The dataset viewer is not available for this subset.
Exception: SplitsNotFoundError
Message: The split names could not be parsed from the dataset config.
Traceback: Traceback (most recent call last):
File "/usr/local/lib/python3.14/site-packages/datasets/inspect.py", line 286, in get_dataset_config_info
for split_generator in builder._split_generators(
~~~~~~~~~~~~~~~~~~~~~~~~~^
StreamingDownloadManager(base_path=builder.base_path, download_config=download_config)
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
)
^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/harbor/harbor.py", line 171, in _split_generators
raise DataFilesNotFoundError("No task.toml or instruction.md files found")
datasets.exceptions.DataFilesNotFoundError: No task.toml or instruction.md files found
The above exception was the direct cause of the following exception:
Traceback (most recent call last):
File "/src/services/worker/src/worker/job_runners/config/split_names.py", line 68, in compute_split_names_from_streaming_response
for split in get_dataset_split_names(
~~~~~~~~~~~~~~~~~~~~~~~^
path=dataset,
^^^^^^^^^^^^^
config_name=config,
^^^^^^^^^^^^^^^^^^^
token=hf_token,
^^^^^^^^^^^^^^^
)
^
File "/usr/local/lib/python3.14/site-packages/datasets/inspect.py", line 340, in get_dataset_split_names
info = get_dataset_config_info(
path,
...<6 lines>...
**config_kwargs,
)
File "/usr/local/lib/python3.14/site-packages/datasets/inspect.py", line 291, in get_dataset_config_info
raise SplitsNotFoundError("The split names could not be parsed from the dataset config.") from err
datasets.inspect.SplitsNotFoundError: The split names could not be parsed from the dataset config.Need help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
QX-NEPHRIEL / Seventh-String Closure
A quantitative rank-three Chollet inequality, with a full analytic argument and reproducible exact-arithmetic certificates.
Release v1.0.0, 3 October 2026. AI-generated derivation by Eve, prepared for Maciej Nowicki.
For complex Hermitian positive semidefinite (7\times7) matrices (A,B), each of rank at most three, the manuscript establishes
Here (\circ) denotes the entrywise product. The coefficient (24/25) is a convenient certified bound; its optimality is not claimed. The unrestricted, arbitrary-rank Chollet conjecture remains outside this result. Publication priority has not been established, and this release has not received external human peer review or proof-assistant formalization.
Read the result
- Complete typeset manuscript
- Main proof: the order-seven argument, including every reduction and rational endpoint bound.
- Higher-order appendix: orders eight and nine, followed by an analytic infinite tail.
- Theorem ledger: exact hypotheses, constants, dependencies and exclusions.
- Sources and attribution: established ingredients and the boundary of the novelty claim.
- Reproduction instructions, verification report, and additional AI review.
What the argument does
After diagonal normalization and a Cauchy-Schwarz reduction, the problem becomes a bound on
An interpolated Bregman row bound controls the numerator. Complex Gaussian moments, spherical Jensen inequalities and a top-eigenvector change of measure control the denominator. Eigenvalue elimination puts both estimates in the same scalar coordinate (t=\lambda_{\max}(C)). At order seven, monotonicity and piecewise log-convexity reduce the entire admissible spectral interval to three endpoint checks. Integer and rational arithmetic then certify a coefficient below one.
The row interpolation and spherical estimates have precedents and are explicitly credited. The contribution claimed by this derivation is the order-seven scalar closure and its quantitative certificate, subject to an unfinished priority audit.
Scope of the supplied bounds
Both matrices must be complex Hermitian PSD and individually have rank at most three.
| Matrix order | Certified coefficient | Supplied argument |
|---|---|---|
| (n=7) | (24/25) | Three analytic endpoints; exact rational checks |
| (n=8) | (3/5) | 21 closed intervals cover ([8/3,8]) |
| (n=9) | (2/5) | 12 closed intervals cover ([3,9]) |
| Every (n\ge10) | (4/5) | Analytic tail with a rational base case |
Thus (24/25) works uniformly for every (n\ge7). These are separate sufficient bounds, not optimal constants or a claimed extremal-ratio curve. An all-order rank-three corollary additionally relies on the cited through-order-six preprint, whose proof is not reproduced or independently audited here.
Reproduce locally
The core verifiers need Python 3.10+, its standard library, and no network access.
python verify_release.py
This checks file integrity and replays the two core scripts in a temporary directory without modifying the release. Expected evidence: 49/49 exact checks; 21/21 order-eight intervals; 12/12 order-nine intervals; no unresolved intervals.
Optional symbolic and exact-matrix checks require SymPy:
python -m pip install -r requirements-audit.txt
python verify_release.py --include-symbolic
The original individual scripts remain available. They regenerate their JSON certificates beside themselves when executed directly.
Status / completeness
| Item | Release evidence | Interpretation |
|---|---|---|
| Finite rational checks | 49/49 passed (100%) | Executed integer/fraction inequalities |
| Auxiliary interval coverage | 33/33 certified (100%) | Complete closed-domain covers for orders eight and nine |
| Optional symbolic/fixture audit | 21/21 passed (100%) | Additional identity and exact-example checks |
| Analytic manuscript | Included; additional AI review found no fatal error | Written proof remains open to mathematical review |
| External human peer review | Not performed | No endorsement claimed |
| Proof-assistant formalization | Not performed (0%) | Scripts do not formalize all analytic steps |
| Priority / optimal coefficient | Unconfirmed | No percentage or first-proof claim assigned |
The percentages above describe completed finite checks, not a probability that the theorem is correct. These verifiers do not mechanically establish the entropy proof, Gaussian pairing identity or continuous analytic reduction. Those steps are written out in the manuscript.
Artifact contents and intended use
This is a research artifact collection hosted in a Hugging Face dataset repository: Markdown/PDF mathematics, exact JSON certificates, verification code, replay logs, citations and an integrity manifest. It contains no trained model, training examples, human-subject data or performance benchmark. The JSON files are structured proof evidence rather than IID samples. Inspect them directly; the release does not define a datasets.load_dataset schema.
Use it for mathematical review, exact reproduction, comparison with existing permanent inequalities, or further formalization. New orders, ranks, constants or learning-system applications require additional arguments.
Provenance, citation and license
The original conversation-produced archive is preserved in provenance. Release preparation adds documentation, a typeset manuscript, fresh replay reports and a local verification runner. The mathematical core scripts are preserved. See release notes.
Use CITATION.cff or citation.bib; no DOI or journal acceptance is implied. Documents and original certificate data are released under CC BY 4.0; Python code under MIT. Third-party sources retain their own rights. See LICENSE.md.
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