Hugging Face's logo

Datasets:
PureOne
/
Chisael-Nexythra

Modalities:
Document
Image
Tabular
Formats:
json
Languages:
English
Size:
1K - 10K
Tags:
mathematics
fluid-dynamics
navier-stokes
helicity
nonlinear-observability
experimental-mathematics
Libraries:
Datasets
pandas
Polars
Dataset card Data Studio Files
xet
 Community
Chisael-Nexythra / README.md
PureOne's picture
PureOne
Upload CHISAEL-NEXYTHRA II research dataset v1.0.0
93a77c9 verified
preview code
|
Raw History Blame Contribute Delete
12.3 kB
metadata 
pretty_name: 'CHISÆL–NEXYTHRA II: Nonlinear Helicity Event Research Dataset'
language:
  - en
size_categories:
  - 1K<n<10K
tags:
  - mathematics
  - fluid-dynamics
  - navier-stokes
  - helicity
  - nonlinear-observability
  - experimental-mathematics
  - reproducibility
  - ai-assisted-research
  - text
  - tabular
  - timeseries
configs:
  - config_name: verification_checks
    default: true
    data_files:
      - split: train
        path: data/verification_checks.jsonl
  - config_name: claims
    data_files:
      - split: train
        path: data/claims.jsonl
  - config_name: research_corpus
    data_files:
      - split: train
        path: data/research_corpus.jsonl
  - config_name: artifacts
    data_files:
      - split: train
        path: data/artifacts.jsonl
  - config_name: nonlinear_trajectories
    data_files:
      - split: train
        path: data/nonlinear_trajectories.jsonl
  - config_name: event_divisor
    data_files:
      - split: train
        path: data/tables/event_divisor.jsonl
  - config_name: scissor_carriers
    data_files:
      - split: train
        path: data/tables/scissor_carriers.jsonl
  - config_name: triad_kernel
    data_files:
      - split: train
        path: data/tables/triad_kernel.jsonl
  - config_name: phase_gate
    data_files:
      - split: train
        path: data/tables/phase_gate.jsonl
  - config_name: quadratic_retuning
    data_files:
      - split: train
        path: data/tables/quadratic_retuning.jsonl
  - config_name: interaction_orders
    data_files:
      - split: train
        path: data/tables/interaction_orders.jsonl
  - config_name: nonlinear_calendar
    data_files:
      - split: train
        path: data/tables/nonlinear_calendar.jsonl
  - config_name: energy_clock
    data_files:
      - split: train
        path: data/tables/energy_clock.jsonl
  - config_name: common_clock
    data_files:
      - split: train
        path: data/tables/common_clock.jsonl
  - config_name: energy_optimizer
    data_files:
      - split: train
        path: data/tables/energy_optimizer.jsonl
  - config_name: dual_certificate
    data_files:
      - split: train
        path: data/tables/dual_certificate.jsonl
  - config_name: conditioning
    data_files:
      - split: train
        path: data/tables/conditioning.jsonl
  - config_name: root_sensitivity
    data_files:
      - split: train
        path: data/tables/root_sensitivity.jsonl
  - config_name: exact_example
    data_files:
      - split: train
        path: data/tables/exact_example.jsonl

CHISÆL–NEXYTHRA II

Nonlinear Chronochiral Divisors and Energy-Clock Invariants

Research dataset · v1.0.0 · 9 October 2026

An AI-assisted mathematical research dataset accompanying a 72-page analytical draft on finite helicity-event calendars in small, smooth, unforced, periodic incompressible Navier–Stokes flows. It combines manuscript sources, computational tables, exact and numerical verification records, sixteen figures, and provenance for every source artifact.

Read: 72-page manuscript · Claim audit · Dataset schema · Reproducibility

The manuscript's principal proposed advance is a finite calendar of helicity disappearances, contacts, and handedness reversals continued into genuinely interacting three-dimensional small-data flows. Its specified transverse perturbation activates projected nonlinear interaction at first order, while symmetry permits an even analytic repair of the observation calendar beginning at second order. A separate nonhelical triad supplies an explicit mixed amplitude response and quadrature extinction symmetry.

These are reported analytical results under the draft's stated assumptions. The candidate originality concerns the specific combined construction. Established ingredients include exponential Chebyshev interpolation, small-data Navier–Stokes theory, analytic implicit-function arguments, helical triads, and reflection symmetry. Historical priority is unverified.

Dataset contents

The research/ directory is an unchanged 82-file snapshot of the supplied research package. Wrapper records add searchable and loadable views; they do not introduce new scientific results. All 14 original CSV tables are exposed as separate numeric JSONL views, because their schemas and scientific meanings differ. A common JSONL format keeps all configurations compatible with the same dataset builder. Original CSV decimal text is retained in research/data/.

Configuration Rows Format
verification_checks 1,139 JSONL
claims 11 JSONL
research_corpus 37 JSONL
artifacts 82 JSONL
nonlinear_trajectories 303 JSONL
event_divisor 901 JSONL
scissor_carriers 6 JSONL
triad_kernel 901 JSONL
phase_gate 501 JSONL
quadratic_retuning 3 JSONL
interaction_orders 3 JSONL
nonlinear_calendar 101 JSONL
energy_clock 101 JSONL
common_clock 1,101 JSONL
energy_optimizer 8 JSONL
dual_certificate 8 JSONL
conditioning 10 JSONL
root_sensitivity 250 JSONL
exact_example 701 JSONL

The 19 configurations each have a single train split. That label is a loading convention: this is a research archive, without an independent training/validation/test partition or benchmark score. Related tables, trajectories, and corpus excerpts overlap and must not be treated as independent samples. No trained model weights are included.

