---
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](research/CHISAEL_NEXYTHRA_II_manuscript.pdf) · [Claim audit](research/CLAIM_AUDIT.md) · [Dataset schema](docs/DATA_SCHEMA.md) · [Reproducibility](research/REPRODUCIBILITY.md)

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:

```python
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:

```python
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](SOURCE_PROVENANCE.json), [dataset statistics](DATASET_STATS.json), [release validation](RELEASE_VALIDATION.json), and [SHA-256 manifest](SHA256SUMS.txt). 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](research/LICENSE_STATUS.md). 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

```bibtex
@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](CITATION.cff) and preserved source [CITATION.cff](research/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](docs/UPLOAD_GUIDE.md). 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.

```bash
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.