A Conditional Derivation of the Point-Particle 2.5PN Sector from the Unified 4D Toy Model

We present a controlled audit of the first dissipative post-Newtonian gate of the unified 4D toy model, namely the nonspinning two-body 2.5PN sector. Carrying forward the exact projection / leakage / Poisson-hook / worldtube reduction framework together with the already-fixed Newtonian+1PN+2PN conservative hierarchy, we first show that the frozen conservative kernels alone cannot generate a local 2.5PN reaction term. We then use a minimal retarded quadrupole prototype to recover the Burke–Thorne member of the standard Iyer–Will family, which fixes the structural target for any successful completion. The main body of the paper is a channel audit. On the natural compact/passive/outgoing small-body branch, the dangerous lower odd scalar channels are derivative-mediated or super-Ohmic and are pushed above universal point-particle 2.5PN; the carried dipole wake is likewise demoted by the outgoing ℓ = 1 threshold law and strict small-body scaling. The only surviving universal point-particle route is the orbital/worldtube STF quadrupole. In particular, the solved 2PN P2 bundle already exhausts the real STF ℓ = 2 content, the low-frequency P2→STF matching is scalar under isotropy, the passive outgoing ℓ = 2 branch carries the correct positive +iω5 parity/sign, and the static overlap gate passes on the natural branch. The strongest honest result is therefore a conditional 2.5PN theorem within a declared closure hierarchy: if the completed moving-throat PDE realizes this passive/outgoing quadrupole branch, then the reduced nonspinning two-body dynamics contains the standard local quadrupolar Burke–Thorne / Iyer–Will reaction term, with all other currently derived odd channels entering only as higher-order finite-size corrections. The remaining serious open problem is no longer generic dissipative physics, but the final passive/outgoing quadrupole normalization, m̂02Γ5 = 2G/(5c5), on the actual moving-throat branch.