Exact Outer Multiset Dimension of the Three-Dimensional Grid Family P₂ □ P₃ □ Pₙ

Ryutaro Yonezu — Independent Researcher. Preprint v1.0, 2026-11-07. For every integer n>=6, odim(P₂ □ P₃ □ Pₙ)=4. Distinct vertices outside the landmark set are distinguished by unordered distance multisets, with multiplicities. The claim covers this three-path family only. Computer-assisted proof: 35-layer collision lifting; 13,921,300-triple finite lower certificate; 336 ordinal types (272 local obstructions, 64 survivors); A/B/C and E0–E4; 24 affine branches including even-N B(N) branch 24; parity-specific upper constructions with n=6,8 exceptions. Symbolic reductions establish all-n coverage; finite scans alone are not the proof. Independent AI review is user-supplied and scope-limited (v0.5 MODEL / PROOF / COMPUTATION PASS reported). Complete independent formalization and all-branch third-party rederivation are not claimed. Windows PowerShell 5.1 reproduction: frozen v0.3/Audit D PASS; v0.5 24/24 branches and 268,528 configurations PASS. Private Windows transcripts and identifiers are excluded. NOVELTY INCONCLUSIVE. REFERENCES PARTIAL. Not human peer-reviewed. All rights reserved. Candidate partial response for one special infinite family to Farhan et al. (2026), Problem 10, as identified in the supplied audit; no full-problem solution or priority claim. Current fetching of the survey and Peng arXiv records was unsuccessful; access limits remain explicit. Historical HOLD records refer to earlier stages. PDF SHA256: ef97dda604d4fd96e492aae21fd1e8948a7c93738ddceb7adac6e0e60c4ea009ZIP SHA256: c3b8671760e747ce5bd23fe3418d032aeefb8f188b4bd6f9a2c2e9d574a871db GitHub repository: https://github.com/yonezaemon1-hub/no58-outer-multiset-dimension-3d-gridGitHub Release v1.0: https://github.com/yonezaemon1-hub/no58-outer-multiset-dimension-3d-grid/releases/tag/v1.0 The accompanying PDF is an eight-page English manuscript. The reproducibility archive contains unchanged mathematical sources and frozen verifiers, exact certificates, sanitized output, execution instructions, and SHA256 manifests. Six release-preparation verifiers passed. This is not an independent Windows rerun of the v1.0 wrapper, a complete formal proof, or human peer review.