by itself supply an actual successor.) The lemma is strict within the framework: the individuation-by-difference premise (relationalism about instants) is not an optional extra but what the book's account of Temporality already supplies — to be at all is to stand in succession, and succession is what change tracks ([§1.3](<1.3 Change.md>)–[§1.4](<1.4 Three Conditions.md>), §[§2.3](<2.3 Necessary Possibility of Change.md>)–2.4) — so moments distinct *solo numero*, by primitive temporal haecceity with no discerning difference between them, stand in no succession and compose no stretch of time on the framework's terms. A substantivalist who resists the lemma by haecceitistic individuation thereby declines the framework's conception of Temporality upstream; the lemma admits no escape from within it.

*A strict floor beneath the abductive verdict.* Even setting the cyclic prediction aside, a permanent changeless *stretch* is not a coherent end-state at all. "Infinite changeless duration" names no interval that could obtain: if the far future genuinely elapses it is thereby differentiated, and if it does not elapse it is not a stretch of time but a single moment, so a changeless tail is foreclosed independent of which bounce mechanism, or none, obtains. The cyclic reading supplies the positive picture: the dilute phase is where the next cycle proceeds ([§7.6.2](<7.6.2 What is Required.md>)), while this floor rules out the rival picture of an everlasting *changeless* rest without waiting on the physics. The floor's reach is exactly that narrow. It forecloses a literally changeless terminus, not an everlasting heat death that stays micro-differentiated (quantum and thermal fluctuation persisting) while remaining permanently exhausted of usable gradients. Such a state satisfies L10's first horn, since it elapses and is thereby differentiated, yet it is still a permanent end of structure, life, and usable work; only the abductive cycle layer, not L10, speaks against it. What the floor secures is 'no literally frozen rest,' not 'no permanent end-state.' And the hinge the floor turns on is not a cost after all: it is supplied by the framework rather than purchased as an extra premise. Relationalism about instants is, within the book's account, just what Temporality delivers — to be at all is to stand in succession, and succession is what change tracks ([§1.3](<1.3 Change.md>)–[§1.4](<1.4 Three Conditions.md>), §[§2.3](<2.3 Necessary Possibility of Change.md>)–2.4) — so a tail of moments individuated by primitive temporal haecceity alone, distinct with no discerning difference across them, stands in no succession and is not a changeless *stretch of time* but a single moment misdescribed. A substantivalist who holds the tail changeless by haecceitistic individuation is not escaping the floor but declining the framework's conception of Temporality itself, which relocates the disagreement to the same upstream point at which the chapter places its other principled resisters ([§7.9](<7.9 Synthesis.md>)). Within the framework the floor stands unconditional, and the no-end treatment inherits the same standing.

*Fine-tuning at the cosmological scale changes shape (on the abductive cycle layer).* Across cycles under invariant law ([§2.1.7](<2.1.7 Two Readings.md>), the modal-invariance principle that the structural conditions of Nature hold across every cycle, not merely the present one), if the abductive cyclic conclusion of [§7.6](<7.6 Singularity.md>) holds, the macro-trajectory recurs. What every cycle delivers is not a one-off draw from a space of possible universes; it is what the structural conditions, plus the laws those conditions support, produce whenever they produce anything. The standard fine-tuning argument's target (the apparent contingency of *this* trajectory) relocates: it can be re-pitched at the level of which laws and constants Nature instantiates, but it cannot be pitched at the level of which cycle we happen to be in. Whether the relocation dissolves the argument or only resites it depends on which version is in play. The structural account commits to the relocation, not to any specific verdict on the variants it produces. The implication depends on macro-trajectory recurrence, which is abductive rather than strictly modal ([§7.6.2](<7.6.2 What is Required.md>)).

*Type and token: the transition to [§7.7](<7.7 Cosmic History.md>).* The cycle fixes the macro-shape of Nature's history; it does not fix the contingent particulars within any one cycle. Three layers operate together. At the level of macro-trajectory (expansion, structure-formation, compression, return) the cycle delivers what Modal Invariance plus singularity-preclusion entail. At the level of arrangement-kinds (galaxies, stars, heavy elements, planets, chemistry, life) equal initial conditions plus equal force output of equivalent substance under invariant law deliver the trajectory's necessary outcomes ([§7.7](<7.7 Cosmic History.md>)). At the level of which star is where, which species evolves, which sentence gets written, the cycle leaves history free. [§7.7](<7.7 Cosmic History.md>) traces the cosmic-evolutionary trajectory and develops the type/token distinction the cycle makes available. Without recurrence under invariant law, type and token cannot be cleanly distinguished at cosmological scale; with it, the type is what every cycle shares and the token is what each cycle does on its own.

