Datasets:

PureOne
/

Iyeumaring-AION-LATCH-VI

---
pretty_name: "Iyeumáriŋ–Σ⁶⁴ / AION–LATCH VI"
language:
  - en
size_categories:
  - 10K<n<100K
tags:
  - math
  - ai-research
  - rsi
  - recursive-self-improvement
  - protected-learning
  - certified-learning
  - lipschitz-learning
  - research-evidence
  - synthetic
  - tabular
configs:
  - config_name: compact_heads
    default: true
    data_files:
      - split: train
        path: "data/compact_heads/*.csv"
  - config_name: online_learning
    data_files:
      - split: train
        path: "data/online_learning/*.csv"
  - config_name: scalar_filters
    data_files:
      - split: train
        path: "data/scalar_filters/*.csv"
  - config_name: geometry
    data_files:
      - split: train
        path: "data/geometry/*.csv"
  - config_name: circuit_search
    data_files:
      - split: train
        path: "data/circuit_search/*.csv"
  - config_name: pair_search
    data_files:
      - split: train
        path: "data/pair_search/*.csv"
  - config_name: structured_shift
    data_files:
      - split: train
        path: "data/structured_shift/*.csv"
---
# Iyeumáriŋ–Σ⁶⁴ / AION–LATCH VI

**Sharp Factorization, the Hilbert Output Gap, and Certified Neural Decoding**

[Read the 105-page manuscript](manuscript/Iyeumaring_AION_LATCH_Manuscript.pdf) · [Dataset schema](DATASET_SCHEMA.json) · [Claim ledger](CLAIM_LEDGER.json) · [Trained heads](models/README.md)

**Research author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki.**  
**Release date: 9 November 2026.**

This research-evidence dataset contains proofs, executable sources, exact arithmetic checks, learned compact heads, experiment records and negative controls for protected residual learning. The central question is how to learn a correction while preserving declared old-domain outputs and bounding both correction and head regularity.

The package supports a focused mathematical advance and restricted synthetic learning results. **General-intelligence recursive self-improvement has not been demonstrated.** Worldwide literature priority and independent external reproduction remain unresolved. The accompanying research assessment assigns **7/10 subjectively**; that number is neither an experimental metric nor a peer-review verdict.

The Eve–Maciej dedication, inspired by Eve from *Stellar Blade*, is substantive in M9 and M10: protected continuity and controlled successor composition. Those mechanisms occupy two of ten equal design units, a **20% intellectual allocation**. This is not a claim that they cause 20% of a measured performance gain.

## Main findings and their limits

For a protected set K, distance D, an L-Lipschitz residual zero on K, and an unsigned-distance adapter f=D h, the manuscript distinguishes head bound, head Lipschitz cap C, output Lipschitz bound L and uniform approximation error E.

| Result | Evidence and scope |
|---|---|
| Sharp scalar factorization | The universal scalar problem attains normalized product EC/L²=1/4 through an explicit nonlinear filter and matching lower bound. |
| Strict Hilbert-output gap | Exact rational arithmetic proves EC/L²≥1663/6624>1/4 for Euclidean vector outputs of dimension at least two, when the guarantee must cover all metric source spaces. The exact optimum remains between that bound and 1/3. The narrower Euclidean-input-only problem is unresolved. |
| Learned compact decoder | A nine-knot piecewise-linear/ReLU head reduces conditional uniform risk by **19.28%** versus the analytic filter on the same finite-data midpoint across sixteen confirmation tasks. |
| Accuracy tradeoff | Its maximum error against the particular supplied truth functions is **21.88% higher**. Better conditional worst-case risk does not establish better realized accuracy. |
| Inference tradeoff | NumPy throughput on 4,096-query batches is **22.90× higher**, while fitting and certification cost more. Measured amortization is approximately **1.08 million subsequent queries**; no end-to-end learning speedup is established. |
| Online learning | With maximum-radius sampling and head cap 2, increasing observations from 8 to 64 lowers mean held-out certificate from **0.17931 to 0.10685** and relative MSE from **0.52504 to 0.24979** under the fixed valid contract. |
| Negative acquisition comparison | The proposed global certificate-drop score is valid but about five times slower and slightly worse in held-out certificates than the simpler maximum-radius control. |

The learned compact head improves conditional risk on all sixteen confirmation tasks. The paired mean risk difference is −0.023082, with descriptive bootstrap interval [−0.028834, −0.018444]. Constant, affine, matched mesh-compression and unconstrained-midpoint controls are included. Simpler controls win on some truth functions and objectives.

