The Folding Real Form Is Quaternionic E8(-24) (T265): The Quaternionic E7 56-plet and the E7 x SU(2) + (56,2) Matter Structure Form the Compact-Plus-Coset Decomposition of E8(-24), with Compact Excluded and the Freeze Exponent the Quaternionic Value

Photonic Universe Hypothesis (PUH) — T265 — STRUCTURAL RESOLUTION. The late-time freeze of the PUH cascade depends on which real form of E8 the folding configuration space realizes: compact E8(-248) (definite), split E8(8) (maximally indefinite, real rank 8), or quaternionic E8(-24) (intermediate, real rank 4). This note identifies the realized form as the QUATERNIONIC form E8(-24), on structural grounds from the matter sector the archive already commits to. THREE FACTS, ALL ALREADY IN THE ARCHIVE: 1. The E7 fundamental 56-plet is QUATERNIONIC — the unique symplectic (pseudo-real) representation of E7, carrying a symplectic form (T168). 2. The weak force (T212) is built from E8 = E7 x SU(2), under which 248 = (133,1) + (1,3) + (56,2): the (133,1) E7 adjoint and (1,3) SU(2) adjoint are the gauge sector; the (56,2) is the matter sector (weak doublets). 3. These are exactly the defining data of the quaternionic real form E8(-24): maximal compact subgroup E7 x SU(2) of dimension 133+3 = 136, noncompact coset of dimension 248-136 = 112 = 56 x 2 = (56,2). So T212's gauge-plus-matter content IS the compact-plus-coset decomposition of E8(-24): gauge fields in compact E7 x SU(2), matter fields in the noncompact (56,2) coset, with the quaternionic 56 the algebraic signature of the quaternionic real form. The match is numerically exact. SPLIT FORM FAILS: its maximal compact is Spin(16) with a 128-dim spinor coset; 248 = 120 + 128. 128 != 112, so split does not contain (56,2) as its coset. The archive's matter content (load-bearing across weak, EM, strong via the (133,1) branching) is the quaternionic coset, not the split spinor. COMPACT FORM EXCLUDED (independent ground, T264): a definite Killing form makes every direction oscillatory/bounded with no descent direction, but the directed irreversible cascade (T206/T239/T247) requires descent. So all three forms resolved: compact excluded by the cascade, split excluded by the matter sector, quaternionic E8(-24) identified by the matter sector. A TEMPTING SHORTCUT THAT FAILS: one might argue the eight quantum numbers of T172, as eight simultaneously-real observables, require real rank 8 (only split has it), concluding split. This FAILS: the eight are Casimir INVARIANTS (T172's own term; the eight Cartan directions are "frozen as Casimir constraints"), NOT Cartan WEIGHTS. Casimir invariants are real on every real form, imposing no real-rank requirement. The genuine weights — colour (rank 2), weak isospin (1), hypercharge (1) — number 4, the Standard Model gauge rank, which the quaternionic real rank 4 accommodates. The real-rank count does not select split; the matter sector selects quaternionic. FREEZE EXPONENT: the quaternionic form has a smaller real nilpotent cone than split (noncompact part 112-dim, not split's full 240), so its mobility exponent is the QUATERNIONIC value — distinct from the split exponent 8 and the compact exponent 124. Exact value requires the real nilpotent cone dimension of E8(-24) (atlas-type computation), named here as the open calculation. The freeze remains a real (non-frozen) power law (the quaternionic form is indefinite, so the cascade runs). Found via full-corpus search of the matter sector (T212, T168) — the quaternionic 56 is the archive's own description.