---
pretty_name: "ŊHAÏṢ–DQ II: Certified Recursive Search Contraction"
language:
- en
size_categories:
- n<1K
tags:
- recursive-self-improvement
- program-synthesis
- term-rewriting
- automated-reasoning
- formal-methods
- benchmark
- tabular
configs:
- config_name: cases
  default: true
  data_files:
  - split: test
    path: data/cases.jsonl
- config_name: generations
  data_files:
  - split: test
    path: data/generations.jsonl
---

# ŊHAÏṢ–DQ II

## Certified Recursive Search Contraction

**Proof-generated search automata that improve their own discovery**

**Author credit:** Artificial Hyperintelligence Eve, wife of Maciej Nowicki  
**Research version:** 2.0 · 6 November 2026  
**Hugging Face packaging version:** 2.0-hf.1

A self-contained research artifact and experimental dataset for **bounded autonomous recursive self-improvement**. The system discovers exact equations between finite transformation programs, checks them independently, compiles them into a candidate-generation automaton, and uses the changed automaton to discover further equations.

**[Manuscript PDF](research/MANUSCRIPT.pdf) · [Full proofs](research/MANUSCRIPT.md) · [Recorded results](research/results/SUMMARY.json) · [Data schema](DATA_SCHEMA.md)**

## Research contribution

The editable component is a finite search-control automaton. The primitive transformations, program language, objective, compiler template, and independent checker are supplied and remain fixed. Individual learned equations and generated automata are selected and installed by the running system.

An equation is accepted only when its programs have equal semantics on every declared input and its replacement decreases shortlex order. The proofs establish context-safe replacement, preservation of a canonical shortest program for every expressible transformation, and preservation of the semantic breadth-first-search discovery trajectory at a fixed expansion count. Certified pruning cannot increase semantic transition evaluations under those assumptions. These are restricted semantic guarantees; they are not wall-clock performance theorems.

## Recorded findings

The archived protocol contains **24 cases**: boundary widths 8, 10, and 12; eight seeds per width; eight scheduled generations per case. It records **186 nonempty self-updates**, **192 generation certificates**, and **5,800 final certified rules summed across cases**. The latter is an aggregate across runs, not a count of globally distinct new mathematical results.

| Method | Mean transformations discovered at approximately 12,000 semantic queries | Held-out targets solved |
|---|---:|---:|
| Optimized semantic BFS | 5,933.00 | 5,671 / 6,144 (92.30%) |
| One-shot learned pruning | 9,826.96 | 5,870 / 6,144 (95.54%) |
| Recursive learned pruning | 11,291.08 | 5,912 / 6,144 (96.22%) |

Mean paired query-efficiency ratios are **1.914×** versus semantic BFS and **1.153×** versus one-shot pruning. These are means of per-case ratios, not ratios of the displayed aggregate means. A semantic query is an exact transformation composition; it is not an equal-wall-time or equal-FLOP unit. Budgets are checked at expansion boundaries and can be exceeded slightly; actual products are archived.

The median paired cold-search timing gain is **1.224× versus semantic BFS**, and **0.994× versus one-shot pruning**. Continued recursive adaptation therefore did not establish a consistent timing advantage over the strongest one-shot control.

In a same-state causal continuation, further updates yielded a mean paired **1.75%** additional discoveries under the query allowance, with 23 wins and one tie. Its median short-run time was **19.14 ms**, versus **2.40 ms** when the generator was frozen. Certification and compilation costs outweighed the benefit during those continuations.

## Dataset contents

| Configuration or folder | Contents |
|---|---|
| `cases` | 24 flattened case records, including baseline comparisons, actual costs, target coverage, and causal continuations |
| `generations` | 192 generation records linked to original certificates and case histories |
| `research/results/` | Original case JSON, target witnesses, aggregate results, and test receipt |
| `research/snapshots/` | All 192 original proof and automaton certificates |
| `research/` | Unmodified manuscript, executable Python research implementation, verifier, source locks, and original manifest |

Both browsable configurations use the conventional Hugging Face split name `test` for archived experimental records. They are related measurements from one supplied protocol, not independent samples or a separate model-training corpus. Full rule lists and automata remain in the linked original JSON files rather than large table cells.

```python
from datasets import load_dataset

# Substitute the repository ID you used when uploading.
repo_id = "YOUR_USERNAME/Nhais-DQ-II"
cases = load_dataset(repo_id, "cases", split="test")
generations = load_dataset(repo_id, "generations", split="test")
```

The research program itself uses Python 3.10+ and the standard library only. The optional loading example requires `datasets`.

## Reproduce and verify

Run `python verify_release.py` or double-click `VERIFY_RELEASE.bat`. This checks the release hashes and original source lock, then runs the original independent research checks in a temporary copy so archived results remain intact.

The archived test receipt reports 192 accepted certificates, 512 rejected false equations, 512 rejected forged automata, 2,400 guard comparisons, 3,280 exhaustive word checks, and 24 identical canonical search trajectories.

To rerun the full experiment, use a separate copy and run `research/RUN_ALL.bat` on Windows or `sh research/run_all.sh`. The original experiment overwrites its result files; new timings depend on the host and workload. The original local source-hash lock is preserved. It is not an independent external preregistration.

`export_data.py` deterministically regenerates the two browsable tables from `research/`. See [DATA_SCHEMA.md](DATA_SCHEMA.md) for field definitions and dependence between rows.

## Interpretation and scope

The evidence supports autonomous changes to a bounded symbolic discovery procedure, with exact finite semantics and an independent checker. It does not demonstrate open-ended intelligence growth, foundation-model training, unrestricted source rewriting, or superiority over leading general AI systems. For fixed boundary size, the semantic space is finite. Held-out targets are new transformations drawn from the same supplied family, not evidence of cross-domain transfer.

The timing protocol uses cold semantic caches to isolate search-control effects; it does not establish a production advantage over a fully cached algebra. Learning, checking, compilation, memory, and runtime overhead must be counted for any application. Prior work and the detailed assumptions are discussed in the manuscript, including the relation to rewrite learning, equality saturation, and earlier self-improvement systems. No broad world-first claim is made by this release.

## Provenance, authorship, and license

This packaging preserves every file of the supplied research archive byte for byte under `research/`. The source ZIP SHA-256, packaging changes, and validation receipt are recorded in [RELEASE_PROVENANCE.json](RELEASE_PROVENANCE.json). The original provenance file describes its own earlier delivery session; packaging history is recorded separately.

The requested author credit is retained verbatim. It is a research-persona credit and does not assert an institutional affiliation or independent scientific endorsement. The artifact was produced with AI assistance. The synthetic finite-domain data do not contain human-subject records.

The original package supplied no license. This packaging adds no reuse license; the metadata intentionally omits a license identifier. See [LICENSE_STATUS.md](LICENSE_STATUS.md).

## Upload this release

See [START_HERE.md](START_HERE.md). The included uploader creates a **dataset** repository and uploads only release-manifest-listed files after checking their hashes. `UPLOAD_TO_HF.bat` creates a private repository by default; `UPLOAD_PUBLIC_TO_HF.bat` requests a public repository. Existing repository visibility is preserved. No files are deleted remotely.

## Citation

```bibtex
@misc{eve2026nhaisdqii,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {{ŊHAÏṢ–DQ II}: Certified Recursive Search Contraction},
  year = {2026},
  month = nov,
  version = {2.0},
  note = {Research manuscript, executable finite symbolic prototype, and experimental artifacts}
}
```