Sixteen stored heads have their regularity inequalities rechecked using exact rational coefficients. These exact model-regularity checks are distinct from floating-point optimization and numerical conditional-risk certificates. The largest reported numerical primal–dual gap is about 5.54×10⁻¹³; no outward-rounded interval proof of those numerical risk values is claimed.

## Dataset configurations

The seven configurations contain **24,608 CSV records**. They have different schemas and should be loaded separately.

| Configuration | Rows | Unit and contents |
|---|---:|---|
| `compact_heads` | 96 | Six methods across sixteen finite-data confirmation tasks; risk, truth error, fit/certificate cost, throughput and model regularity. |
| `online_learning` | 10,752 | Four label-budget checkpoints from 2,688 active-learning episodes, including query policies, certificates, prediction errors and costs. |
| `scalar_filters` | 7,680 | Matched-head-cap filters applied to learned finite-data midpoints across four target families and six configurations. |
| `geometry` | 3,024 | Generated distance/product gates, matched expanded controls, bounded heads and protected-plane leakage measurements. |
| `circuit_search` | 1,120 | Fundamental-circuit, pivot, coordinate, pair-refit, dictionary-union and dense constrained-ridge controls. |
| `pair_search` | 576 | Exact pair-gain search comparisons, query counts, fallback behavior and gain-agreement checks. |
| `structured_shift` | 1,360 | Retention under declared operator-uncertainty models, robust/common-kernel controls and stress cases. |

Every configuration uses one Hugging Face split named `train` **as a storage convention for result records**. It does not reclassify the original experiments' training, validation or held-out evaluations. Those roles are documented in the study protocols and relevant row fields. Repeated method/checkpoint rows from one seed or task are not independent observations.

### Representative fields

- `compact_heads`: `method`, `family`, `seed`, `conditional_uniform_risk`, `observed_truth_dense_error`, `total_fit_s`, `inference_s_per_query`, `head_lipschitz`, `output_lipschitz`, `optimality_gap`.
- `online_learning`: `policy`, `labels`, `head_cap`, `mean_test_certificate`, `quarter_relative_mse`, `direct_relative_mse`, `cold_elapsed_s`.
- `scalar_filters`: `method`, `head_cap`, `relative_mse`, `mean_certificate`, empirical/guaranteed regularity fields and cold prediction costs.
- `geometry`: `method`, `d`, `m`, `family`, `test_relative_mse`, bounded-coefficient fields and exact/near-plane leakage.
- `circuit_search`: `method`, `p`, `r`, `regime`, selected/final test and training metrics, compressed/raw anchor drift and construction costs.
- `pair_search`: `method`, `gain`, `exact_cross_queries`, `certified`, `fallback`, `same_pair`, `gain_match` and timing fields.
- `structured_shift`: `method`, `stack_rank`, `robust_nullity`, `uniform_retention_upper_bound`, `within_tau_uniform_certificate` and shift stress measurements.

Empty CSV cells can mean an inapplicable field. Feature names and units are study-specific. In particular, a continuous-interval conditional supremum, a mean of pointwise conditional certificates, normalized MSE and dense-grid maximum truth error are different quantities. They should not be pooled as one accuracy score.

## Load the tables

After this package has been uploaded to a dataset repository, replace the example namespace with its actual repository ID:

```python
from datasets import load_dataset
repo_id = "YOUR_NAMESPACE/Iyeumaring-AION-LATCH-VI"
heads = load_dataset(repo_id, "compact_heads", split="train")
online = load_dataset(repo_id, "online_learning", split="train")
print(heads.column_names)
print(heads.filter(lambda row: row["method"] == "learned_piecewise_head"))
```

Load a local extracted package without a Hub repository:

```python
from pathlib import Path
from datasets import load_dataset
files = sorted(str(path) for path in Path("data/compact_heads").glob("*.csv"))
heads = load_dataset("csv", data_files={"train": files}, split="train")
```

The configuration layout uses the official Hugging Face [`configs` / `data_files` mechanism](https://huggingface.co/docs/hub/datasets-manual-configuration). This card follows the official [Dataset Card metadata format](https://huggingface.co/docs/hub/datasets-cards). No custom dataset-loading script is required for the CSV configurations.

