T1/T2/T2* Eects on Spinning Stars and Binary Systems: Sump Torques, Modied Braking Indices, and a Phase Discontinuity in the Binary Neutron Star Inspiral Wave- form at a = rT2∗

The T1/T2/T2* sump hierarchy (Papers XXXIV, XXXV) applies to rota- tional and orbital degrees of freedom as well as to linear acceleration. We derive six consequences. (1) Sump torque on spinning stars: the global T1 sump exerts a small torque on any spinning focal zone, producing a fractional spin-down correction δ ˙Ω/ ˙Ω∼a0R∗/c2Ω, negligible for all known pulsars but setting the oor for spin-down measurements. (2) Modied pulsar braking index: the T2* coherent brane fabric within rT2∗of a neutron star carries angular momentum, increasing the eective mo- ment of inertia by ∆I/I ∼M∗a0r3 T2∗/(I∗c2) and systematically reducing the observed braking index below the pure magnetic dipole value n = 3. This is a candidate ex- planation for the longstanding pulsar braking index anomaly (nobs < 3 for all young pulsars). (3) Binary orbital decay: the T2 orbital coherence mode of a binary carries a small additional angular momentum in the brane fabric, producing a correction to ˙Pb of order a0a/c2 ∼10−18 for the Hulse-Taylor binary, consistent with observations. (4) T2* zone overlap in compact binaries: when the orbital separation a < rT2∗, the companion enters the primary's T2* coherent focal zone. The orbital mode tran- sitions from the T2 viscous regime to the T2* elastic regime, modifying the eective tidal deformability. (5) Phase discontinuity in the GW inspiral: the T2 →T2∗ orbital transition at a = rT2∗(occurring ∼104 s before merger at fGW ∼1 Hz for double neutron stars) produces a fractional change δ ˙f/ ˙f ∼a0rT2∗/c2 ∼10−17 in the chirp rate. (6) Hypermassive neutron star stability: the post-merger hypermassive neutron star is stabilised by the T2* coherent brane fabric extending to rT2∗, increasing its maximum mass before collapse by ∆M/M ∼a0rT2∗/c2 ∼10−17. The α covariance theorem (Paper III) ensures all these corrections are self-consistent with frozen constants in the astronomical epoch. Five new predictions follow (Predictions 96100). Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.