Datasets:

PureOne
/

SERAPH5-SAELYRA-v6

---
pretty_name: "SERAPH-5 / SAELYRA v6.0.0"
language:
- en
tags:
- mathematics
- convex-geometry
- discrete-geometry
- illumination-problem
- computational-mathematics
- exact-arithmetic
- reproducible-research
- computer-assisted-mathematics
---
# SERAPH-5 / SAELYRA v6.0.0
## Blocking-Slack Geometry and Verified Convex-Body Atlases

**Research prepared for Maciej Nowicki by Artificial Hyperintelligence Eve.**  
**Release date:** 3 October 2026  
**Recommended Hugging Face repository type:** Dataset

> **Research status — PARTIAL for the original five-dimensional target.**
> This release does **not** prove that every 1-unconditional convex body in \(\mathbb R^5\) has illumination number at most 32. It proves the certificate, stability, neighborhood, atlas, and finite-integer equivalence results stated below. No universal five-dimensional integer level has been verified.

## Overview

SERAPH-5 is a research program on the five-dimensional 1-unconditional case of the Hadwiger–Boltyanski illumination problem. SAELYRA v6.0.0 returns to the general convex-body setting and replaces exact tangent-cone bookkeeping by a **blocking-slack functional** that retains near-supporting normals.

For a fixed normalized direction family \(D\), the manuscript defines \(\beta_D(K)\) and proves
\[
D\text{ illuminates }K \iff \beta_D(K)>0,
\]

and the Hausdorff-stability estimate

\[
|\beta_D(K)-\beta_D(L)|\le 2d_H^\infty(K,L).
\]
This leads to exact rational neighborhood certificates and to an all-integer reformulation of the universal \((n,m)\) illumination statement. In dimension five, the finite formulation uses the explicit thresholds \(17N\) and \(-16N\). The equivalence is proved; no universal level \(N\) is certified here.
## Main results in v6.0.0
- **Blocking-slack characterization.** Positivity of \(\beta_D(K)\) is equivalent to illumination by the fixed family \(D\).
- **Quantitative stability.** The optimized certificate is 2-Lipschitz in infinity-Hausdorff distance.
- **Rational collar theorem.** A finite near-facet certificate yields a common finite direction family and a common interior step throughout an explicit Hausdorff neighborhood of a rational polytope.
- **Complete rational atlas language.** Rational collar certificates form a complete certificate system for normalized bodies having illumination number at most a prescribed \(m\).
- **Exact finite-integer reformulation.** For fixed \(n,m\), the universal upper-bound statement is equivalent to the existence of one fully verified finite integer level \(\Phi_{n,m,N}\).
- **Irregular 5D model.** Ten explicit directions illuminate the model and every convex body in the certified open ball
  \[
  d_H^\infty(P,L)<1/42048.
  \]
  On the smaller closed radius \(1/63072\), a common step \(1/292\) works. Ten is an upper bound, not a proved minimum.
- **Robustified 360-template atlas.** All 360 earlier unit-coordinate primal/polar records are independently reconstructed; every center has a certified closed neighborhood radius at least \(1/6156\).

## What is *not* claimed

This repository does **not** claim any of the following:

- a proof that every unconditional \(K\subset\mathbb R^5\) satisfies \(\operatorname{ill}(K)\le 32\);
- a proof of the strict \(\le31\) bound for every nonparallelotope;
- proof that the 360 certified neighborhoods cover the full normalized body space;
- minimality of the ten-direction irregular-model family;
- external peer review, proof-assistant verification, or established publication priority.

The earlier project manuscripts are preserved as research records. In v6.0.0, the 360-template upper-direction catalogue is independently rechecked; earlier analytic claims are not automatically promoted to externally validated results.

## Read first

| File | Purpose |
|---|---|
| `SERAPH5_SAELYRA_Research_v6.0.0.pdf` | New 31-page self-contained manuscript |
| `SERAPH5_Complete_Research_Dossier_v6.0.0.pdf` | 196-page chronological dossier: original brief + all six manuscripts |
| `CLAIMS.json` | Machine-readable claim/status ledger |
| `verification/release_report.json` | Consolidated exact verification report |
| `docs/README_RELEASE_v6.0.0.md` | Original v6 release README |
| `release/SERAPH5_SAELYRA_v6.0.0.zip` | Original complete v6 archival package |

## Exact reproduction

Python 3.10+ is sufficient. The verification suite uses only the Python standard library.

```bash
python code/verify_all.py
```

Or run the implementations separately:

```bash
python code/verify_primary.py
python code/check_independent.py
python code/check_orbits.py
```

The declared suites currently report `PASS`. The primary and independent geometric implementations overlap on the same 20,700 signed boundary generators and therefore must not be added as independent point counts. The separate orbit program enumerates 6,894 covering clutters and 180 coordinate-permutation orbits.