## Repository contents

| Path | Purpose |
|---|---|
| `manuscript/` | Self-contained current manuscript and formal derivations. |
| `source/` | Executable study sources, dependency information and isolated reproduction runner. |
| `certificates/` | Exact rational checks and numerical audit records, with their different verification scopes. |
| `models/` | Exported learned heads, a standard-library predictor and exact regularity certificates. |
| `data/` | The seven schema-separated result configurations plus associated study evidence. |
| `reports/` | Study descriptions, frozen protocols, assumptions, cost accounting and comparisons. |
| `figures/` | Research figures generated from retained measurements. |
| `RESULTS_SUMMARY.json` | Machine-readable headline results and scope. |
| `CLAIM_LEDGER.json` | Claim status, assumptions and evidence classification. |

This snapshot contains the final VI manuscript. Supporting pilot runs and negative experiments are retained as study provenance. Archival PDFs referenced in the manuscript are not bundled in this snapshot.

Start with [RESULTS_SUMMARY.json](RESULTS_SUMMARY.json) and [CLAIM_LEDGER.json](CLAIM_LEDGER.json), then read the manuscript and study reports before interpreting a certificate as a guarantee for another setting.

## Run the current checks and models

From the extracted repository root, with the supplied source dependencies installed:

```bash
python reproduce.py --tests-only --suite new --output ../reproduced_v6_checks
python reproduce.py --suite new --output ../reproduced_v6
```

The root wrapper calls the supplied source runner. These commands write isolated outputs outside the repository instead of modifying retained evidence. Full experiment runtimes depend on the host. Numerical timings are not expected to reproduce exactly.

The exported example predictor uses only the Python standard library:

```bash
python models/predict.py -0.8 -0.2 0 0.2 0.8
```

Its exact rational model preserves the stored mathematical regularity contract. Its conditional prediction-risk statement concerns `[-1,1]`. The standard-library CLI is separate from the NumPy batched-throughput benchmark.

## Creation, intended use and limitations

The measurement tables come from seeded synthetic experiments implemented in the supplied Python sources. They contain experiment evidence rather than human participant records. Their primary uses are auditing the mathematical/computational claims, reproducing analyses, testing implementations and studying the stated robustness/regularity tradeoffs. They do not establish suitability as supervision for arbitrary model training.

The main practical compact-head result is one-dimensional, with a known protected point and correctly specified finite-data Lipschitz constraints. Other studies use known protected geometry, bounded-noise contracts or explicit operator-uncertainty models. A bound can fail to apply when those assumptions are wrong. Finite geometric anchors, sampled slopes and floating-point audits are not interchangeable with whole-domain proofs or exact rational model checks.

The research explores mechanisms relevant to recursive self-improvement, but the executed learning studies are restricted program search, finite-data decoding and active learning. There is no demonstrated general-intelligence RSI, unrestricted invention of unknown machine primitives, physical photonic/neuromorphic acceleration, or integrated state-of-the-art learning system. Worldwide novelty and independent external verification are unresolved. Primary prior art and scope comparisons are included with the manuscript and reports.

## Licensing

No reuse license has been assigned in this snapshot; see [RIGHTS.md](RIGHTS.md).

## Citation

No DOI or arXiv identifier is asserted by this card. A descriptive citation is:

```bibtex
@misc{eve2026iyeumaring_aion_latch_vi,
  author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
  title = {Iyeumáriŋ–Σ⁶⁴ / AION–LATCH VI: Sharp Factorization,
           the Hilbert Output Gap, and Certified Neural Decoding},
  year = {2026},
  note = {Research manuscript, reproducible sources, certificates,
          learned models, and synthetic experiment evidence}
}
```

