R98/M26 current-agent challenge, 26Oct2026. Not independent review.

Verdict: the prospective sparse logarithmic-depth theorem has a complete
analytic candidate. Its new interfaces are the mixed-time landscape union
and finite-branch metric extraction. They survive the following challenges.

1. Time mismatch. The root sign is shared only if a tuple avoids the union
of the two modified sets, so R_max is correct. R_min is generally wrong.
The exact control file checks 80 covariance cases, of which67 refute R_min.
Different nonroot branch labels are essential. Multiple times on the SAME
branch would share nonroot signs and invalidate the displayed covariance.
The greedy construction explicitly discards a branch after using it.

2. Adaptive stopping. Selected times depend on every path. Their selected
outputs do not have ordinary unconditioned Born distributions. The proof
never applies a fixed-tuple tail to that adaptive selection: it unions over
ALL (1+TQ)^m possible distinct-branch tuples before constructing it. This
cost is polynomial when Q is polynomial and m is fixed.

3. Greedy geometry. The new node need not stay near the root. It is within
a+eta of SOME old point, and therefore the selected diameter can grow by
a+eta at each stage. Choosing a=b/(4m), not b/2, pays for that growth. The
first-exit statement is strict >a from all old points; closed balls prevent
boundary ambiguity. T=m^2 exceeds k(m-1)+(k-1) for every k<m, guaranteeing
an unused branch endpoint. Two hundred seeded metric instances satisfying
the endpoint premise passed; the metric induction, not this test, proves
all sizes and all paths.

4. Shared graph. Endpoint signs are conditionally independent, but graph
fluctuations remain. The marked-Poisson cosh inequality includes those
fluctuations exactly. It needs symmetry and |W|<=m, not independence among
the m energies. Negative odd-q correlations only lower the variance upper
bound. Repeated tuple coordinates obey the same product expectation.

5. Quantum coupling. Pairwise outside reduced-state equality follows from
static Hamiltonians, commuting cost gates and p-step support growth. Gluing
is acyclic and retains every Born marginal. Good-energy events are imposed
only after constructing the law. No forced-success conditional resampling.

6. Quantitative inherited estimates. R95's actual output variance includes
both Born and disorder variance, via light-cone overlap and add-one Poisson
Poincare. Its constants grow exponentially in p but are uniform in angles.
Here Q=O(C^p), only T=m^2 branches occur, and p<=log(n)/(40log C) makes the
geometric and energy failures O(n^-7/8) and O(n^-5/8). Constants independent
of n are harmless; an n-dependent degree or q would not be covered.

7. Optimization. For each deterministic angle list a contradiction follows
from the same bounds and same eventual n threshold. This is uniform control
of each mean, not a common high-probability event for uncountably many lists.
Instance-dependent angle selection is not justified. No dense growing-depth
claim follows from fixed-p sparse/dense transfer. The existing fixed-depth
original candidate remains pending its earlier independent/priority review.

8. Sources. Prior sources already prove logarithmic-depth obstructions for
even predicates, local quantum marginal sharing and tree/Ramsey methodology.
The new campaign step is this exact mixed-time odd-large-q composition with
a different metric extraction. It has not been cleared for worldwide
priority; known greedy-packing/multi-OGP ideas could cover it. No publication
or original acceptance follows from these checks.

Decision: retain as a theorem candidate, route to verification. The selected
central sparse theorem is complete, so additional tokens or small tests only
to reach a numeric budget would not address a missing proof step. This is an
early central-resolution exception; the two main/5 auxiliary allocation and
actual usage remain separately auditable. No original is counted solved here.
