# Verification report

The manuscript's theorem is accepted by the originating researcher after
a detailed self-audit of the integral normal form, rank-one criterion,
rerooting equation, branch independence, state cap, recurrence, deque
evaluation, multiplicity truncation and witness reconstruction.

The normal and Python -O checker runs agree on the same 2,657 small
instances and 445,497 enumerated effective divisors. Every optimum agrees
with both a direct cubic dynamic program and an independent exact-rational
Laplacian-class oracle. The tests include 13,071 choices of root and 65,005
positive-root checks on reconstructed witnesses, plus 80 star-formula
tests, 80 heavy-edge tests, 1,940 signed normal-form tests, 1,940 principal
invariance tests, four larger instances and seven rejected invalid inputs.
The all-instance SHA-256 digest is
503b60389dc0346069373e485e65219d295e16e032de86604ad67a77c6a57b2a.

All rooted unlabelled tree shapes through five vertices are included with
each multiplicity between one and four, plus 60 seeded trees on six to
eight vertices. The larger cases extend to 600 vertices; only witness
validity, not exhaustive optimality, is checked there. Binary-weight tests
include multiplicities of 10^1000 without edge expansion.

The infinite-size theorem is proved in the manuscript. Finite tests do not
replace that proof, establish priority or amount to formal verification.
The general genus bound for arbitrary multigraphs remains unresolved here.
No independent reviewer or proof assistant is represented as having approved
the result. AI assistance is disclosed in the manuscript.

The final package-readiness receipt separately binds compiler success,
all-page visual review, a portable source rebuild, replayed exact checks,
file hashes and a source archive that excludes third-party PDFs.