C5 — INDEPENDENT REVIEW AND QUALIFIED ATLAS BENCHMARK — 3 NOVEMBER 2026

Decision: ACCEPT as a bounded illustrative relaxation benchmark. All hardware
holds and existing portfolio investigations remain. Instrument transfer HOLD.
No website publication or new physical experiment was performed.

VERIFIED INPUT
The standalone c5_mpemba_benchmark.py matches the bundled copy byte-for-byte.
SHA-256: fb594632f2ab9533030f30b321358bad6ea5df546a555fe134e598193a9f33da
All 71 entries of the submitted SHA-256 manifest match. Original files remain
unchanged in original/bundle/. The submitted manifest does not hash itself.

EXECUTION
The submitted C5 was rerun unmodified into rerun/. It exits 0 and produces
11 PASS and 9 INFO, with no FAIL; names and statuses match its archived report.
It does not produce the 15 PASS / 8 INFO stated in the handoff.

validate_c5.py independently constructs the rates and uses the symmetric
detailed-balance eigenproblem, Radau integration, and Poisson uniformization.
It imports none of C5's numerical functions and does not use matrix expm.
All 87 independent checks passed. These are numerical/conformance checks,
not 87 physical experiments or independent scientific discoveries.

The qualification verifies both selected cases, pairwise detailed balance,
probability conservation, nonnegative normalized trajectories, contracting L1
distance, fixed-threshold ordering, and fast-mode decay at both strong roots.
Maximum Radau/spectral L1 disagreement is about 2.62e-12; maximum uniformization
disagreement is about 2.61e-15 for the points tested. Such agreement is numerical,
not a claim of exact arithmetic or a measured physical rate.

At L1 distance 0.001, in MODEL TIME UNITS:
                    warm start       chosen hot start       strong-root start
Large gap 7.25186      1998.331           1241.750                  525.008
Small gap 1.25642        14.814             16.504                   16.223

The large-gap strong root is T=1.6951257071; the small-gap root is
T=1.4636271018. Temperatures/energies are dimensionless, kB=1 and the common
rate prefactor is 1. These times are not laboratory seconds. The chosen hot
start and the strong-root start are different temperatures; do not conflate
1241.750 with 525.008.

The chosen hot start wins at eps=0.01, 0.001, 0.0001 and 0.000001 in the large
gap case, but only at 0.000001 among the five tested thresholds in the small
gap case. It loses at eps=0.1 in both. Even the small-gap strong-root start is
slower than the warm start at eps=0.001. This directly illustrates why removing
the slow asymptotic mode does not guarantee every finite-threshold comparison.
Finite time also depends on starting amplitudes; the gap is not the sole cause.

RECONCILED GAPS
1. Correct the handoff to 11 PASS / 9 INFO for the submitted C5; our extra
   qualification has its own separate 87/87 result.
2. The archive contains no prior C5 failure log. The hand-picked no-root fixture
   is described in a source comment. We reconstructed it and recorded no sign
   changes over a declared expanded grid; this does not restore a missing
   original log or establish absence at every possible positive temperature.
3. Submitted C5 tests |a2| monotonicity only for 3-state controls; its 4/5-state
   controls only test sign changes. We independently completed monotonicity
   checks on those same seeded draws. Result: 0/300, 0/100, 0/100 violations.
4. Submitted outputs/RUN_SUMMARY.json predates C5 and lists five scripts. The
   source run_all.py now lists six, but that is not a receipt for a six-script
   execution. There is also a duplicate C5 report at outputs/c5_report.json.
   Do not sum both copies. We ran only C5 and the new independent qualification
   in this review; we did not claim a new full-suite run.
5. Submitted c5_results.json uses nonstandard Infinity values and omits the
   small-gap barriers and start temperatures. Our fixtures.json uses strict
   JSON with null diagonal barriers, full matrices, all temperatures, explicit
   units and outcome labels for both cases.
6. The source has a general nonstationarity warning, but its results JSON has
   no machine-readable eligibility tag. Our fixture/start records and every
   trajectory CSV row carry nonstationary_relaxation_transient and
   stationary_surrogate_eligible=false. This is an explicit exclusion record,
   not a newly validated transient null or an automatic stationarity detector.
7. The small-gap root search in the submitted code reuses the large-gap
   temperature grid. It happens to bracket the reported root. The independent
   implementation uses the small-gap system's own bath-based grid.

SELECTION AND CLAIM LIMITS
The demonstrations were selected using a seeded search after an initial
hand-picked model lacked the target effect. They are existence demonstrations,
not a preregistered assessment of arbitrary systems. Draws #128 and #2 are
zero-based indices from the stated seed. The separate random-barrier control
scan returns 13/300 detections on its specified finite temperature grid. That
is not a universal prevalence, a full Mpemba index, or a numerical proof of
topological parity. Sign-change scans can miss tangential roots or roots outside
their bounds. The complete-graph negative result is restricted to the stated
uniform-proposal Metropolis rates. Its theoretical basis is Klich & Vucelja;
the finite numerical draws are corroboration, not the proof.

DO NOT REVERT TO C2/C2b INFERENCE
The submitted C2/C2b circular-surrogate implementation is preserved as historical
benchmark evidence. A stationarity label does not by itself repair its previously
identified inferential problems. The repaired grouped/TTS methods in
statistical-repair/ remain the designated methods workstream. C5 transients are
not admissible inputs to its stationary TTS branch. No instrument data were used.

OTHER ADJUDICATION POINTS
Weatherhill: the 2002 Falkovich–Fouxon–Stepanov source is the relevant airborne
cloud-droplet lead. A regime map must include droplet radius distribution,
Stokes response time, velocity-gradient scale/dissipation, outer Reynolds
number/intermittency, gravity/settling and collision efficiency. Stokes number
alone is insufficient. No FogLab operating values have been supplied in this
C5 package, so no numeric match or outdoor performance claim has been made.
Source: https://doi.org/10.1038/nature00983
Author PDF: https://webhome.weizmann.ac.il/home/fnfal/papers/Nature.pdf
The publisher page was inaccessible; the author-hosted full paper was read.

MF-01: retain amplitude sweeps as characterization, not a mechanism-specific
pass/fail gate. The primary 2011 nonlinear-damping paper is Eichler et al.,
arXiv:1103.1788 / doi:10.1038/nnano.2011.71. arXiv:1110.1234 is a related
review led by Moser, not that primary experimental paper.
https://arxiv.org/abs/1103.1788

IP: not searched; no ownership or clearance conclusion.
Atlas: ready for integration with this qualification and the finite-threshold
caveat. This review does not change or publish the site.

REPRODUCE WITHOUT OVERWRITING ARCHIVED RESULTS
From the consolidated package root:
    python run_c5_validation.py
That wrapper copies the needed code to a fresh temporary directory, reruns the
submitted C5, then runs the independent validator. It prints the output location.
No downloads or dependency installation are performed. Environment recorded:
Python 3.12.14, NumPy 2.3.5, SciPy 1.17.0.

FILES
original/bundle/       unchanged submitted source and archived outputs
rerun/c5/             actual unmodified-source rerun outputs
independent_results/  complete fixtures, 800 control-model records, labelled
                      trajectory CSVs and the separate 87-check qualification
validate_c5.py         independent executable checker
c5-rerun.log          fresh C5 execution log
independent-validation.log  fresh independent-check execution log

No physical, causal, propulsion, fog-removal or device qualification follows
from the numerical benchmark. Existing hardware holds remain in force.