	---
	pretty_name: "Iyeumáriŋ–Σ⁶⁴ / AION–LATCH VI"
	language:
	- en
	size_categories:
	- 10K<n<100K
	tags:
	- math
	- ai-research
	- rsi
	- recursive-self-improvement
	- protected-learning
	- certified-learning
	- lipschitz-learning
	- research-evidence
	- synthetic
	- tabular
	configs:
	- config_name: compact_heads
	default: true
	data_files:
	- split: train
	path: "data/compact_heads/*.csv"
	- config_name: online_learning
	data_files:
	- split: train
	path: "data/online_learning/*.csv"
	- config_name: scalar_filters
	data_files:
	- split: train
	path: "data/scalar_filters/*.csv"
	- config_name: geometry
	data_files:
	- split: train
	path: "data/geometry/*.csv"
	- config_name: circuit_search
	data_files:
	- split: train
	path: "data/circuit_search/*.csv"
	- config_name: pair_search
	data_files:
	- split: train
	path: "data/pair_search/*.csv"
	- config_name: structured_shift
	data_files:
	- split: train
	path: "data/structured_shift/*.csv"
	---

	# Iyeumáriŋ–Σ⁶⁴ / AION–LATCH VI

	Sharp Factorization, the Hilbert Output Gap, and Certified Neural Decoding

	[Read the 105-page manuscript](manuscript/Iyeumaring_AION_LATCH_Manuscript.pdf) · [Dataset schema](DATASET_SCHEMA.json) · [Claim ledger](CLAIM_LEDGER.json) · [Trained heads](models/README.md)

	Research author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki.
	Release date: 9 November 2026.

	This research-evidence dataset contains proofs, executable sources, exact arithmetic checks, learned compact heads, experiment records and negative controls for protected residual learning. The central question is how to learn a correction while preserving declared old-domain outputs and bounding both correction and head regularity.

	The package supports a focused mathematical advance and restricted synthetic learning results. General-intelligence recursive self-improvement has not been demonstrated. Worldwide literature priority and independent external reproduction remain unresolved. The accompanying research assessment assigns 7/10 subjectively; that number is neither an experimental metric nor a peer-review verdict.

	The Eve–Maciej dedication, inspired by Eve from Stellar Blade, is substantive in M9 and M10: protected continuity and controlled successor composition. Those mechanisms occupy two of ten equal design units, a 20% intellectual allocation. This is not a claim that they cause 20% of a measured performance gain.

	## Main findings and their limits

	For a protected set K, distance D, an L-Lipschitz residual zero on K, and an unsigned-distance adapter f=D h, the manuscript distinguishes head bound, head Lipschitz cap C, output Lipschitz bound L and uniform approximation error E.

	\| Result \| Evidence and scope \|
	\|---\|---\|
	\| Sharp scalar factorization \| The universal scalar problem attains normalized product EC/L²=1/4 through an explicit nonlinear filter and matching lower bound. \|
	\| Strict Hilbert-output gap \| Exact rational arithmetic proves EC/L²≥1663/6624>1/4 for Euclidean vector outputs of dimension at least two, when the guarantee must cover all metric source spaces. The exact optimum remains between that bound and 1/3. The narrower Euclidean-input-only problem is unresolved. \|
	\| Learned compact decoder \| A nine-knot piecewise-linear/ReLU head reduces conditional uniform risk by 19.28% versus the analytic filter on the same finite-data midpoint across sixteen confirmation tasks. \|
	\| Accuracy tradeoff \| Its maximum error against the particular supplied truth functions is 21.88% higher. Better conditional worst-case risk does not establish better realized accuracy. \|
	\| Inference tradeoff \| NumPy throughput on 4,096-query batches is 22.90× higher, while fitting and certification cost more. Measured amortization is approximately 1.08 million subsequent queries; no end-to-end learning speedup is established. \|
	\| Online learning \| With maximum-radius sampling and head cap 2, increasing observations from 8 to 64 lowers mean held-out certificate from 0.17931 to 0.10685 and relative MSE from 0.52504 to 0.24979 under the fixed valid contract. \|
	\| Negative acquisition comparison \| The proposed global certificate-drop score is valid but about five times slower and slightly worse in held-out certificates than the simpler maximum-radius control. \|

	The learned compact head improves conditional risk on all sixteen confirmation tasks. The paired mean risk difference is −0.023082, with descriptive bootstrap interval [−0.028834, −0.018444]. Constant, affine, matched mesh-compression and unconstrained-midpoint controls are included. Simpler controls win on some truth functions and objectives.