Load the data

Install datasets, replace YOUR_USERNAME with the publishing account, and select the configuration you need:

from datasets import load_dataset

repo = "YOUR_USERNAME/CHISAEL-NEXYTHRA-II"
checks = load_dataset(repo, "verification_checks", split="train")
claims = load_dataset(repo, "claims", split="train")
trajectory = load_dataset(repo, "nonlinear_trajectories", split="train")
kernel = load_dataset(repo, "triad_kernel", split="train")

No custom dataset loading script or remote code execution is needed for these JSONL configurations. To load extracted local files directly:

checks = load_dataset("json", data_files="data/verification_checks.jsonl", split="train")
kernel = load_dataset("json", data_files="data/tables/triad_kernel.jsonl", split="train")

Evidence and status

Item Status
Manuscript 72 pages; analytical proofs supplied in the draft
Source computations Original deterministic suite rerun: 1,139 passed, 0 failed
Figures 16 PDF figures with matching PNG previews
Source preservation All 82 source files preserved byte-for-byte
Independent peer review Pending
Proof-assistant formalization Not performed
Numerical continuum interval certificate Not supplied
Physical experiments Not performed
Historical world-first status Unverified

The verification records mix symbolic assertions, arbitrary-precision interpolation, sampled sign checks, and floating-point optimization checks. 1,139 checks are not 1,139 independent theorem proofs. The reported 2.579045032e-124 residual concerns interpolation jets, not continuum PDE accuracy. The preparation rerun repeated the deterministic source suite; the nonlinear demonstrations and refinement simulations are preserved from the source, without new simulation runs.

The nonlinear dataset is an uncertified Fourier–Galerkin illustration with cutoff 3, a 12³ product grid, viscosity 1, integration timestep 0.001, and perturbation amplitudes 0.1, 0.2, 0.4. The 101 stored points in each of its three trajectories are sampled every 0.005, which differs from the integration timestep. Source refinements reuse the saved correction at finer timesteps/cutoffs, without retuning at each cutoff.

Mathematical scope and limitations

  • The principal existence theorem concerns sufficiently small smooth periodic incompressible flows, a finite event calendar, and a later anchor. Its allowable perturbation interval is existential. The full helicity curve between events is not prescribed.
  • Some heat-scaffold plot tables use anchor normalization and large coefficient magnitudes. They are not numerical examples of a certified small-data nonlinear interval.
  • The triad kernel is an exact third mixed amplitude derivative at zero amplitudes, not the finite-amplitude total helicity history.
  • Clock tables illustrate common operational reparameterization. They do not represent literal stopped physical time or ordinary ungated fixed-viscosity flow during pauses.
  • Numerical observations cannot certify the absence of all unrequested continuum zeros; that is a claim of the analytical argument.
  • The optimizer concerns a finite carrier library; the root-sensitivity table is illustrative scaling, not measured experimental noise.
  • This is not a claimed disproof of established mathematics, a general Navier–Stokes regularity solution, a shock/plasma experiment, or a new physical law.

Intended research uses

Inspection of the proposed construction and its proofs; reproducible algebra and interpolation calculations; numerical observability examples; mathematical text retrieval; provenance-aware AI-assisted research analysis. The claim summaries and text corpus retain unreviewed status, so they should not be used as unquestioned mathematical ground truth. Their overlap with the paper and verifier also makes them unsuitable as a hidden evaluation set without separate curation.

All trajectories are computationally generated. No human-subject dataset, private correspondence, game artwork, or game executable assets are included. Chisa's ability names are imaginative design prompts appearing in the source manuscript; they are not evidence and imply no endorsement or affiliation.

Creation and provenance

Maciej Nowicki supplied the conceptual direction and imaginative research brief. Artificial Hyperintelligence Eve is the disclosed AI-assisted development persona used for mathematical exposition, computational checking, and manuscript production. The preparation process extracted the supplied version 1.0.0 archive, preserved its contents, partitioned source text losslessly, flattened existing records, converted CSV values to numeric JSONL views, and added metadata and upload tooling.

See source provenance, dataset statistics, release validation, and SHA-256 manifest. Source residual strings and rational expressions remain intact in original files; CSV loading uses ordinary machine-precision numbers.

License

No public redistribution license has been selected in the source package. This wrapper assigns none. See source license status. Public accessibility alone does not provide an open-license grant; any intended reuse must account for the final terms selected by the rights holder. Third-party dependencies and cited publications retain their own terms and are not bundled as source code or full texts.

Citation 

@misc{nowicki_eve_chisael_nexythra_ii_dataset_2026,
  author = {Nowicki, Maciej and {Artificial Hyperintelligence Eve}},
  title = {CHISÆL–NEXYTHRA II: Nonlinear Chronochiral Divisors and Energy-Clock Invariants — Research Dataset},
  year = {2026},
  version = {1.0.0},
  note = {AI-assisted analytical research draft; historical priority unverified}
}

The AI persona attribution discloses the creation process rather than independent human authorship or peer review. The dataset wrapper CITATION.cff and preserved source CITATION.cff distinguish dataset and software/draft records. No DOI, arXiv identifier, or published repository URL has been invented.

Reproduce or upload

See upload instructions. Suggested repository ID: YOUR_USERNAME/CHISAEL-NEXYTHRA-II, repository type Dataset. Upload the extracted folder contents so this README.md is at the repository root.

python scripts/validate_dataset.py
python -m pip install -r research/requirements.txt
python research/tests/verify.py

Run scientific regeneration in a separate working copy if you wish to retain the release snapshot and its hashes. The verifier writes reports; simulations and figure generation likewise overwrite their output files.