PUH Theorem 336 (Chronology Protection from Core Permanence) — Closed Timelike Curves Are Forbidden Because the Core Count Is Monotonic and Casimir Conservation Forbids Splitting; a Topological Arrow, Not a Statistical One, and PUH Is Therefore Not CCC

Photonic Universe Hypothesis (PUH) — Argument Assembled. Backward Time Travel Impossible THE WEAKER ARGUMENT, AND WHY IT FAILS. It is tempting to argue that time is emergent from mass, so a universe without mass has no time, and that this forbids backward travel. THE FIRST HALF IS DEFENSIBLE and is essentially Penrose's: a photon's own interval is exactly zero, so massless particles carry no clocks. THE SECOND HALF DOES NOT FOLLOW. A universe with no clocks is not one in which going backward is impossible; it is one in which "backward" has no meaning. ABSENCE OF A MEASURE IS NOT A PROHIBITION. There is also an internal objection the weaker argument cannot survive: if time emerged from mass alone, no parameter would govern the lattice before mass exists — yet the framework derives Maxwell from lattice phase modes, and a wave equation contains a time derivative. SOMETHING IS ALREADY TICKING. Three notions must be kept apart: PARAMETER time (requires a dynamical medium; supplied by the lattice whenever it exists), PROPER time (requires a massive worldline; supplied by mass), and ORDERED time (requires an irreversible counter; supplied by core amalgamation). The framework should claim the second and third and not the first. THEOREM 336.1 (the core count is monotonic). T172 establishes that a Planck core cannot split, in terms of conservation rather than thermodynamics: "A single leaf cannot split into two leaves through any smooth Hamiltonian evolution, because smooth evolution preserves the Casimir values exactly. To split would require simultaneously changing the Casimir values of a single state into two different sets of values — which contradicts the conservation of Casimir invariants." T206 draws the consequences: cores cannot split, cannot slowly lose mass, and cannot disappear; they are "topological knots in the E8 lattice," not thermodynamic objects that decay. LET N(t) BE THE NUMBER OF DISTINCT CORES. Formation increases it (while material accumulates); merger decreases it; accretion leaves it unchanged; SPLITTING WOULD INCREASE IT AND IS FORBIDDEN. PROOF: after formation ceases the only permitted operations are merger and accretion, so N is non-increasing, and a non-increasing integer sequence cannot revisit a value it has left. ∎ RESULT 336.2 (closed timelike curves are excluded). A closed timelike curve requires the universe to return to a state it has previously occupied, and in this framework a state includes its core configuration. IF N NEVER RETURNS TO A PREVIOUS VALUE, NO SUCH RETURN EXISTS. The exclusion is TOPOLOGICAL RATHER THAN DYNAMICAL: the standard routes to chronology protection invoke energy conditions (which exotic matter may violate) or quantum backreaction diverging near a would-be Cauchy horizon (a statement about the semiclassical approximation failing). NEITHER IS USED HERE — the obstruction is a conservation law and a counting argument. And it is sharply falsifiable: OBSERVE A CORE SPLITTING, OR ANY BLACK HOLE LOSING MASS BY ANY MECHANISM INCLUDING HAWKING EVAPORATION, and everything here fails. RESULT 336.3 (stronger than the thermodynamic arrow). Entropy is statistical, and the Poincaré recurrence theorem guarantees a bounded closed system returns arbitrarily close to any prior state given sufficient time — the second law is overwhelmingly probable, not impossible to violate. THE CORE-COUNT ARROW ADMITS NO FLUCTUATION AND NO RECURRENCE: a merged core is not improbably restored; its restoration is forbidden by conservation. And the counter is fine-grained rather than coarse: T179's holographic balance gives N = (R/l_P)² ≈ 7.4×10¹²², roughly 123 orders of magnitude of strictly irreversible transitions — a clock with more distinguishable states than the observable universe has particles, every tick one-way. A DEPENDENCY THAT MUST BE DISCLOSED. T206 derives permanence "directly from the Rank Drop Theorem combined with the topological classification of E8 configurations." And T331, filed three days ago, showed the rank drop from 8 to 0 is UNATTAINABLE on T175's own constraint surface, the Hessian being bounded below by a positive multiple of the identity because every E8 Casimir degree is even and every coupling positive. THAT WOULD BE FATAL IF PERMANENCE RESTED ON THE RANK DROP ALONE. IT DOES NOT: the non-splitting argument runs through Casimir conservation independently and is untouched by T331. A critic auditing this note would reach T206, then T331, and conclude the foundation had been removed — it has not, but the route by which it survives is stated rather than assumed. RESULT 336.4 (the framework is not a conformal cyclic cosmology). This argument requires cores to PERSIST rather than vanish, and that has a consequence. Conformal cyclic cosmology requires a massless far future: once only radiation remains the metric loses its scale, and the conformal boundary is glued to the next beginning. A UNIVERSE RETAINING PERMANENT MASSIVE OBJECTS CANNOT BE RESCALED THAT WAY. The framework's cycle works differently and its own papers say so: the rebound is triggered when the tension reaches its threshold, "before the singularity is reached in finite time," with stored tension released as outward kinetic energy — MASS NEVER HAS TO DISAPPEAR. T206's title states the requirement directly: "the Rebound Cycle Requires Permanent Topological Seeds." Tabulated: CCC has a massless far future, conformal rescaling as trigger, conformal structure alone carried across, and an arrow reset each aeon; this framework has persisting cores, a tension threshold, the cores themselves carried across with their history, and an arrow that never resets. THE RESEMBLANCE IS SUPERFICIAL — both are cyclic — AND THE MECHANISMS ARE INCOMPATIBLE. KILL-CONDITIONS: (i) if a core is observed to split, or a black hole to lose mass by any mechanism, Theorem 336.1 fails and everything with it — the sharpest available test, and an ordinary astrophysical observation; (ii) if Casimir invariants are not conserved under the relevant evolution, the non-splitting argument fails; (iii) if core formation never ceases, N is not monotonic and the argument applies only asymptotically; (iv) if a closed timelike curve can be traversed without returning the universe to a prior GLOBAL state — a local loop in a region whose core configuration is unchanged — the counting argument does not exclude it, and this note does not address local constructions. NOT CLAIMED: that time is emergent from mass in the strong sense, which Section 1 rejects; that the thermodynamic arrow is wrong, only that it is weaker; that chronology protection has been proved in general relativity, since this is an argument within one framework about its own content; that core permanence has been established independently here, since it is taken from T172 and T206 with its dependency disclosed; or that the framework's cyclic cosmology has been verified, only that it differs in mechanism from the conformal one.