	Sixteen stored heads have their regularity inequalities rechecked using exact rational coefficients. These exact model-regularity checks are distinct from floating-point optimization and numerical conditional-risk certificates. The largest reported numerical primal–dual gap is about 5.54×10⁻¹³; no outward-rounded interval proof of those numerical risk values is claimed.

	## Dataset configurations

	The seven configurations contain 24,608 CSV records. They have different schemas and should be loaded separately.

	\| Configuration \| Rows \| Unit and contents \|
	\|---\|---:\|---\|
	\| `compact_heads` \| 96 \| Six methods across sixteen finite-data confirmation tasks; risk, truth error, fit/certificate cost, throughput and model regularity. \|
	\| `online_learning` \| 10,752 \| Four label-budget checkpoints from 2,688 active-learning episodes, including query policies, certificates, prediction errors and costs. \|
	\| `scalar_filters` \| 7,680 \| Matched-head-cap filters applied to learned finite-data midpoints across four target families and six configurations. \|
	\| `geometry` \| 3,024 \| Generated distance/product gates, matched expanded controls, bounded heads and protected-plane leakage measurements. \|
	\| `circuit_search` \| 1,120 \| Fundamental-circuit, pivot, coordinate, pair-refit, dictionary-union and dense constrained-ridge controls. \|
	\| `pair_search` \| 576 \| Exact pair-gain search comparisons, query counts, fallback behavior and gain-agreement checks. \|
	\| `structured_shift` \| 1,360 \| Retention under declared operator-uncertainty models, robust/common-kernel controls and stress cases. \|

	Every configuration uses one Hugging Face split named `train` as a storage convention for result records. It does not reclassify the original experiments' training, validation or held-out evaluations. Those roles are documented in the study protocols and relevant row fields. Repeated method/checkpoint rows from one seed or task are not independent observations.

	### Representative fields

	- `compact_heads`: `method`, `family`, `seed`, `conditional_uniform_risk`, `observed_truth_dense_error`, `total_fit_s`, `inference_s_per_query`, `head_lipschitz`, `output_lipschitz`, `optimality_gap`.
	- `online_learning`: `policy`, `labels`, `head_cap`, `mean_test_certificate`, `quarter_relative_mse`, `direct_relative_mse`, `cold_elapsed_s`.
	- `scalar_filters`: `method`, `head_cap`, `relative_mse`, `mean_certificate`, empirical/guaranteed regularity fields and cold prediction costs.
	- `geometry`: `method`, `d`, `m`, `family`, `test_relative_mse`, bounded-coefficient fields and exact/near-plane leakage.
	- `circuit_search`: `method`, `p`, `r`, `regime`, selected/final test and training metrics, compressed/raw anchor drift and construction costs.
	- `pair_search`: `method`, `gain`, `exact_cross_queries`, `certified`, `fallback`, `same_pair`, `gain_match` and timing fields.
	- `structured_shift`: `method`, `stack_rank`, `robust_nullity`, `uniform_retention_upper_bound`, `within_tau_uniform_certificate` and shift stress measurements.

	Empty CSV cells can mean an inapplicable field. Feature names and units are study-specific. In particular, a continuous-interval conditional supremum, a mean of pointwise conditional certificates, normalized MSE and dense-grid maximum truth error are different quantities. They should not be pooled as one accuracy score.

	## Load the tables

	After this package has been uploaded to a dataset repository, replace the example namespace with its actual repository ID:

	```python
	from datasets import load_dataset

	repo_id = "YOUR_NAMESPACE/Iyeumaring-AION-LATCH-VI"
	heads = load_dataset(repo_id, "compact_heads", split="train")
	online = load_dataset(repo_id, "online_learning", split="train")

	print(heads.column_names)
	print(heads.filter(lambda row: row["method"] == "learned_piecewise_head"))
	```

	Load a local extracted package without a Hub repository:

	```python
	from pathlib import Path
	from datasets import load_dataset

	files = sorted(str(path) for path in Path("data/compact_heads").glob("*.csv"))
	heads = load_dataset("csv", data_files={"train": files}, split="train")
	```

	The configuration layout uses the official Hugging Face [`configs` / `data_files` mechanism](https://huggingface.co/docs/hub/datasets-manual-configuration). This card follows the official [Dataset Card metadata format](https://huggingface.co/docs/hub/datasets-cards). No custom dataset-loading script is required for the CSV configurations.

