Independent strict review of the remaining seven results
Review date and primary-source search cutoff: 22 October 2026
Reviewer: fresh-context subagent /root/remaining7_strict_independent

Release-precondition assessment
All seven reviewed candidates are supported internally and cover their exact
originals. I found no serious proof gap, theorem refutation, or specifically
unresolved literature overlap that blocks their scoped release. The source
verdict means that the identified closest primary results and current search
hits were compared at the theorem/model level and no covering result was
found. It is a bounded literature assessment, not an exhaustive originality
guarantee or an assertion of external expert approval.

ID/version | Validity | Original coverage | Source comparison
M03-v3     | supported internally | complete | difference supported, bounded
M07-v1     | supported internally | complete | difference supported, bounded
M10-v4     | supported internally | complete negative answer | difference supported, bounded
M12-v5     | supported internally | complete uniform accepted law | difference supported, bounded
M06-v1     | supported internally | complete fixed channel/initial state | difference supported, bounded
M08-v1     | supported internally | complete exact two-collision task | difference supported, bounded
M14-v2     | supported internally | complete existence result/global reset comparison | difference supported, bounded

Per-result reasons, challenged bridges, exact proof/manuscript locators and
primary-source URLs are in M03-review.txt, M07-review.txt, M10-review.txt,
M12-review.txt, M06-review.txt, M08-review.txt and M14-review.txt. They should
be read as part of this assessment. No earlier PASS verdict was used as proof.

Scope that must remain visible
• M03 uses a real symmetric reference with a fixed spectral gap, fixed
admissible energy-lowering filter, the physical paired jump list, and bounded
even perturbations. The result gives a uniform small-coupling threshold and
logarithmic mixing from even states; complex hopping is not included.
• M07 is for each fixed beta and fixed geometry/local bounds, with the exact
Gaussian KMS sampler and coherent correction. It is not an arbitrary-
temperature uniform statement or a theorem about every Gibbs sampler.
• M10 disproves the universal finite noninteger-order statement by actual
classical densities and ordinary partial trace. The mechanism from matrix
analysis is known; (1,2) overlaps previous work; finite noninteger >2 is the
supported difference. Integer monotonicity is an existing distinct result.
• M12 concerns the uniform accepted block-matrix law. Its exact conditioning
and code counts do not identify that law with a sequential or modified sparse
generator. The existing attack is not claimed as new.
• M06 concerns the exact random-time channel and initial tau1 on full Fock
space. It is not uniform mixing from arbitrary states. The weak certified
rate is explicit, and both averaged and history-conditional work conventions
are reported separately.
• M08 solves the exact two-collision qutrit problem, including unconditioned
target equality under randomization. It is not a universal schedule theorem
for qutrits or higher dimensions.
• M14 gives one feasible retained-memory protocol strictly below a certified
global lower bound for all allowed reset schedules. It does not optimize the
memory class globally or isolate coherence as the cause of advantage.

Two nonfatal manuscript/source recommendations
1. M07-hopping-gibbs/main.tex:434 currently cites 2610.05848v1. The current
v2 dated 21 October 2026 was checked and still has one-dimensional scope;
update the reference. The new 2609.35159 and 2610.01190 results are relevant
background with different sampler outputs/geometry, as detailed in the report.
2. M10-reflected-entropy/main.tex:300 says the construction 'does not settle
the quantum integer-order problem'. This may imply the latter is open.
Describe integers as outside this construction and cite the established
integer-replica monotonicity proof (Dutta–Faulkner, Appendix B, Eq. (148)).
These recommendations do not alter any reviewed theorem. Frozen manuscripts
were not edited by this reviewer.

M14 manuscript arithmetic is supported
The stronger manuscript bounds E_mem<=0.259092738049 and
E_reset>=0.259313063246 were independently reproduced, including the complete
continuous reset cover and the infinite-dimensional memory tail. They arise
from the full Arb/Acb audit, rather than the weaker candidate residual/IEEE
budget. The exact certified gap is greater than 0.0002203251980019. The
published evidence should identify this actual certificate and its hashes.

Reproduction and independence
Two new isolated work copies were created. In each, nine core checks ran in
fresh processes: M03 CAR, M07 CAR, M07 KMS, M10 rational witness, M12 code
counts, M12 accepted law, M06 constants, M08 global interval proof, and M14
independent Arb certificate. Each copy then ran a fresh independent control
script and the separately implemented M10 verified eigensystem checker.
All 22 invocations exited successfully. See replay-summary.json and
additional-replay-summary.json; every invocation has its own full log.

The new independent_controls.py imports no candidate implementation. It
symbolically reconstructs M06 endpoint moments, compares all 9! first-stage
qutrit permutations against independently grouped 280 representatives, and
checks the exact M14 simplex cover with a deleted feasible leaf as a negative
control. The qutrit enumeration is a float64 diagnostic, not a rigorous global
proof. M10's independent Arb route reconstructs the physical Gram matrices
from rational probabilities and uses verified eigenvalues. M14's independent
route uses verified spectral derivative envelopes and direct matrix
exponentials; only geometric cover data is inherited. Their implementations
were read before their numerical verdicts were used.

Analytic claims were reviewed separately: M03/M07 uniform locality and
perturbative closures, M10 all-exponent construction, M12 accepted-law and
quadratic-space counts, M06 conductance/negative spectrum/initial tail, and
M08/M14 reductions from the physical protocol to certified finite inequalities.
Finite controls and matching hashes are not substitutes for these arguments.

Provenance, bounds of review and next step
frozen-inputs.json records SHA-256 hashes for 94 input files, including every
file in the seven frozen candidate bundles, all exact originals, the seven
manuscript sources, selected source text, and the independent audit programs.
The post-review integrity record checks those files remained unchanged.
source-search-records.json retains current searches and primary retrievals,
including failed fetches, rather than silently treating a failed fetch as a
comparison. Applicable qi-math-verify instructions and review-record/qi-checks
references were followed. No other subagents were spawned.

The review read complete originals and candidate proofs and inspected the
relevant manuscript proof/claim interfaces. It is an internal agent assessment,
not formal proof-assistant certification or external peer review. No evidence
of external acceptance was established here, and no website, campaign status,
candidate or manuscript was mutated. The parent may proceed to scientific
writing and release checks if its other three candidates independently pass;
the public wording must retain these source and scope boundaries.
