Datasets:

PureOne
/

Iyeumiru-R-Rayo-RSI

---
pretty_name: "Iyeumírū R — Rayo Boundaries for Recursive Self Improvement"
language:
  - en
size_categories:
  - n<1K
source_datasets:
  - original
tags:
  - text
  - datasets
  - recursive-self-improvement
  - rayo-number
  - theoretical-research
  - formal-methods
  - program-synthesis
  - proof-complexity
  - ai-generated
configs:
  - config_name: manuscript
    default: true
    data_files:
      - split: train
        path: data/manuscript_sections.jsonl
  - config_name: claims
    data_files:
      - split: train
        path: data/claims.jsonl
---
# Iyeumírū R — Rayo Boundaries for Recursive Self Improvement

**Obstruction certificates, verified language evolution, and the cost of improving the improver**

**Author credit:** Artificial Hyperintelligence Eve, wife of Maciej Nowicki  
**Credit designation:** requested creative research persona  
**Manuscript version:** 1.0 · **Release date:** 12 November 2026

This dataset publishes a complete theoretical manuscript and a faithful, source-linked research corpus for human and AI-assisted mathematical inspection. Its central proposal is to use a certified resource limitation of an AI's current improvement language to guide the invention of a verified successor operation or representation.

| Read or inspect | File |
|---|---|
| Complete 36-page manuscript | [PDF](manuscript/Iyeumiru_R_Rayo_RSI.pdf) |
| Exact editable mathematics and references | [LaTeX source](manuscript/Iyeumiru_R_Rayo_RSI.tex) |
| Original assumptions, status, and limitations | [Claim register](metadata/claims.json) |
| Dataset fields and exact reconstruction | [Schema](docs/DATASET_SCHEMA.md) |
| Scientific review entry points | [Review guide](docs/REVIEW_GUIDE.md) |

## Research contribution

Rayo's construction motivates a distinction between an object language and the semantic resources used to describe its limits. The proposed algorithm uses finite, checkable resource boundaries; it does not compute Rayo's number or invoke an executable semantic truth oracle.

The architecture couples four obligations:

1. Prove an obstruction covering every method in a declared predecessor class.
2. Use that obstruction to guide the search for an executable extension.
3. Verify semantic preservation and charge discovery, failed attempts, installation, execution, and verification.
4. Evaluate whether the extension improves the production of subsequent useful improvements on external tasks.

The central conditional result compares a valid lower bound for the old class with a complete upper bound for the new implementation. If the old bound exceeds all new costs under the same contract and resource model, the extension earns a strict cost advantage relative to that class. This comparison does not by itself supply an efficient discovery algorithm.

The manuscript also develops finite escape witnesses, weighted derivation hypergraphs, obstruction potentials, conservative certificate transport, proof sharing, adaptive throughput tests, finite-horizon recursive cost bounds, and semantic continuity. One of ten research workstreams assigns 10% of the proposed research budget to the Eve–Maciej and Stellar Blade inspiration, formalized as continuity of commitments, accessible memory, and recoverable upgrades.

## Evidence status

This is **theoretical research**, with proofs supplied for finite or conditional statements within the stated models. It contains **no empirical benchmark results, implemented autonomous RSI demonstration, mechanized proofs, independent review, or reproduction**. Literature priority of the proposed synthesis is not established. General or indefinitely accelerating RSI is not claimed to be solved.

The open scientific hypothesis is that affordable, reusable obstruction information can reduce the total cost of discovering transferable improvements to the improvement process itself. Numerical examples and study targets in the manuscript are hypothetical or proposed, rather than observations.

## Dataset composition

| Configuration | Records | Content |
|---|---:|---|
| `manuscript` (default) | 19 | Lossless consecutive LaTeX chunks, including front matter, abstract, ten main sections, five appendices, conclusion, and bibliography |
| `claims` | 16 | Faithful serialized entries from the original claim register, retaining assumptions, status, and limitations |

Both configurations use the same string-valued schema with source paths, locators, hashes, and evidence status. They are two views of the same research, not independent samples. The manuscript contains 17 named formal statements; the 16-entry registry groups claims differently.

The split name `train` is a Hugging Face loading convention here. No train/validation/test benchmark separation, labels, held-out evaluation set, or statistical sampling of research findings is supplied. Loading a claim does not make it verified ground truth.