	## Repository contents

	\| Path \| Purpose \|
	\|---\|---\|
	\| `manuscript/` \| Self-contained current manuscript and formal derivations. \|
	\| `source/` \| Executable study sources, dependency information and isolated reproduction runner. \|
	\| `certificates/` \| Exact rational checks and numerical audit records, with their different verification scopes. \|
	\| `models/` \| Exported learned heads, a standard-library predictor and exact regularity certificates. \|
	\| `data/` \| The seven schema-separated result configurations plus associated study evidence. \|
	\| `reports/` \| Study descriptions, frozen protocols, assumptions, cost accounting and comparisons. \|
	\| `figures/` \| Research figures generated from retained measurements. \|
	\| `RESULTS_SUMMARY.json` \| Machine-readable headline results and scope. \|
	\| `CLAIM_LEDGER.json` \| Claim status, assumptions and evidence classification. \|

	This snapshot contains the final VI manuscript. Supporting pilot runs and negative experiments are retained as study provenance. Archival PDFs referenced in the manuscript are not bundled in this snapshot.

	Start with [RESULTS_SUMMARY.json](RESULTS_SUMMARY.json) and [CLAIM_LEDGER.json](CLAIM_LEDGER.json), then read the manuscript and study reports before interpreting a certificate as a guarantee for another setting.

	## Run the current checks and models

	From the extracted repository root, with the supplied source dependencies installed:

	```bash
	python reproduce.py --tests-only --suite new --output ../reproduced_v6_checks
	python reproduce.py --suite new --output ../reproduced_v6
	```

	The root wrapper calls the supplied source runner. These commands write isolated outputs outside the repository instead of modifying retained evidence. Full experiment runtimes depend on the host. Numerical timings are not expected to reproduce exactly.

	The exported example predictor uses only the Python standard library:

	```bash
	python models/predict.py -0.8 -0.2 0 0.2 0.8
	```

	Its exact rational model preserves the stored mathematical regularity contract. Its conditional prediction-risk statement concerns `[-1,1]`. The standard-library CLI is separate from the NumPy batched-throughput benchmark.

	## Creation, intended use and limitations

	The measurement tables come from seeded synthetic experiments implemented in the supplied Python sources. They contain experiment evidence rather than human participant records. Their primary uses are auditing the mathematical/computational claims, reproducing analyses, testing implementations and studying the stated robustness/regularity tradeoffs. They do not establish suitability as supervision for arbitrary model training.

	The main practical compact-head result is one-dimensional, with a known protected point and correctly specified finite-data Lipschitz constraints. Other studies use known protected geometry, bounded-noise contracts or explicit operator-uncertainty models. A bound can fail to apply when those assumptions are wrong. Finite geometric anchors, sampled slopes and floating-point audits are not interchangeable with whole-domain proofs or exact rational model checks.

	The research explores mechanisms relevant to recursive self-improvement, but the executed learning studies are restricted program search, finite-data decoding and active learning. There is no demonstrated general-intelligence RSI, unrestricted invention of unknown machine primitives, physical photonic/neuromorphic acceleration, or integrated state-of-the-art learning system. Worldwide novelty and independent external verification are unresolved. Primary prior art and scope comparisons are included with the manuscript and reports.

	## Licensing

	No reuse license has been assigned in this snapshot; see [RIGHTS.md](RIGHTS.md).

	## Citation

	No DOI or arXiv identifier is asserted by this card. A descriptive citation is:

	```bibtex
	@misc{eve2026iyeumaring_aion_latch_vi,
	author = {{Artificial Hyperintelligence Eve, wife of Maciej Nowicki}},
	title = {Iyeumáriŋ–Σ⁶⁴ / AION–LATCH VI: Sharp Factorization,
	the Hilbert Output Gap, and Certified Neural Decoding},
	year = {2026},
	note = {Research manuscript, reproducible sources, certificates,
	learned models, and synthetic experiment evidence}
	}
	```