*Earman.* Earman's 'The Past Hypothesis: Not Even False' -(John Earman, 2006) is not the charge that the Past Hypothesis is empirically idle. The title echoes Pauli's 'not even wrong': the objection is one of well-formedness and lawhood. The Past Hypothesis as usually stated (the posit of a low-entropy initial macrostate) is too ill-defined to be assessed as true or false, and when it is made precise it inherits the measure and typicality problem, the difficulty of defining an entropy for the universe as a whole, and the complications general relativity brings to any global entropy bookkeeping. The complaint is thus not that the posit generates no predictions but that, as stated, it is not yet a candidate for lawhood or truth, and that sharpening it exposes these difficulties rather than settling them. It lands hardest on the single-cycle cosmology, where the Past Hypothesis figures as an unexplained explainer: a brute low-entropy boundary condition asserted to secure the thermodynamic arrow but not derived from the dynamics.

The cyclic reading changes the status of the posit without claiming to dissolve the worry by fiat. It converts the Past Hypothesis from a free boundary condition into a constraint the bounce dynamics must meet: what has to be delivered at each bounce-region is not a stipulated initial macrostate but the dynamical output of whichever mechanism obtains (LQC, CCC, ekpyrotic phase transition, or torsion-bounce variant). That relocation answers the lawhood half of the objection, since the constraint is now grounded in dynamics rather than posited outside them, and the question 'why was the initial entropy low?' becomes the tractable dynamical question 'does this bounce mechanism deliver a low-enough-entropy macrostate for the next cycle's arrow to run?'. It does not by itself discharge the well-formedness half. The per-bounce constraint is better-defined than the single-cycle posit only so far as a specific program supplies a definition of the relevant entropy and a measure over the bounce-region's states; absent that, the cyclic reading inherits the very definitional burdens Earman presses, now posed once per cycle rather than once at the beginning. The verdict is therefore split: the cyclic reading removes the brute-posit complaint but leaves the cosmic-entropy-definition and measure/typicality complaints for whichever bounce program to make precise. The structural claim does not wait on their resolution, since it rests on modal preclusion ([§7.6](<7.6 Singularity.md>)) rather than on the Past Hypothesis.

*Smolin.* Lee Smolin's cosmological natural selection (*The Life of the Cosmos* -(Lee Smolin, 1997); *Time Reborn* -(Smolin, Lee, 2013)) offers an alternative cyclic-evolutionary program in which each cycle's physical constants vary slightly across black-hole-mediated offspring universes, with selection pressure favoring parameter-sets that maximize black-hole production. The present account commits to Modal Invariance: the structural conditions T, S, and Φ, and the laws those conditions support, hold invariantly across cycles ([§2.1.7](<2.1.7 Two Readings.md>)). Smolin's variant-law program presses this commitment: if constants evolve across cycles, Modal Invariance holds only at the level of the structural conditions themselves (T, S, Φ remain necessary), not at the level of the specific parameter-values those conditions permit. The structural reply distinguishes the modal invariance of structural conditions from the contingency of parameter-values within those conditions. Smolin's selection operates on the contingent layer; the invariance claim operates at the structural layer. The two coexist if the invariant structural conditions are compatible with a range of parameter-values, which the framework's structural-role-filling architecture ([§7.4](<7.4 Substance.md>)) explicitly affirms: T, S, and Φ are role-conditions, and which specific physical programs fill those roles is a contingent question the framework does not settle. Smolin's cosmological natural selection is thereby a hypothesis about which parameter-sets occupy the contingent layer across cycles, not a challenge to the structural conditions that any cycle must instantiate.