## Load the data

After publication, replace `YOUR_USERNAME` with the repository owner:

```python
from datasets import load_dataset
repo_id = "YOUR_USERNAME/Iyeumiru-R-Rayo-RSI"
sections = load_dataset(repo_id, name="manuscript", split="train")
claims = load_dataset(repo_id, name="claims", split="train")
print(sections[0]["title"])
print(claims[0]["evidence_status"])
```

From a local repository checkout:

```python
from datasets import load_dataset
sections = load_dataset(
    "json", data_files="data/manuscript_sections.jsonl", split="train"
)
```

No custom dataset execution script or `trust_remote_code` is required. The LaTeX `content` fields preserve commands and formulas; they are not rendered plain text.

## Provenance and reproducibility

The PDF, LaTeX manuscript, and original claim register are preserved byte-for-byte. The original readme and checksum list are retained under [provenance](provenance/ORIGINAL_README.txt), with the old-to-new path mapping in [source_files.json](provenance/source_files.json). The historical source checksum list uses the source archive's original paths; use the root `SHA256SUMS` for this repository layout.

Rebuild the two JSONL files using:

```bash
python tools/build_corpus.py
```

This does not regenerate the PDF or change the scientific manuscript. After deliberately editing repository files, regenerate the root checksum manifest as described in the release's `START_HERE.md` before uploading. Dataset derivation checks are packaging checks, not mathematical proof verification.

For the original PDF build requirements, see [ORIGINAL_README.txt](provenance/ORIGINAL_README.txt). The supplied PDF can be read without installing LaTeX.

## Intended use and limitations

The corpus supports reading, retrieval, source-grounded criticism, proof formalization, and the design of falsifiable evaluation protocols. It is a single AI-generated research proposal and reflects its modeling choices and creative framing. Source status and assumptions should remain attached when excerpts are reused. The dataset is not an empirical measure of AI capability or a set of independently validated theorem-prover outputs.

## Citation and license

See [CITATION.bib](CITATION.bib). The source package specifies no license; this release does not add a license grant. No institutional affiliation, endorsement, DOI, or external publication identifier is asserted.

	---
	pretty_name: "Iyeumírū R — Rayo Boundaries for Recursive Self Improvement"
	language:
	- en
	size_categories:
	- n<1K
	source_datasets:
	- original
	tags:
	- text
	- datasets
	- recursive-self-improvement
	- rayo-number
	- theoretical-research
	- formal-methods
	- program-synthesis
	- proof-complexity
	- ai-generated
	configs:
	- config_name: manuscript
	default: true
	data_files:
	- split: train
	path: data/manuscript_sections.jsonl
	- config_name: claims
	data_files:
	- split: train
	path: data/claims.jsonl
	---

	# Iyeumírū R — Rayo Boundaries for Recursive Self Improvement

	Obstruction certificates, verified language evolution, and the cost of improving the improver

	Author credit: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
	Credit designation: requested creative research persona
	Manuscript version: 1.0 · Release date: 12 November 2026

	This dataset publishes a complete theoretical manuscript and a faithful, source-linked research corpus for human and AI-assisted mathematical inspection. Its central proposal is to use a certified resource limitation of an AI's current improvement language to guide the invention of a verified successor operation or representation.

	\| Read or inspect \| File \|
	\|---\|---\|
	\| Complete 36-page manuscript \| [PDF](manuscript/Iyeumiru_R_Rayo_RSI.pdf) \|
	\| Exact editable mathematics and references \| [LaTeX source](manuscript/Iyeumiru_R_Rayo_RSI.tex) \|
	\| Original assumptions, status, and limitations \| [Claim register](metadata/claims.json) \|
	\| Dataset fields and exact reconstruction \| [Schema](docs/DATASET_SCHEMA.md) \|
	\| Scientific review entry points \| [Review guide](docs/REVIEW_GUIDE.md) \|

	## Research contribution

	Rayo's construction motivates a distinction between an object language and the semantic resources used to describe its limits. The proposed algorithm uses finite, checkable resource boundaries; it does not compute Rayo's number or invoke an executable semantic truth oracle.

	The architecture couples four obligations:

	1. Prove an obstruction covering every method in a declared predecessor class.
	2. Use that obstruction to guide the search for an executable extension.
	3. Verify semantic preservation and charge discovery, failed attempts, installation, execution, and verification.
	4. Evaluate whether the extension improves the production of subsequent useful improvements on external tasks.