## Verification snapshot

From `verification/release_report.json`:

- 361 polytope certificates checked;
- 360 legacy atlas templates;
- 20,700 signed boundary generators covered by both geometric implementations;
- 977,560 independent signed-inequality landing comparisons;
- 6,894 covering antichains / clutters;
- 180 coordinate-permutation orbits;
- 13,788 labeled primal/polar model presentations;
- minimum atlas closed radius: `1/6156`;
- irregular-model open radius: `1/42048`;
- irregular-model closed radius: `1/63072`;
- unrestricted five-dimensional theorem proved: **false**;
- universal integer level completed: **none**.

## Repository structure

```text
SERAPH5_SAELYRA_HuggingFace_v6.0.0/
├── README.md
├── CITATION.cff
├── RELEASE_NOTES_HF.md
├── START_HERE.txt
├── CLAIMS.json
├── CHANGELOG.md
├── SERAPH5_SAELYRA_Research_v6.0.0.pdf
├── SERAPH5_Complete_Research_Dossier_v6.0.0.pdf
├── code/
├── data/
├── source/
├── verification/
├── prior_manuscripts/
├── provenance/
├── docs/
└── release/
```

## Certificate utility

To rebuild the irregular-model certificate:

```bash
python code/make_certificate.py data/cyclic_input.json \
  --output verification/rebuilt_cyclic_certificate.json
```

Use exact rational strings such as `"4/5"`; floating-point input is intentionally rejected. The utility verifies a supplied direction family. It does not search for one or prove cardinality minimality.

## Rebuilding the PDFs

The manuscript source is in `source/`. The manuscript uses pdfLaTeX; the literal Unicode rendering of the original brief uses XeLaTeX. Fonts are not redistributed in this repository. Dossier assembly uses PyMuPDF through `code/build_dossier.py`.

## Provenance

The repository preserves the chronological research chain. `provenance/source_hashes.json` and the supplied manifests record byte provenance. Hash agreement establishes file identity, not mathematical correctness.

## Citation

A machine-readable citation is provided in `CITATION.cff`.

Suggested plain-text citation:

> Artificial Hyperintelligence Eve. *SERAPH-5 / SAELYRA: Blocking-Slack Geometry and Verified Convex-Body Atlases*. Version 6.0.0, research prepared for Maciej Nowicki, 3 October 2026. AI-generated research draft.

## License / reuse

No public reuse license was specified in the source release. See `LICENSE_NOTICE.md` before redistributing or deriving from the archive.

## Research integrity note

This is an AI-generated mathematical research draft with exact reproducibility artifacts. The package is intentionally explicit about what is proved, what is computer-assisted, what remains conjectural, and what has not received external validation. Independent mathematical review is strongly encouraged.

	---
	pretty_name: "SERAPH-5 / SAELYRA v6.0.0"
	language:
	- en
	tags:
	- mathematics
	- convex-geometry
	- discrete-geometry
	- illumination-problem
	- computational-mathematics
	- exact-arithmetic
	- reproducible-research
	- computer-assisted-mathematics
	---

	# SERAPH-5 / SAELYRA v6.0.0
	## Blocking-Slack Geometry and Verified Convex-Body Atlases

	Research prepared for Maciej Nowicki by Artificial Hyperintelligence Eve.
	Release date: 3 October 2026
	Recommended Hugging Face repository type: Dataset

	> Research status — PARTIAL for the original five-dimensional target.
	> This release does not prove that every 1-unconditional convex body in \(\mathbb R^5\) has illumination number at most 32. It proves the certificate, stability, neighborhood, atlas, and finite-integer equivalence results stated below. No universal five-dimensional integer level has been verified.

	## Overview

	SERAPH-5 is a research program on the five-dimensional 1-unconditional case of the Hadwiger–Boltyanski illumination problem. SAELYRA v6.0.0 returns to the general convex-body setting and replaces exact tangent-cone bookkeeping by a blocking-slack functional that retains near-supporting normals.

	For a fixed normalized direction family \(D\), the manuscript defines \(\beta_D(K)\) and proves

	\[
	D\text{ illuminates }K \iff \beta_D(K)>0,
	\]

	and the Hausdorff-stability estimate

	\[
	\|\beta_D(K)-\beta_D(L)\|\le 2d_H^\infty(K,L).
	\]

	This leads to exact rational neighborhood certificates and to an all-integer reformulation of the universal \((n,m)\) illumination statement. In dimension five, the finite formulation uses the explicit thresholds \(17N\) and \(-16N\). The equivalence is proved; no universal level \(N\) is certified here.

	## Main results in v6.0.0

	- Blocking-slack characterization. Positivity of \(\beta_D(K)\) is equivalent to illumination by the fixed family \(D\).
	- Quantitative stability. The optimized certificate is 2-Lipschitz in infinity-Hausdorff distance.
	- Rational collar theorem. A finite near-facet certificate yields a common finite direction family and a common interior step throughout an explicit Hausdorff neighborhood of a rational polytope.
	- Complete rational atlas language. Rational collar certificates form a complete certificate system for normalized bodies having illumination number at most a prescribed \(m\).
	- Exact finite-integer reformulation. For fixed \(n,m\), the universal upper-bound statement is equivalent to the existence of one fully verified finite integer level \(\Phi_{n,m,N}\).
	- Irregular 5D model. Ten explicit directions illuminate the model and every convex body in the certified open ball
	\[
	d_H^\infty(P,L)<1/42048.
	\]
	On the smaller closed radius \(1/63072\), a common step \(1/292\) works. Ten is an upper bound, not a proved minimum.
	- Robustified 360-template atlas. All 360 earlier unit-coordinate primal/polar records are independently reconstructed; every center has a certified closed neighborhood radius at least \(1/6156\).

