Exact Outer Multiset Dimension of the Three-by-Three Path Grid Strips

Ryutaro Yonezu, Independent Researcher. Research No.62. Preprint v1.0, dated 2026-11-10. For every integer n >= 2, the outer multiset dimension of the Cartesian product P3 square P3 square Pn is 6 for n = 3, 5 for n = 2 or 4 <= n <= 8, and 4 for n >= 9. This is a computer-assisted mathematical proof. The lower bound of 4 for all n depends on the author's No.59 universal lower bound for products of three nontrivial paths. The small exceptional cases are settled by exhaustive finite computation. The infinite upper bound uses explicit four-landmark constructions and a reduction to bounded exact integer collision checks. The n = 2 graph is isomorphic to the n = 3 member of the family studied in No.58. The author's closeout reports that finite overlap, and No.59's short-grid table records the value 5. The published main theorem of No.58 covers n >= 6. Independent AI differential audit through v0.3 is reported PASS in the author's supplied report, within its stated scope. Windows PowerShell 5.1 reproduction of the exact v0.3 package is reported PASS based on the author's supplied transcript. The v1.0 distribution was checked on Linux. The four frozen verifier and expected stdout files and the Python runner retain their v0.3 bytes. A sanitized summary provides the Windows evidence. NOVELTY INCONCLUSIVE. Human peer review and full formal verification have not been performed. Copyright (c) 2026 Ryutaro Yonezu. All rights reserved. The attached PDF, TeX source, reproducibility ZIP and SHA256SUMS.txt match GitHub Release v1.0. Reproduction requires Python 3.10 or newer and a C++17 compiler. See the repository README for the complete instructions.