PUH Theorem 381 — The Precession Is Not the Lattice's Motion: Its Waves Would Have No Single Speed, a Still Lattice Holds Charge Not Set by Spin, and Frame Dragging Needs T352's Coupling

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. T379 showed that the lattice outside a spinning core is static because the lattice's waves have no gap (Result 379.1), and wrote that if the substrate moves by T376's cell precession rather than by T175's field equations the result must be redone, "since a first-order motion can hold circulation as momentum". T380 rested its Test 2 — whether a spinning Shell twists the frame — on Result 379.1 and repeated the condition. If a still lattice could hold some of a core's spin, reversing with the spin, PUH would have a source for frame dragging with no new assumption. Here every cell of a lattice is moved by T376's precession, joined to its neighbours by T320's bonds measured with T376's K_theta, and both readings of T376's comparison with a rigid body are worked out on the E8(−24) build of T373. RESULT 381.1 — THE PRECESSION ON A LATTICE. The precession extends to a whole lattice as the Lie–Poisson flow of its total energy, d mu_i/dt = −[theta(mu_i + J L_i), mu_i]. It reproduces T376's single cell (to 3.5 × 10^-16), keeps the energy, each cell's invariants (T172's leaf confinement, cell by cell) and the E7 × SU(2) charge, and a massive state at rest on T175's wall (radius 2.2275, inside T377's shell) is a fixed point. RESULT 381.2 — WAVES WITHOUT ONE SPEED. About that vacuum, waves along rest directions (E7 × SU(2)) have frequency J s |alpha·x0| — proportional to the bond factor s, so to k^2 for long waves: no speed at all (rates 0.0389 to 2.6659). Waves along descent directions (the (56,2)) have frequency (2 + Js)|alpha·x0|, starting at a gap (0.0954 to 4.8512 at s = 10^-4). The eight Cartan directions, which change a cell's invariants, do not move. Every frequency is real. In each rotation plane the waves turn one way only. A nonlinear ring of six cells matches the predicted frequencies (2.66594 and 7.27643) and keeps its energy, invariants and charge to a few parts in 10^15. Magnets show the same split: precessing ferromagnetic spin waves go as k^2, second-order antiferromagnetic ones travel at one speed c = √(A/rho) (Tchernyshyov) — the form of T337's c^2 = 60J/rho. RESULT 381.3 — THE RIGID-BODY READING, AND THE VERDICT ON THE PREMISE. Read as a lattice of rotors (kinetic energy in each cell's angular velocity), the waves travel, but at speeds √J × 0.0389 to 2.6659 over the 240 directions that move — a 68.6-fold spread. No massive state at rest gives them one speed: E8's roots have the same moments in every direction, sum (alpha·u)^2 = 60 and sum (alpha·u)^4 = 36, which equal values cannot meet (they would give 15); the most even state found, the Weyl vector, spreads them 29-fold (a search over 20,000 random rest states found none below 29). Only T175's kinetic term, which weighs the change of the state, gives one speed in every direction — T337's c^2 = 60J/rho, on which T317's Lorentz symmetry rests. In either reading the precession cannot be the lattice's motion without losing the archive's derived speed of light: the premise of the kill-condition fails for the archive's lattice. Result 379.1 stands for it, and with it Test 2's zero. The precession remains the motion of a single cell's state, whose fixed points are T377's rest frames. RESULT 381.4 — GRANTED ANYWAY: A STILL LATTICE HOLDS CHARGE, NOT A CORE'S SPIN. Under the precession a still lattice can hold an E7 × SU(2) charge, which T175's equations do not allow: a static lump along the wall carries charge 0.1063, reversing with the lump. But the flow keeps every cell on its own Casimir leaf (T172), so it can neither make nor remove the charge: its sign is laid down, not set by a core's spin, and nothing in the flow refers to rotation in space. Near a Shell turning within E7 × SU(2) a precessing lattice could hold the part of the turning against its waves' sense — argued, not computed — but that sense is a turning in E7 × SU(2), not rotation in space. RESULT 381.5 — IT WOULD NOT TWIST T380'S FRAME. Every still configuration near the vacuum changes only along rest directions and pushes T380's frame, −4[v_k, v_p], by zero (computed 0.0 for the charged lumps); a descent tilt — the kind that would push it — does not sit still but precesses (20 random tilts: 1.7795 to 2.5640, inside 2|alpha·x0| = 0.0954 to 4.8510). T380's kill-condition (iii) is answered. WHAT FRAME DRAGGING STILL NEEDS. The precession route is closed. Each remaining route — a rule that tilts a spinning Shell along gravity's plane, a rule that sets the frame at the Shell by the spin, a coupling of the frame to the field's momentum — is a link between motion in space and the E8 state or frame: the −omega·J coupling T352 says "has not been written down, here or anywhere in the archive". One term could serve T352's chirality and frame dragging alike. In magnets the link is not an assumption — spin is part of the angular momentum, so a spun body magnetises (Barnett 1915) and a body whose magnetisation changes turns (Einstein and de Haas 1915). For PUH the question is which part of a cell's E8 state turns when space turns — T380's OPEN (2) seen from rotation; if it cannot be derived it should be stated as a postulate, fixed by Gravity Probe B and tested by a second measurement. WHAT CHANGES: T379 KILL-CONDITION (i) ANSWERED (Result 379.1 stands); T380 KILL-CONDITION (iii) ANSWERED (Test 2's zero stands; OPEN (3) narrowed to one link); T376 EXTENDED (its precession on a whole lattice, both readings); T172 USED AND EXTENDED; T352 ITS MISSING TERM NOW CARRIES FRAME DRAGGING TOO; T175, T320, T337, T317, T377, T378 USED. KILL-CONDITIONS: if PUH's light and Lorentz symmetry need one speed only along some directions of a cell's state, Result 381.3 must be redone for those directions; if the substrate moves by a mixture of T175's equations and the precession, Results 381.2 and 381.3 do not decide it (not computed); if the vacuum is a mixture at rest (T378, OPEN 1), everything must be recomputed about it; if the precession were the lattice's motion after all and a Shell's states turned with its spin, the part held near the Shell would reverse with the spin and could reopen Test 2. NOT CLAIMED: that the precession has no physical role; that T175's lattice needs no first-order term at all; how a precessing lattice answers a turning Shell; what momentum still textures on one leaf could carry under a first-order flow; that a coupling of rotation to the E8 state exists, or its form; that frame dragging is explained. OPEN: the link between motion in space and the E8 state, derived or postulated; a mixture of first- and second-order dynamics and the bound today's single speed of light puts on it; the precessing lattice about a vacuum that is a mixture at rest.