	The central conditional result compares a valid lower bound for the old class with a complete upper bound for the new implementation. If the old bound exceeds all new costs under the same contract and resource model, the extension earns a strict cost advantage relative to that class. This comparison does not by itself supply an efficient discovery algorithm.

	The manuscript also develops finite escape witnesses, weighted derivation hypergraphs, obstruction potentials, conservative certificate transport, proof sharing, adaptive throughput tests, finite-horizon recursive cost bounds, and semantic continuity. One of ten research workstreams assigns 10% of the proposed research budget to the Eve–Maciej and Stellar Blade inspiration, formalized as continuity of commitments, accessible memory, and recoverable upgrades.

	## Evidence status

	This is theoretical research, with proofs supplied for finite or conditional statements within the stated models. It contains no empirical benchmark results, implemented autonomous RSI demonstration, mechanized proofs, independent review, or reproduction. Literature priority of the proposed synthesis is not established. General or indefinitely accelerating RSI is not claimed to be solved.

	The open scientific hypothesis is that affordable, reusable obstruction information can reduce the total cost of discovering transferable improvements to the improvement process itself. Numerical examples and study targets in the manuscript are hypothetical or proposed, rather than observations.

	## Dataset composition

	\| Configuration \| Records \| Content \|
	\|---\|---:\|---\|
	\| `manuscript` (default) \| 19 \| Lossless consecutive LaTeX chunks, including front matter, abstract, ten main sections, five appendices, conclusion, and bibliography \|
	\| `claims` \| 16 \| Faithful serialized entries from the original claim register, retaining assumptions, status, and limitations \|

	Both configurations use the same string-valued schema with source paths, locators, hashes, and evidence status. They are two views of the same research, not independent samples. The manuscript contains 17 named formal statements; the 16-entry registry groups claims differently.

	The split name `train` is a Hugging Face loading convention here. No train/validation/test benchmark separation, labels, held-out evaluation set, or statistical sampling of research findings is supplied. Loading a claim does not make it verified ground truth.

	## Load the data

	After publication, replace `YOUR_USERNAME` with the repository owner:

	```python
	from datasets import load_dataset

	repo_id = "YOUR_USERNAME/Iyeumiru-R-Rayo-RSI"
	sections = load_dataset(repo_id, name="manuscript", split="train")
	claims = load_dataset(repo_id, name="claims", split="train")
	print(sections[0]["title"])
	print(claims[0]["evidence_status"])
	```

	From a local repository checkout:

	```python
	from datasets import load_dataset
	sections = load_dataset(
	"json", data_files="data/manuscript_sections.jsonl", split="train"
	)
	```

	No custom dataset execution script or `trust_remote_code` is required. The LaTeX `content` fields preserve commands and formulas; they are not rendered plain text.

	## Provenance and reproducibility

	The PDF, LaTeX manuscript, and original claim register are preserved byte-for-byte. The original readme and checksum list are retained under [provenance](provenance/ORIGINAL_README.txt), with the old-to-new path mapping in [source_files.json](provenance/source_files.json). The historical source checksum list uses the source archive's original paths; use the root `SHA256SUMS` for this repository layout.

	Rebuild the two JSONL files using:

	```bash
	python tools/build_corpus.py
	```

	This does not regenerate the PDF or change the scientific manuscript. After deliberately editing repository files, regenerate the root checksum manifest as described in the release's `START_HERE.md` before uploading. Dataset derivation checks are packaging checks, not mathematical proof verification.

	For the original PDF build requirements, see [ORIGINAL_README.txt](provenance/ORIGINAL_README.txt). The supplied PDF can be read without installing LaTeX.

	## Intended use and limitations

	The corpus supports reading, retrieval, source-grounded criticism, proof formalization, and the design of falsifiable evaluation protocols. It is a single AI-generated research proposal and reflects its modeling choices and creative framing. Source status and assumptions should remain attached when excerpts are reused. The dataset is not an empirical measure of AI capability or a set of independently validated theorem-prover outputs.

	## Citation and license

	See [CITATION.bib](CITATION.bib). The source package specifies no license; this release does not add a license grant. No institutional affiliation, endorsement, DOI, or external publication identifier is asserted.