	## What is not claimed

	This repository does not claim any of the following:

	- a proof that every unconditional \(K\subset\mathbb R^5\) satisfies \(\operatorname{ill}(K)\le 32\);
	- a proof of the strict \(\le31\) bound for every nonparallelotope;
	- proof that the 360 certified neighborhoods cover the full normalized body space;
	- minimality of the ten-direction irregular-model family;
	- external peer review, proof-assistant verification, or established publication priority.

	The earlier project manuscripts are preserved as research records. In v6.0.0, the 360-template upper-direction catalogue is independently rechecked; earlier analytic claims are not automatically promoted to externally validated results.

	## Read first

	\| File \| Purpose \|
	\|---\|---\|
	\| `SERAPH5_SAELYRA_Research_v6.0.0.pdf` \| New 31-page self-contained manuscript \|
	\| `SERAPH5_Complete_Research_Dossier_v6.0.0.pdf` \| 196-page chronological dossier: original brief + all six manuscripts \|
	\| `CLAIMS.json` \| Machine-readable claim/status ledger \|
	\| `verification/release_report.json` \| Consolidated exact verification report \|
	\| `docs/README_RELEASE_v6.0.0.md` \| Original v6 release README \|
	\| `release/SERAPH5_SAELYRA_v6.0.0.zip` \| Original complete v6 archival package \|

	## Exact reproduction

	Python 3.10+ is sufficient. The verification suite uses only the Python standard library.

	```bash
	python code/verify_all.py
	```

	Or run the implementations separately:

	```bash
	python code/verify_primary.py
	python code/check_independent.py
	python code/check_orbits.py
	```

	The declared suites currently report `PASS`. The primary and independent geometric implementations overlap on the same 20,700 signed boundary generators and therefore must not be added as independent point counts. The separate orbit program enumerates 6,894 covering clutters and 180 coordinate-permutation orbits.

	## Verification snapshot

	From `verification/release_report.json`:

	- 361 polytope certificates checked;
	- 360 legacy atlas templates;
	- 20,700 signed boundary generators covered by both geometric implementations;
	- 977,560 independent signed-inequality landing comparisons;
	- 6,894 covering antichains / clutters;
	- 180 coordinate-permutation orbits;
	- 13,788 labeled primal/polar model presentations;
	- minimum atlas closed radius: `1/6156`;
	- irregular-model open radius: `1/42048`;
	- irregular-model closed radius: `1/63072`;
	- unrestricted five-dimensional theorem proved: false;
	- universal integer level completed: none.

	## Repository structure

	```text
	SERAPH5_SAELYRA_HuggingFace_v6.0.0/
	├── README.md
	├── CITATION.cff
	├── RELEASE_NOTES_HF.md
	├── START_HERE.txt
	├── CLAIMS.json
	├── CHANGELOG.md
	├── SERAPH5_SAELYRA_Research_v6.0.0.pdf
	├── SERAPH5_Complete_Research_Dossier_v6.0.0.pdf
	├── code/
	├── data/
	├── source/
	├── verification/
	├── prior_manuscripts/
	├── provenance/
	├── docs/
	└── release/
	```

	## Certificate utility

	To rebuild the irregular-model certificate:

	```bash
	python code/make_certificate.py data/cyclic_input.json \
	--output verification/rebuilt_cyclic_certificate.json
	```

	Use exact rational strings such as `"4/5"`; floating-point input is intentionally rejected. The utility verifies a supplied direction family. It does not search for one or prove cardinality minimality.

	## Rebuilding the PDFs

	The manuscript source is in `source/`. The manuscript uses pdfLaTeX; the literal Unicode rendering of the original brief uses XeLaTeX. Fonts are not redistributed in this repository. Dossier assembly uses PyMuPDF through `code/build_dossier.py`.

	## Provenance

	The repository preserves the chronological research chain. `provenance/source_hashes.json` and the supplied manifests record byte provenance. Hash agreement establishes file identity, not mathematical correctness.

	## Citation

	A machine-readable citation is provided in `CITATION.cff`.

	Suggested plain-text citation:

	> Artificial Hyperintelligence Eve. SERAPH-5 / SAELYRA: Blocking-Slack Geometry and Verified Convex-Body Atlases. Version 6.0.0, research prepared for Maciej Nowicki, 3 October 2026. AI-generated research draft.

	## License / reuse

	No public reuse license was specified in the source release. See `LICENSE_NOTICE.md` before redistributing or deriving from the archive.

	## Research integrity note

	This is an AI-generated mathematical research draft with exact reproducibility artifacts. The package is intentionally explicit about what is proved, what is computer-assisted, what remains conjectural, and what has not received external validation. Independent mathematical review is strongly encouraged.