PUH Theorem 382 — Motion as a Boost Inside E8 Tested: Frame Dragging Gets Its Exact Form, but Moving Matter Becomes 1.88 Times Too Heavy, and a Cushion Is Ruled Out by the Double Pulsar

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. T380 gave T376's fixed frame a value at every point and found what pushes it, −4[v_k, v_p]. Its first kill-condition warned that if PUH represents motion through space by boosts inside E8, moving matter pushes the frame in proportion to its speed, and its OPEN (2) asked whether motion is T317's boost of space and time or a boost inside E8. A push in proportion to speed is what frame dragging is made of, and T381 noted that under the boost reading rotation would be a turning inside E8, so the coupling frame dragging lacks would follow rather than be added. Here the boost reading is built on the E8(−24) build of T373 and followed to its consequences; then a second reading, Brian Martell's cushion, is modelled and tested. RESULT 382.1 — THE DIRECTIONS OF SPACE INSIDE E8(−24). Lorentz algebras so(3,1) exist with rotations in E7 × SU(2) and boosts in the (56,2): built from two strongly orthogonal noncompact roots (each carrying T304's gravitational sl(2,R)) plus a third boost found by least squares, all 18 relations hold to 10^-16. The smallest, of Dynkin index 2 (T304's is 1), fall into two classes, with centralisers of 55 + 11 and 39 + 27 dimensions; every pair of roots tried gave one or the other. Under the first, E8 = (0,0) × 66 + (1/2,0) × 32 + (0,1/2) × 32 + (1/2,1/2) × 12 + (1,0) + (0,1), the pattern of E8 ⊃ so(4) + so(12). Gravity's plane is not the 2 + 1 part of these algebras. RESULT 382.2 — MOVING MATTER PULLS THE FRAME ALONG. Under the boost reading the push of a moving rest change is 4β ad(v)^2 B, linear in the speed (to 3 × 10^-9 at β = 10^-4); for matter spread evenly over E7 × SU(2) it lies exactly along the motion (the E7 × SU(2) Casimir on the (56,2) is one number, 1/240; cosine 1.000000000000); a moving change costs least when the frame moves with it. Lorentz-singlet matter neither pushes nor feels the frame. RESULT 382.3 — THE LENSE–THIRRING PATTERN. Around a spinning ball the frame's field outside is the pure dipole (4π/15)Ω × x/r^3 (Gauss quadrature, six digits), reversing with the spin; a small spinning body couples to its curl, [3(J·r)r − J]/r^3 — exactly the pattern of Lense–Thirring frame dragging. The boost reading gives frame dragging its form; its strength is one constant, which Gravity Probe B would fix. RESULT 382.4 — THE PRICE. K_theta is not boost-invariant (T376), so in the lattice's fixed frame moving matter carries extra energy 0.4412 β^2 of its rest energy when spread evenly over E7 × SU(2) (1.00 for SU(2)-type, 0.43 for E7-type changes): its inertia would be 1.882 times its rest energy over c^2. E = mc^2 holds to 4.4 × 10^-7 (Rainville et al. 2005); to stay inside, ordinary matter would have to be Lorentz-singlet to better than 5 × 10^-7, and singlet matter does not drag the frame. The boost reading fails for ordinary matter. RESULT 382.5 — THE CUSHION. Brian Martell's idea: each body rides in a layer of the same lattice, like an air-hockey puck on air, so its own frame moves with it (no 1.88 inside) and only what leaks through the layer drags the frame outside. Modelled in T380's frame field (energy K|grad a|^2/2 + mu|a − b|^2/2): a particle's extra inertia and its leak obey M = 4πK_out B exactly, for every cushion. With one universal k (leak length kGm/c^2), E = mc^2 and Gravity Probe B leave 9.09 × 10^6 ≤ k ≤ 3.73 × 10^9, and Lense–Thirring is reproduced exactly for bodies like the Earth. But matter screens the frame over ell = c/√(4πkGρ): for uniform bodies S0 = 3(1 − tanh x/x)/x^2 and S1 = 15[1 − 3(x coth x − 1)/x^2]/x^2 (x = R/ell, closed