M14-v2 and its stronger manuscript certificate — independent strict review
22 October 2026

Judgments
Validity: supported internally through the independently read and replayed
Arb/Acb certificate. No proof gap or refutation found.
Original coverage: complete existence result at T=4/5. A feasible three-pulse
memory protocol is compared against EVERY reset protocol of at most four
pulses with arbitrary phases, labels and nonnegative durations of total<=4/5.
This is a global reset lower bound, not a global memory optimization or a
claim that memory advantage is specifically a coherence advantage.
Source comparison: difference supported in the bounded current comparison;
no identified unresolved covering theorem blocks release.
External status: no external expert acceptance established by this review;
no publication or submission performed.

Frozen inputs and the two arithmetic routes
Original campaign/originals/M14.tex:7–15. Candidate proof.txt, reset-cover.npz,
all code, manuscript main.tex and the independent m14_arb_audit.py are hashed
in frozen-inputs.json. Candidate proof.txt:5–7 records weaker bounds
E_mem<=0.259093772014, E_reset>=0.259300152798 from a residual/MPFR/IEEE budget.
The manuscript deliberately uses the stronger subsequent Arb/Acb audit:
E_mem<=0.259092738049 and E_reset>=0.259313063246.
These are the same physical witness and cover, but a different proof-arithmetic
route. I inspected the complete audit implementation and independently
replayed it twice; the stronger numbers are supported, not a clerical claim
based on equality of hashes or on an earlier PASS verdict.

Proof audit
1. proof.txt:10–20; manuscript main.tex:86–135: resetting the selected bath
factorizes it from the target and any unused mode. Even if the latter was
correlated with the target, the selected fresh mode means the target update
depends only on its marginal. Starting diagonal, target populations stay
diagonal. Number-phase conjugations remove pulse phase from the population
kernel. Labels have identical kernels; zero durations embed fewer pulses.
Thus four scalar time variables cover the original reset class.
2. The truncated initial r<=10 and four bath l<=10 weights remain unnormalized.
Omitted contributions to energy are nonnegative, so no tail subtraction is
needed on the reset lower side. The reachable r<=10+5j bounds prevent an
unintended intermediate projection. The final space r<=30 and sector K<=60
used by the Arb audit suffice for all retained trajectories.
3. The global derivative envelope 2(A0 A2-A1^2) is the exact absolute Fourier
sum of squared eigenvalue differences; signed eigenvalues in A1 are correct.
The audit obtains verified eigensystems for this bound, and DIRECT Acb matrix
exponentials and derivatives at interval centres. It does not trust the
candidate's approximate spectral proposals, cached envelopes or lower scores.
Outward integer grids feed a rowwise linear-program relaxation; allowing
different times per occupation only lowers the true reset optimum. Row mass
is preserved as a lower constraint. The stated int64 bound is below overflow.
4. The cover is reconstructed from the root and every leaf used. All feasible
points, including zero durations and simplex faces, are retained. The fresh
audit visits 28097 nodes, with 14049 leaves, 211 time intervals and 177 centres.
A separate new exact traversal accepts the cover but rejects deletion of the
feasible origin leaf; this checks that coverage is not merely trusting the
number of stored boxes.
5. proof.txt:84–101; manuscript main.tex:227–280: memory evolution preserves
each bath parity and L=r+floor(l1/2)+floor(l2/2). Complete sectors L<=18 are
propagated through all three pulses without intervening projection. Omitted
L>18 implies initial total occupation S>18, and conservation bounds final
target occupation by S. The positive negative-binomial tail thus gives an
upper bound. Correlations are retained throughout the finite-sector product.

Fresh certified values (both clean runs)
Global reset lower bound: 2593130632467262 / 10^16.
Retained memory energy:
  0.25908293553576687947466117711970963664513459 +/- 1.49e-45.
Tail upper bound:
  0.0000098025129573887852747006543467614473292495 +/- 8.51e-47.
Memory upper bound:
  0.25909273804872426825993587777405639809246384 +/- 2.07e-45.
Certified separation:
  0.00022032519800193174006412222594360190753616 +/- 2.07e-45.
The manuscript's outward rounded 12-place bounds are therefore conservative.
The evidence is in clean-run-{1,2}/M14-independent-Arb.log and each run's
work/campaign/reviews/2026-10-21-strict/m14-arb-audit.json.

Sources and manuscript correspondence
• Png–Hu–Scarani, 2512.10703v2, conclusion §V: retained-machine/non-Gaussian
extensions are proposed, without this bounded four-collision reset optimum.
The same paper's short-pulse analysis does not prove this comparison.
https://arxiv.org/html/2512.10703v2
• Taranto et al., 2004.00323v2, Theorem 1: finite-dimensional machines,
arbitrary joint control and the limiting many-cycle memory advantage. These
architecture/control/asymptotic hypotheses do not give the fixed cubic,
three-oscillator, at-most-four-collision gap here.
https://arxiv.org/html/2004.00323v2
The theorem at manuscript main.tex:70–84 and certificate narrative (137–225,
227–280) match the stronger audit route, including exact reset comparator and
tail direction. The weaker candidate arithmetic need not establish the tighter
digits: the complete stronger route does so independently. Retain the result
with the actual Arb/Acb evidence and its hashes attached to the release.
