PUH Theorem 380 — The Frame as a Field: E8(−24) Kept With Positive Energy, Massive Matter at Rest Left Alone, but a Spinning Core Does Not Twist It — for Frame Dragging the Move Is Bookkeeping

Photonic Universe Hypothesis (PUH) — Theorem paper. STATED UP FRONT. Two tests were fixed before they were run: the frame's ripples must stay hidden from today's observations, and a spinning Shell must twist the frame by the measured amount of frame dragging (Gravity Probe B). If the second failed, the move would be only bookkeeping for frame dragging. It fails. THE QUESTION. T376 measures every change of the field with K_theta(x, y) = −K(x, theta y): one fixed frame, the Cartan involution theta, which keeps the energy positive but gives up E8(−24)'s 112 noncompact symmetries; its alternative, a field on the coset E8(−24)/(E7 × SU(2)), keeps them but rebuilds T175's field. T379 found that with K_theta gravity's plane is a bowl, while a spinning body's gravity (T302) needs a saddle. Here T175's field is kept and the frame itself becomes a field: a point e = gK of the coset at every point, with energy K_e(v, w) = −K(v, theta_e w). Every number is computed on the E8(−24) build of T373, with T376's K_theta, T377's sign and T238's couplings. RESULT 380.1 — A FRAME AT EVERY POINT. K_e is positive for every frame and depends on the frame alone (to 2.7 × 10^-15); boosting field and frame together leaves the energy unchanged (2.8 × 10^-14), where boosting the field alone with the frame fixed changes it by factors 0.033 to 30.031 — so all of E8(−24) is a symmetry again; where the frame is uniform and equal to theta, K_e = K_theta exactly and every result at rest stands. Price: 112 more directions per point (360 in all), a stiffness for the frame the archive does not fix (without one, a seed's change could be made to cost as little as one likes: 240, 4.396, 0.08051, 0.001475), and 112 kinds of frame ripple that no symmetric potential can give a mass (argued). RESULT 380.2 — WHAT PUSHES THE FRAME. The first change of K_e(v, v) under a boost of the frame is −4K(Y, [v_k, v_p]) (checked to 1.3 × 10^-11): only changes whose rest and descent parts do not commute push it. T378's and T379's cores of massive rest states leave a uniform frame where it is; a state boosted inside E8 costs least in its own rest frame (302.7841 there, 577.4467 in the fixed frame). RESULT 380.3 — GRAVITY'S PLANE IS A SADDLE IN THE FRAME'S SPACE. The frame's space is the coset, where gravity's plane (T303–T304, T379) is a Lie triple system, totally geodesic, with metric 120(db^2 + sinh^2(2b) dphi^2) and curvature −1/30 exactly. The twist T302 needs can be carried by the frame while T175's field stays as it is — structurally. RESULT 380.4 — TEST 1: NOT SETTLED. Massive matter at rest never pushes the frame and feels its ripples only at second order (0.657 to 1.363 × size^2), however it moves (theta-symmetry, T378). A lone light wave does not push it in either of the archive's readings of the photon — T167's phase ripple or T377's massless seeds of T374 — because its time and space terms cancel (computed 0.0; a seed's space term alone pushes 0.3651 per unit energy). But crossing waves push it through their cross term, T377's mixtures at rest push it (0.0806 to 0.1187), and states boosted inside E8 push it in proportion to the boost (0.185 to 0.335 per unit boost). No observational bound can be computed until the frame's stiffness is fixed. RESULT 380.5 — TEST 2: FAILED AS POSED. T379's spinning cores push the frame by exactly zero. Reversing the spin leaves the Shell's flattening (spin squared, T359) and its rest states unchanged, so nothing outside the core knows the spin's direction, while frame dragging reverses with it (T303: −2J cos(theta)/r^2). A Shell tilted along gravity's plane would twist the frame — to first order the push is 0.1346 per unit tilt per unit energy and reverses exactly with the tilt (cosine −1.000000), and T378's tilt does not die away — but nothing in the archive tilts a spinning Shell or sets the frame's value at it. For frame dragging the frame field is bookkeeping: it gives the twist a home, not a source. The gap is precise: PUH's field already carries momentum, K_theta(dphi/dt, dphi/dx) (T379), which reverses with the motion — the kind of mass current frame dragging follows — but the frame does not respond to it, so any rotating body made of massive states at rest (the Earth's measured dragging included, if that is what it is made of) needs the same missing coupling, derived or stated as a postulate. And a twist of the internal frame is not yet a gyroscope's turning: the link comes only with T303's identification of gravity's plane with Ernst's (clock rate, twist potential), which is not derived. BEYOND THE EARTH: GALAXY LENSING. A rotating galaxy lenses as if the half moving toward us were lighter, and the other half heavier, by a fraction 2v/c (Sereno 2002) — 1.334, 1.668 and 2.001 × 10^-3 for rotation speeds of 200, 250 and 300 km/s (computed). To first order this mimics a shift of the lens (Asada and Kasai 2000); it shows in time delays (nearly 0.2 days, Sereno 2005), in about 10 micro-arcseconds of image position for spirals (Capozziello et al. 2003), or in stacked dipoles of rotating haloes (Tang et al. 2020: not yet detectable with about 400 clusters). It has not been seen. For PUH it is a later test: as T380 stands the frame field predicts no such term; once PUH has a source, fixed first against Gravity Probe B, galaxy lensing would test it on galaxy scales. WHAT CHANGES: T376 OPEN (1) WIDENED (three readings); T379 OPEN (2) NARROWED (a handed Shell, a spin-set frame at the Shell, or a coupling of the twist to the field's momentum), OPEN (3) now decisive; T303 THEOREM 303.2'S PLANE CARRIED BY THE FRAME, STRUCTURALLY; T167 AND T377 FLAGGED — TWO PHOTONS (a seed is not a direction along the wall at T379's clock state: cosine 0.707107); T377 EXTENDED; T378 USED AND EXTENDED (its OPEN 1 now bears on Test 1); T374 EXTENDED; T317 USED; T333 PASS STANDS; T302, T304, T359 USED. KILL-CONDITIONS: if PUH represents motion through space by boosts inside E8, moving matter pushes the frame and Test 1 fails for matter too; if the vacuum is a mixture at rest, a field turning through it pushes the frame; if the substrate moves by T376's precession, T379's Result 379.1 must be redone and Test 2 reopens; a rule that tilts a spinning Shell or sets the frame at it by the spin reverses Test 2; a frame energy that breaks the full symmetry undoes Results 380.1 and 380.3. NOT CLAIMED: that the frame field is built (stiffness, field equation, ripple speed); that its effects are hidden from or excluded by observation; how much crossing light stirs it; which photon is PUH's; that a spinning Shell is handed; that frame dragging is explained; that K_theta or the coset is excluded; that a twist of the internal frame turns gyroscopes; that galaxy lensing has detected frame dragging, or will soon. OPEN: the frame's stiffness and equation; which sense of motion PUH means; what makes a spinning Shell handed, sets the frame at it, or couples the twist to the field's momentum; K_theta, the coset or the frame field (frame dragging counts against K_theta if T303 is kept, but cannot separate the other two); which photon is PUH's; once a source exists, its prediction for rotating galaxy lenses.