R95/M26 current-agent challenge, 26October2026; no independent review.
Retain the sparse-model extension as a mathematical candidate, with R94's
landscape/extraction lemmas explicitly inherited. No dense growing-depth
claim and no new original completion.

The finite marked Poisson process has square-integrable energy mean because
|F|<=M/sqrt(d), so the add-one Poincare inequality applies. The exact primary
statement was checked in Last--Penrose, Lectures on the Poisson Process,
Theorem18.7, equation18.19:
https://stoch.math.kit.edu/img/Last/lastpenrose2017.pdf .
Only this variance inequality and the usual Palm/Campbell identities are
imported. Their application to the local QAOA functional is supplied here.

Exploration reveals all remaining incidences at each newly visited vertex;
the unexposed process is Poisson on the complement of those already
queried tuple sets. Its incident intensity is at mostdq. Previously seen
edges introduce no new randomness, and collisions can only reduce the
number of distinct new vertices. This justifies the branching upper bound
even for adaptive vertex labels and repeated ordered tuples. Palm insertion
of the tested edge is paid by q initial vertices and one fixed occurrence.
The C0 second-moment recurrence uses E[Y(Y-1)]<=E[Y^2], deliberately loose.

An added occurrence cannot affect an old term's expectation outside its
backward p-layer light cone. This relies on STATIC commuting cost layers,
not a sequential circuit implementation that artificially enlarges the cone.
The angle list is fixed independently of the instance; reoptimizing angles
after adding an edge would invalidate this bound and is expressly excluded.
Quantum output covariance vanishes only for disjoint backward supports;
counting every overlapping pair is a safe overestimate.

The probability union includes all QT+1 outputs. The enormous Ramsey T
has log T=o(log n) in the chosen log-log depth regime, so the variance
bound still beats that union. The forbidden-tuple union includes T choose m
and Q+1 and is dominated by exp(-c n). The geometry Chebyshev step uses
n>=Q, which holds eventually in this regime. No approximation replaces the
exact Poisson rare-event calculation in R94.

The conclusion is uniform over deterministic angle lists at each finite n,
because all error estimates are angle-independent. It remains on the SPARSE
Poisson graph at fixed q,d. Applying fixed-p sparse/dense correspondence to
p(n) would be an invalid exchange of limits and is not done. The result
also does not remove the need to compare existing local-algorithm literature
or independently review the entire R94 proof. Park this branch unless a
quantitative sparse/dense theorem or a genuinely different original gap
is supplied; do not renew merely by substituting a larger depth constant.
