M05 independent research-owner proof/dependency review
22 October2026. Candidate global-composition proof63a1a4ebeb5586ad0f66bd7148b2956bbe8c1da8f821e6ee770a378c0d3f0345.
Verdict: supported internally; covers exact original under its stated source
input model, with explicit polynomial input-bit overhead. No publication claim.

Read original M05 and the complete R44 coherent filter, R45 recursive reset,
R46 singular correction/local simulator and R47 global-composition proofs.
Rechecked source2610.03578v1 Theorem3.11, Remark3.12, Eq4.16/4.17 and the entire
Eq5.31 parameter inequality against the immutable full mathematical snapshot.
Live arXiv version records22October2026 still list v1 for2610.03578,
2610.01190 and2609.18757. Earlier owner adoption reviews read the corresponding
full source and Low--Wiebe/stacked-oracle interfaces; no newer version replaces
the pinned premises in this check. General source theorems are imported, not
claimed to have been proved from scratch here.

The decisive resource bridge is sound within those inputs. The positive QBP
filter samples a binary quantile register whose size is logarithmic in its
large node count; it never enumerates the grid. Interaction-picture simulation
charges local terms, arbitrary onsite phase bits and coherent time control.
R45's time-ordered LCU uses parameter2beta at a full Gibbs merge, explicitly
constructs the inverse ODE (rather than substituting the adjoint), and charges
all child/inverse calls in fixed-point amplification. Normalization is expO(x)
per merge and the reset tree height is O(x), not O(log log(N/epsilon)). The
larger localization region needs dressing only. Recurrence precision growth
therefore gives exp(Cx^3)Q^(Cx+c), not a hidden quasipolylog factor.

The actual collective reset stack has expO(x) normalization without a Kraus
list. Its loss S is encoded by the projected stack product. R46's direct
odd kernel omits only norm-controlled endpoint intervals, uses logarithmic
LCU mass and computes inverse quantiles in polynomial binary work. Its
Hermitian wrapper is exactly involutive because it reverses actual compiled
gates. Approximate projected V and G define a true nearby Lindbladian. Both
semigroups are CPTP, so diamond Duhamel has linear T error, not exp(T||L||).
The imported simulator sees the coherent correction's normalization, not the
physical H onsite norm. Its classical coefficient/arithmetic cost is charged.

For global glue, dimensionless input rounding is paid once. The Gibbs-state
trace perturbation bound2||DeltaK|| follows from the integral derivative and
Schatten Holder. The integer ell/T choice has been substituted into the actual
source5.31 inequality: first two residuals <=ell/8 and last <=ell/4. Increasing
T is not justified merely by monotonicity; the new exponentially decaying
locality estimate is explicitly checked. All constants are fixed by dimension
and range. n<ell goes directly through the temperature-height recursion, while
n>=ell retains every labelled boundary block and the exact coverage countell.
The source's discrete P^k contraction suffices for preparation. Thus no global
Poisson or all-input global-semigroup simulation obligation remains.

Dyadic-label probabilities differ from uniform by <=epsilon/(64k), and channel
convexity plus diamond telescoping bound their total effect. This produces a
randomized algorithm whose averaged output density is the target approximation;
no assertion is made that each random trajectory is independently close. The
source permits this random-update preparation model. Offline label sorting,
template joining, expanded gate-list copying and address arithmetic account
for the global classical work without a unit-cost N-way quantum selector.
All random seeds have bounded work. All ancillas, synthesis bits and resets
are charged within the displayed resource bound.

Original mapping: every fixed local dimension/range chain, all N, beta>=0
and target epsilon, source local-matrix input, output half trace distance<=epsilon,
both elementary-gate and classical bit costs. x=1+beta Jint, temperature
prefactorexp(Cx^3), explicit log(N/epsilon) exponentO(x). Requested-precision
bounded source inputs give the card's shape; arbitrary longer descriptions
retain a polynomial(1+b)^c input factor, as the card asks input costs to be
specified. No extra uniform-in-temperature polylog claim is required. Huge
onsite fields with their explicit magnitude bits are an additional extension.
The exact input-reading convention is stated rather than silently removed.

Checks are predominantly analytic. Helper's two clean scalar/local diagnostic
runs and parent's independent replay are retained; owner does not claim a
separate compiled end-to-end many-body circuit execution. This is sufficient
for the complexity theorem's analytic proof, while internal review remains
fallible. Source methods (QBP, Dyson, fixed-point amplification, interaction-
picture simulation, stacked Lindbladian simulation, DS mixing) are attributed.
The missing implementation bound in source Remark3.12 is the original-scale
delta. Worldwide novelty and external expert confirmation remain unverified.

Recommendation: freeze a complete M05-v1 candidate with all four proof stages,
source versions and parent/owner reviews, then let parent update effective
original status. Do not modify earlier partial receipts or publish/manuscript.