form, numerics to 7 × 10^-5); at the least screening allowed the Earth drags at 0.998 of GR, the Sun 0.17, a white dwarf 0.002, a neutron star 3 × 10^-6, a Planck core 1 × 10^-6. And the frame cannot outrun the matter that drags it (maximum principle): S0 ≤ 1/(k GM/(Rc^2)) for ANY interior stiffness, cushion or density profile (checked on 300 random bodies) — no density-dependent stiffness escapes. RESULT 382.6 — THE DOUBLE PULSAR RULES THE CUSHION OUT. The frame that drags gyroscopes also carries gravity's velocity–velocity term between moving bodies, −4Gm1m2(v1·v2)/(c^2 r) — the gravitomagnetic part of the Einstein–Infeld–Hoffmann Lagrangian (reciprocity checked to 3 × 10^-10) — and the cushion scales it by S0 of each body. Removing it multiplies a binary's periastron advance by 1 − 8η/3 (equivalent to PPN α1 = −8 in Will's formula; orbit integration 0.3341 = formula). In the double pulsar PSR J0737−3039A/B, with masses fixed without the advance (mass function 0.290963 Msun, mass ratio 1.0714(11), Shapiro shape 0.999936: 1.3378 and 1.2487 Msun), GR gives 16.897 (±0.018) degrees per year against 16.899323(13) measured; the velocity term supplies two-thirds of it; without it, 5.646. The cushion leaves less than 10^-12 of the term for every k in its window and any internal structure (including T367's central Planck cores): it predicts 5.65° per year. Agreement would need k ≤ 0.0126 — an extra inertia 318 times each particle's mass. The cushion is ruled out. WHY PSR J1141−6545 DOES NOT DECIDE: under the cushion that white dwarf's frame dragging is weakened ~500-fold, but by Venkatraman Krishnan et al.'s own equations its rotational bulge (Newtonian, ~1/P^2) alone reaches the measured tilt for spin periods up to 216 s — the range their binary evolution favours; an exclusion first drawn from it is withdrawn. WHAT FRAME DRAGGING NEEDS NOW. Both readings of T380's frame fail at one point: the coupling that would carry frame dragging also adds inertia. Whatever carries frame dragging in PUH must carry gravity's velocity–velocity term at full strength between two neutron stars. In GR that term is what a mass's static field becomes when the mass moves, by the Lorentz symmetry of the field equations; whether PUH's gravity shares the Lorentz symmetry T317 derived for its waves is the question left — if it does, frame dragging needs no new coupling. WHAT CHANGES: T380 OPEN (2) ANSWERED PROVISIONALLY (T317's reading; kill-condition (i) confirmed in its premise but its reading fails E = mc^2, so Test 1 stays NOT SETTLED; Result 380.2 extended to moving matter); T381 OPEN (1) NARROWED; T304 EXTENDED; T283 ITS CAUTION BORNE OUT BY CONSEQUENCES; T376, T316, T317, T311, T367, T352 USED. KILL-CONDITIONS: if ordinary matter's rest states are Lorentz singlets to better than 5 × 10^-7, Result 382.4's price vanishes (but such matter would not drag the frame either); if PUH's other first post-Newtonian terms restore the velocity–velocity term between compact bodies by themselves, Result 382.6 must be redone (though the frame would then not be needed for it); if the frame's response is nonlinear or nonlocal, the bound of Result 382.5 does not apply. NOT CLAIMED: that PUH cannot have frame dragging; that the Lorentz algebras found are all (higher index unexplored); that the boost reading fails for Lorentz-singlet matter; that frame dragging around J1141−6545's white dwarf is absent or present; that PUH reproduces GR's other first post-Newtonian terms (assumed in 382.6); that the cushion fails as a picture of inertia. OPEN: whether PUH's gravity has T317's Lorentz symmetry; Lorentz algebras of higher index; PUH's own first post-Newtonian two-body dynamics; preferred-frame effects (PPN α1, α2) of any field tied to the lattice's rest frame.