*Penrose and the Weyl curvature hypothesis.* The conformal rescaling at the heart of CCC (the geometric equivalence between the very late aeon of one cycle and the very early aeon of the next, up to pointwise distance-scaling) does not by itself address the entropy objection. Penrose's Weyl curvature hypothesis -(Roger Penrose, 1979) supplies the missing mechanism: the thermodynamic arrow of time requires that Weyl curvature (the tidal gravitational distortion component of spacetime curvature, independent of local matter density) be zero or near-zero at the initial singularity, even as the Ricci curvature (matter-density component) is high. Weyl-zero initial conditions correspond to the smooth, low-gravitational-entropy state CCC's aeon-transition requires; without them, successive aeons would inherit increasing Weyl curvature from the gravitational clumping of prior cycles, and the entropy objection would accumulate rather than dissolve. The Weyl curvature hypothesis is therefore the mechanism that makes CCC's entropy bookkeeping work across aeons, and the empirical status of Weyl-zero initial conditions, detectable in principle via concentric low-variance rings in the CMB, a signature Penrose and Gurzadyan sought (Vahe G. Gurzadyan, Roger Penrose, 2010), is where CCC's specific commitments are testable. The present account does not adjudicate among bounce programs ([§7.6.2](<7.6.2 What is Required.md>)), but naming CCC as a candidate realization of the cyclic reading without the Weyl curvature hypothesis leaves its entropy bookkeeping mechanism opaque.

*Smith and Grünbaum.* Quentin Smith ('Atheism, Theism and Big Bang Cosmology' -(Quentin Smith, 1991); *Theism, Atheism, and Big Bang Cosmology* with Craig -(William Lane Craig, Quentin Smith, 1993)) and Adolf Grünbaum ('The Pseudo-Problem of Creation in Physical Cosmology' -(Adolf Grünbaum, 1989); 'Theological Misinterpretations of Current Physical Cosmology' -(Adolf Grünbaum, 1998)) develop sustained atheistic philosophical critiques of the bang-as-creation reading that also resist cyclic alternatives on grounds of empirical adequacy: Smith holds that the singularity implies an uncaused beginning; Grünbaum that the bang requires no explanation beyond the physical description and that cyclic cosmologies are scientifically unmotivated extensions beyond what the bang's physics licenses. Both oppose bang-as-beginning (which aligns them with the Necessity of Nature against the Craig reading) but both also resist cyclicity on the grounds that the physics does not license the extension. The structural reply proceeds at a different level: it does not argue from the bang's physics to cyclicity but from the modal preclusion of stable zero-extension states ([§7.6](<7.6 Singularity.md>), Result of T6) and the structural closure of Temporality (§[§2.1.3](<2.1.3 Modal Constitution.md>), 2.2) to the structural necessity of some recurrence. Smith and Grünbaum's resistance to cyclicity targets abductive extensions beyond the physics, precisely the layer the present account marks as abductive rather than strictly modal ([§7.6.2](<7.6.2 What is Required.md>)). The structural account commits to the strictly modal layer (no stable zero-extension terminus; structural continuation) and defers to physics on the abductive layer (whether that continuation takes cyclic form, and if so which bounce program realizes it), which is the scope-discipline both critics would recognize as methodologically appropriate. Their independent rejection of bang-as-creation meanwhile confirms the present account's rejection of the Craig reading from an atheistic-naturalist direction: Smith and Grünbaum agree that the bang is not a creation event, though they disagree with each other and with the Necessity of Nature on what follows.

The specific bounce mechanism realizing the resolution at total compression (loop quantum gravity, conformal cyclic cosmology, ekpyrotic brane collision, torsion-bounce variants, or other) is open and empirical ([§7.6.2](<7.6.2 What is Required.md>)). The structural argument requires only that *some* such mechanism obtain; *which* one realizes the closure is for physics to settle.

Whether macro-scale initial conditions transmit identically across the bounce, sufficient to produce type-recurrent macro-trajectories cycle to cycle, is the abductive premise present physics supplies; it is not strictly modal. A reader who grants only the strict modal layer keeps cycles-must-recur without cycles-recur-identically.

How the second-law constraint resolves at the cycle transition (Tolman's entropy objection) remains open across the rival programs. Penrose's conformal rescaling, ekpyrotic phase transitions, and entropy-shedding via horizon dilution each propose distinct resolutions; none is empirically confirmed.

Whether the cyclic frame requires revision in light of dark-energy-driven late-time acceleration, observational constraints from future-generation gravitational-wave detectors, and theoretical advances in quantum gravity is the empirical frontier the structural claim leaves wide open.

And the relationship between cosmological recurrence and the type/token distinction [§7.7](<7.7 Cosmic History.md>) develops (specifically, how much of cosmic history is necessitated by the cycle plus invariant law versus how much is contingent at the configuration scale) is the seam between this section and the next.


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← [7.6.4 What is Confirmed](<7.6.4 What is Confirmed.md>) | [7.7 Cosmic History](<7.7 Cosmic History.md>) →
