Datasets:

PureOne
/

Qhiunalum-Four-Dimensional-Intelligence-Fields

File	Contents
Research manuscript	Complete 123-page, self-contained manuscript with proofs, methods, experiments, comparisons, and references.
Complete research package	All 475 final-release files: source, manuscript, exact checkers, certificates, figures, archived evidence, runner, and integrity manifest.
Full technical README	Original final-release documentation, detailed file map, theorem domains, evidence, and reproduction commands.
Citation	Exact research title, author credit, and release version.
Packaging record	Final-release hashes and preservation checks.
Repository checksums	SHA-256 hashes for every other repository file.

This repository distributes a mathematical research artifact and executable experiments. The complete source archive is the authoritative runnable release. It is preserved byte for byte, including its archived logs and the original manifest covering 474 release files. No earlier paper or archive is needed.

Research overview

Qhïunalūm connects continuous contraction cycles, nonlinear interactions between four-dimensional cells, and a bounded recursive learner that installs verified operations for later discovery.

The final manuscript develops four linked contributions:

An exact contraction-attainment boundary. For even-dimensional linear error dynamics with half-rank coordinate damping and bounded skew mixing, the manuscript gives a necessary-and-sufficient condition for attaining the full-cap determinant contraction limit. An explicit schedule attains the limit throughout the supported horizon range.
Interacting nonlinear fields. A specified skew coupling class preserves the complete radial energy history of the local cycle through an orthogonal moving-frame factorization. Interaction has an explicit actuator cost.
Multiple generations of verified method improvement. A finite synthesis language admits universally checked macros into an acyclic library. Learned operations become ingredients of later discovery, with frozen-vocabulary and informed-compiler comparisons.
Joint state and work contracts. Contraction, representation changes, orthogonal growth, disturbances, and paid discovery are accounted for separately. Only realized execution savings fund later campaigns after an initial allowance.

The archive also retains the polynomial-recognition, recursive-elimination, exact-checking, algebraic, and boundary foundations used by the complete manuscript.

Central control statement

For the declared class of schedules fixed across all initial states,

$\dot e=(K(t)-\gamma(t)P)e,\qquad P=\operatorname{diag}(0_n,I_n),\qquad K^T=-K,\quad \|K\|_2\le\Omega,\quad 0\le\gamma\le\Gamma,$

the determinant yields $|U(T)|_2\ge e^{-\Gamma T/2}$. For positive damping and positive time, the final manuscript states that equality is attainable exactly when

$\Gamma<2\Omega,\qquad T\ge\frac{\pi}{\sqrt{\Omega^2-\Gamma^2/4}}.$

This concerns attaining the full-cap determinant limit in the specified linear class. It does not provide the entire optimal norm function before that threshold or establish optimality over arbitrary nonlinear feedback.

Recorded final-release evidence

The following records are included in the complete archive under Qhiunalum/results/final/. These are the final research release's recorded results; this repository rebuild preserves them unchanged.

Evidence	Recorded result
Complete reproduction	15 stages passed, with retained rational-trace and controller audits
Field certificates	43
Exact adaptive state-energy comparisons	36
Largest graph	1,024 cells / 4,096 coordinates
Recursive generations	8
Candidate words considered	11,905
Semantic evaluations / universal proofs	181 / 8
Exact recursive output comparisons	2,048
Invalid field and recursive controls rejected	32
Generation-eight primitive representation	256 dampers + 255 rotations
Frozen vocabulary / informed compiler	1 of 8 / 8 of 8 generations
Reference / deployed execution	1,034,240 / 27,648 logical work units
Learning and checking	298,240 logical work units

The informed compiler supplied with the normal form achieves the same outputs at lower total compilation/checking cost than the learner. Logical work units are a declared accounting model; they are not wall-clock speedups, FLOPs, or physical control time.

Reproduction

Download and extract Qhiunalum_Complete_Research_Package.zip, then run from its Qhiunalum directory:

cd Qhiunalum
python -m pip install -r requirements.txt
python run_all.py

The recorded environment is Python 3.12.14 with NumPy 2.3.5. The runner writes fresh outputs to results_reproduced/ and preserves the archived results/ directory. No external services, model downloads, or credentials are required for the research experiments. On Windows, RUN_ALL.bat is included inside the research archive.

To run only the final two suites:

python final_field_experiments.py --output-dir my_results/final/field
python final_recursive_learning.py --output-dir my_results/final/recursive

To download the complete archive with the Hugging Face Python client after publication:

from huggingface_hub import hf_hub_download

archive = hf_hub_download(
    repo_id="PureOne/Qhiunalum-Four-Dimensional-Intelligence-Fields",
    repo_type="dataset",
    filename="Qhiunalum_Complete_Research_Package.zip",
)
print(archive)

Scope

The nonlinear field guarantee concerns radial error about the declared target; it does not imply incremental contraction between arbitrary trajectories. The recursive experiment uses a specified language, exact checker, and resource model. The field and recursive suites test separate components of the interface.

The release does not establish open-ended general-intelligence growth or universal optimizer superiority. Its precise priority claims remain unestablished. Full assumptions, proofs, comparisons, resource distinctions, and boundaries appear in the manuscript and original technical README.

Citation

Use CITATION.cff, or cite the title and author exactly as shown above, with version 5.0-final and date 5 November 2026.

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