# Verification report

The originating researcher checked the complete proof against Thorisson's exact allocation-only question and the mass-stationarity definition. The continuous horizontal stabilizer and discrete vertical period reduce every admissible deterministic allocation to a finite map. Positivity makes the finite map surjective, and distinct weights then force its root type to remain unchanged. The mass-sampling experiment instead returns the weight-proportional root law. An explicit Campbell calculation identifies the corresponding stationary parent and Palm law.

The result covers all measurable pointwise equivariant preserving allocations on the canonical orbit, without restrictions on continuity, bijectivity or bounded displacement. The measure is diffuse and locally finite, but singular with invariant directions. It does not contradict the positive-density theorem, and it does not settle the Markovian-kernel question.

Normal and optimized Python runs agree on 102825 exact finite diagnostics: 100136 finite-map cases, 2233 window cases, 70 kernel identities, 385 shift cases and the binary witness. These checks are not a substitute for the general proof or a formal proof certificate. The manuscript and proof_audit.md contain the argument and its scope.

Attribution: Last--Thorisson's weighted atomic obstruction (2009), Lebesgue-product treatment (2015), and invariant-direction transport example (2023). A bounded primary-source search found related methods, but does not establish priority or exhaustive novelty. Self-audited and unrefereed; no independent review is claimed.

PDF layout and portable source-build checks are recorded in the package manifest and readiness receipt after completion. Until those receipts exist, this document alone does not certify package readiness. No external publication is implied by any local verification.