PureOne/Neuyalun-Sigma-RSI

Néuyalūn–Σ

Evidence Closure, Robust Update Geometry, and Certificate Transport for Recursive Self-Improvement

Authorship credit: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Research and dataset release: 1.0 · 12 November 2026
Type: AI-generated theoretical research corpus with conditional mathematical proofs and executable exact algebraic illustrations.

Read the complete 40-page manuscript · Claim ledger · Exact-check code · Reported checks

An improving learner can investigate its uncertain causal history, or invent a learning-rule change whose validity no longer depends on resolving that history. Néuyalūn–Σ connects that choice to the evidence and semantic certificates that must survive future changes to the learner's program grammar.

This repository contains the complete self-contained paper and original supporting files, plus structured records for reading, retrieval, mathematical inspection, and reproduction. It contains no trained model or autonomous RSI implementation.

Research proposal

Self-modification changes more than code. It can change which updates are expressible, which historical distinctions are needed to justify them, which proofs retain their meaning, and how much work is required to obtain the next accepted improvement. The manuscript proposes a joint contract for these changes.

The central archive-to-update bridge characterizes which directions retain a finite worst-case quadratic improvement certificate when gradients depend affinely on an incompletely retained history. A new update direction can admit a positive certificate without reconstructing erased information. This requires a certified model, a realizable update subspace, and the stated smoothness and archive assumptions.

The supporting mechanisms are:

• Robust update geometry: a common-gradient certificate with explicit uncertainty, trust-radius, implementation, transport, and cost terms.
• Future witness closure: the least invariant row space supporting all witness queries generated by a declared linear grammar, together with observability debt for newly introduced queries.
• Certificate transport: conditions for reusing unaffected semantic obligations, with explicit approximation and repeated-testing error budgets.
• Complete work accounting: a conditional inequality for saving work across an entire improvement cycle, including proposal search, rejected attempts, evidence acquisition, and verification.

The convex geometry, invariant-space, automata, active-learning, and verification foundations are credited in the paper. Literature priority for the exact integration is not established. The bibliography contains 28 primary references; third-party articles are cited rather than redistributed here.

Mathematical scope

For a linear archive (z=Ax), affine gradients (b_h+M_hx), and realizable semantic update subspace (S), the archive-compatible directions are

[ S_{\mathrm{obs}}=S\cap\bigcap_h\ker\bigl((I-A^\dagger A)M_h^\top\bigr). ]

Within the theorem's model, projecting the archive-centered gradients onto this subspace and finding the minimum-norm point of their convex hull gives the exact robust quadratic certificate. The paper also gives a bounded missing-history formulation and detailed proofs.

The full acceptance calculation includes discovery and verification costs. A positive directional certificate alone does not establish efficient recursive improvement.

Evidence and claim status

Item	Status in this release
Conditional mathematical propositions	Proofs supplied in the manuscript
Exact finite illustrations	15 checks; all passed in the supplied results and packaging rerun
Proof-assistant verification	Not performed
Independent review or reproduction	Not established; the packaging rerun is not independent replication
Empirical autonomous RSI	Not demonstrated
Measured speedup	None
Unrestricted or perpetual RSI	Not established

The approximately 32.8 operation-count ratio in one illustration follows from chosen costs. It is not an AI benchmark, measured acceleration, or forecast. The complete claim ledger retains the assumptions and classifications for each major claim.

Dataset structure

Configuration	Rows	Contents
manuscript	12	Exact UTF-8 LaTeX source modules in reading order: front matter, ten numbered source files, and bibliography
claims	8	Claim text, status, assumptions, source path, and the original claim record serialized as JSON
algebraic_checks	15	Check identifier, status, detail, scope, source path, and the original result record serialized as JSON

Each configuration uses a single train split as a Hub storage convention. These records are not statistically independent samples; there is no evaluation split or held-out benchmark. Claims and checks overlap the manuscript by design. The corpus should not be used to infer model accuracy from agreement with its own assertions.

