PUH Theorem 373 — Time Makes Diversity, Made Exact: The SPF Is the One Fully Symmetric E8 State, Where Nothing Can Change; Change and Distinction Are One Space; the First Departure Needs a Seed

Photonic Universe Hypothesis (PUH) — Derivation. What is the origin of time? THE CONJECTURE: the Super Polariton Field (SPF) has no time and no reference frames — there is no way to tell one thing from another; the Rebound made separate frames and individual things; time is what makes the diversity of things possible. SETTING. The substrate's state is a point μ in E8's 248-dimensional algebra (T172, T292); between Snaps it moves only along its leaf (T156, T288); the folding real form is E8(−24) (T264, T265). Every number is computed from an E8 structure-constant build (Frenkel–Kac signs; Jacobi to 2 × 10⁻¹⁴; E8(−24) checked: 128 compact roots, Killing signature −24). RESULT 373.1. The only state that all 248 generators leave unchanged is μ = 0. The SPF — V8's "most symmetrical structure", T261's maximally symmetric ground state — is the zero state, where all eight invariants vanish and the energy is least. RESULT 373.2. At μ = 0 no law of motion that respects E8 — Hamiltonian, or the dissipative Snap class of T288 — can move the state: its velocity would have to be a fully symmetric direction, and there is none but zero. The SPF is timeless by necessity, not by stillness. T172's "time is mathematically frozen" point is the SPF, not a core. RESULT 373.3. At every state, the directions in which it can change and the directions in which it can be told apart are one space — the tangent space of its leaf, of dimension equal to the rank of ad μ. Time and diversity are one condition, vanishing together only at the SPF. RESULT 373.4. Differentiation comes in jumps. In E8(−24): 0 at the SPF; at least 58 directions for any other state — first the nilpotent seed of the gravitational sl(2,ℝ) (T303–T304; 58 = 56 + 2), on a massless cone rising to 216 (T295–T296); off the cone at least 114 — the photon generator H_θ (T167, T290) and a descent direction in the (56,2) — rising to 240. RESULT 373.5. Nothing inside the SPF can start the Rebound. Any seed on the massless cone can grow along a descent direction as e^(2t) with all eight invariants exactly zero; a seed of 10⁻⁶ reaches size 1 at t = 6.91, of 10⁻³ at 3.45, of 0.1 at 1.15 — a delay logarithmic in the seed, the law T295 found for the fold's ignition. The photon generator has the same spectrum, imaginary instead of real: it rotates the seed with period 2π, a massless clock. The seed must come from outside the SPF — in V8's cycle a Planck Star; for a first Rebound, a boundary condition. RESULT 373.6. Mass is a second, separate step: leaving the massless cone changes the invariants, which only Snap-class events do (T288) and T175's constraint enforces (T314); every allowed state then has at least 114 directions. The textbook symmetry-breaking potential is T175's constraint written as a penalty; the threshold itself is fixed by the algebra (T313, T315). THE CHOICE. Cores carry nonzero invariants and are not frozen (T314, T332), so a core's interior cannot be the timeless zero state: the "same state as the SPF" of V8, T231 and T356 holds only as "same structure" (T261) — or the SPF is not timeless. WHAT CHANGES: V8's ground-state SPF CONFIRMED AND MADE EXACT; T261 target (i) SUPPLIED, (iii) ANSWERED, (ii) PARTLY SUPPLIED; V8/T231/T356 core-interior identification — THE FORK; T172's third result RELOCATED; T224 and T242's second part QUALIFIED (T242's state-triggered Rebound STANDS); T336 REFINED; T288 EXTENDED. KILL-CONDITIONS: an SPF with a preferred direction; a PUH law of motion that does not respect E8; a folding real form other than E8(−24) (changes the massless rungs only). NOT CLAIMED: that PUH's own Hamiltonian produces the growth shown; the origin of the first seed; any mass value; the SPF's spatial character. OPEN: the seed; the fork; the signs of the invariants on elliptic states (the photon generator's degree-2 invariant is −120 against +120 for a descent direction).