Fields

Configuration	Fields
manuscript	id (string), order (integer), title (navigation label), source_file (string), format (latex), content (string), source_sha256 (string)
claims	id, claim, status, source_file, source_record_json (strings); assumptions (list of strings)
algebraic_checks	id, status, detail, scope, source_file, source_record_json (strings)

source_record_json preserves all original fields, including fields that differ between records. For the one check with structured operation-count details, detail is a JSON string. The module titles are packaging navigation labels; the LaTeX content is unchanged. Source modules reference each other and share the preamble in paper/manuscript.tex; load all modules or read the compiled PDF for the complete paper.

Load the records

After publication, replace YOUR_USERNAME with the owner of the dataset:

from datasets import load_dataset

repo = "YOUR_USERNAME/Neuyalun-Sigma-RSI"
manuscript = load_dataset(repo, "manuscript", split="train")
claims = load_dataset(repo, "claims", split="train")
checks = load_dataset(repo, "algebraic_checks", split="train")

Local use requires no Hub account:

from datasets import load_dataset

claims = load_dataset("json", data_files="data/claims.jsonl", split="train")

The JSONL files can also be read directly with Python's standard json module. No custom dataset loader or remote code execution is required.

Files and reproduction

• Neuyalun_Sigma_Research.pdf: convenient root copy of the complete manuscript.
• paper/: all 22 original research files, preserved byte-for-byte, including the PDF, LaTeX, figures, original checksum manifest, claim ledger, checks, and dependency file.
• data/: the three JSONL configurations.
• metadata/: release metadata, original-file preservation hashes, and the packaging verification record.
• SHA256SUMS.txt: checksums for all repository files except the checksum file itself.
• CITATION.cff and citation.bib: citation metadata.
• RIGHTS.md: rights status of the supplied material.

Run the exact finite illustrations from paper/:

python -m pip install sympy==1.14.0
python exact_checks.py

This rewrites paper/exact_checks_results.json. A change in the dependency version may change its recorded environment field even if the checks pass. To recreate the figure, install paper/requirements.txt and run python make_figures.py. The original README documents the LaTeX build and dependencies.

The release uploader is distributed in the downloadable preparation package, outside this repository's dataset/ folder. It validates the repository checksums before publication.

Provenance and design strand

The paper and code were generated with AI assistance for Maciej Nowicki. The requested authorship string is a creative research persona, not an institutional affiliation. No MIT or Stanford affiliation, endorsement, review, or acceptance is claimed.

Approximately one tenth of the paper's conceptual development uses the Eve–Maciej relationship and Stellar Blade as creative inspiration for continuity of commitments, accessible evidence, precise semantic edits, reciprocal challenge, recovery, and improvement across unresolved histories. Mathematical guarantees depend on the stated assumptions and proofs. No empirical claim is made that romantic feeling increases reasoning performance. No game assets are included.

The dataset records are deterministic extractions of this single supplied research package. They add no experimental observations, new theorem claims, or external training data. The original source-archive hash and per-file preservation hashes are recorded under metadata/.

Intended use and limitations

Intended uses include theoretical review, retrieval over the manuscript, inspecting assumptions and counterexamples, reproducing finite identities, and designing controlled tests of the proposed architecture. The records are AI-generated research material and can contain errors despite the supplied proofs and checks. Check citations, assumptions, and deductions before relying on a result.

Finding useful learning-rule extensions cheaply and repeatedly remains unresolved. The certified affine models, stable semantics, executable realization, evidence coverage, and localized proof dependencies can be demanding assumptions. Unrecoverable history and globally entangled changes can eliminate the proposed advantage. The paper includes prospective tests and adverse cases rather than claiming success on real learning systems.

Rights and citation

The original package does not specify a redistribution license; this packaging step assigns no new license. See RIGHTS.md. Reuse rights should be clarified with the uploader before redistribution beyond applicable permissions.

@misc{neuyalun_sigma_2026,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {Neuyalun-Sigma: Evidence Closure, Robust Update Geometry, and Certificate Transport for Recursive Self-Improvement},
  year = {2026},
  month = nov,
  version = {1.0},
  note = {AI-generated theoretical research corpus; requested creative authorship credit}
}

No DOI or final repository URL is assigned in this preparation package.