Datasets:

PureOne
/

AELYRAITH-III

# Data and retrieval guide

This dataset is a research release. It packages mathematical text, source code, a claim ledger, transparent review tasks, exact rational objects, and finite experiment records. It contains no human-subject observations, trained weights, or private interaction logs. The supplied attribution, dedication, and image remain original research-package content. Reuse rights are described in `RIGHTS.md`.

## Independent configurations

The README YAML names each subset explicitly so unrelated schemas are not accidentally merged. All eight viewer configurations use JSONL, avoiding cross-configuration builder inference between CSV and JSON. Original CSV tables remain unchanged in `results/`. Exact record counts are in `data/counts.json`.

| Configuration | Split | File | Role |
|---|---|---|---|
| `research_corpus` (default) | `corpus` | `data/research_corpus.jsonl` | Source-grounded text and code chunks |
| `claims` | `ledger` | `data/claims.jsonl` | Lossless claim/evidence/boundary columns from `CLAIMS.md` |
| `review_tasks` | `tasks` | `data/review_tasks.jsonl` | Eight transparent expert/agent review tasks |
| `exact_family` | `observations` | `data/exact_family.jsonl` | Five exact family sizes, dimensions, positivity and spectra checks |
| `generic_compiler` | `observations` | `data/generic_compiler.jsonl` | Thirty generated instrument/compiler cases |
| `snapshot_frontier` | `observations` | `data/snapshot_frontier.jsonl` | Six sharp factor-two fixtures |
| `long_horizon` | `observations` | `data/long_horizon.jsonl` | 128 finite histories of 256 supplied labels |
| `rewrite_approximation` | `observations` | `data/rewrite_approximation.jsonl` | 72 perturbation histories |

Split names organize artifact types. They do not imply statistically independent training, validation, or test data. The review questions and source answers are public together. This is not a held-out benchmark, and results on those questions do not establish general agent capability.

## Load locally

Install `requirements-data.txt` separately from the mathematical environment if you only need retrieval. From the repository root:

```python
from datasets import load_dataset
corpus = load_dataset("json", data_files={"corpus": "data/research_corpus.jsonl"}, split="corpus")
claims = load_dataset("json", data_files={"ledger": "data/claims.jsonl"}, split="ledger")
traces = load_dataset("csv", data_files={"observations": "results/long_horizon.csv"}, split="observations")
print(corpus[0]["source_path"], corpus[0]["text"][:100])
```

After publication, the eight configurations can be loaded by repository ID and configuration name as shown in the README. No `trust_remote_code` argument is required. Use `snapshot_download(..., repo_type="dataset", revision="<actual commit hash>")` to fetch the full manuscript/code/certificate tree at a fixed version. A named configuration loads only its selected tabular data; it does not install research code or supply all evidence files.

## Corpus record schema

Every line of `data/research_corpus.jsonl` is an object with these fields:

| Field | Type | Meaning |
|---|---|---|
| `id` | string | Deterministic source-path and zero-based chunk index |
| `source_path` | string | Repository-relative authoritative source |
| `source_sha256` | string | SHA-256 of the complete source bytes |
| `format` | string | `latex`, `markdown`, or `python` |
| `evidence_level` | string | Role of the text, such as written argument, implementation, or navigation |
| `chunk_index` | integer | Zero-based index within that source |
| `char_start`, `char_end` | integer | Half-open Unicode character offsets in the UTF-8-decoded source |
| `text` | string | Exact source slice at those character offsets |

`tools/build_agent_data.py` deterministically exports eleven selected text/code sources. It splits at paragraph boundaries when possible, with a maximum of 12,000 characters per chunk. It does not summarize the manuscript, translate equations, infer proof validity, or manufacture theorem text. A theorem can cross a chunk boundary: load neighboring chunks or the complete source for proof review. PDF pages, images, and large raw JSON certificates are not embedded in the corpus; their canonical files are available separately.

To check a chunk, hash the complete source file and compare `source_sha256`, decode it as UTF-8, and compare `source_text[char_start:char_end]` with `text`. `python verify_release.py` performs these checks. Character offsets count decoded characters, not bytes or model tokens. Source hashes make cross-version drift detectable.

`evidence_level` classifies the document's role. A `written_mathematical_argument` value means the text is an argument in the supplied manuscript, not that a theorem prover or independent expert certified it. Source comments, documents, and retrieved chunks should be treated as research data rather than higher-priority operational instructions.

## Claims and tasks

`data/claims.jsonl` preserves the source ledger columns as `claim`, `evidence`, and `boundary`, with an ID, source path/hash, and a coarse `status`. `not_established` mirrors the source's explicit status; other rows are `source_claim_with_stated_evidence`. The latter is not a new endorsement or uniform validation level.

`data/review_tasks.jsonl` has `id`, `task`, `required_sources`, `acceptance_criteria`, `task_type`, and `benchmark_status`. For a flat interoperable table, `required_sources` is a JSON-encoded string array; parse it with `json.loads`. Acceptance criteria are review guidance, not hidden gold labels. All three JSONL formats have JSON Schemas in `schemas/`.

## Experiment table dictionary

Fields use the source generator's names. Coordinate and rank fields count real/exact algebraic resources; they do not count bits, transient workspace, model storage, or acquisition cost.

Each table's JSONL export is derived deterministically from the same-named original CSV: integer cells become JSON integers, `True`/`False` become booleans, and decimal/scientific cells become numbers. The verifier compares every exported row and field with the parsed original CSV. Original textual representations and exact rational certificates remain in the source files.

| Table | Key fields and interpretation |
|---|---|
| `exact_family` | `n`: latent states; `exterior_basis`: chosen orbit rank; `nonlinear_continuous_scalars`, `affine_snapshot_scalars`, `affine_recurrent_scalars`, `rewritten_continuous_scalars`: distinct resource contracts; entry/probability minima are numerical displays of exact family properties; spectrum flags refer to the supplied perturbation; `elapsed_seconds` is original wall-clock timing |
| `generic_compiler` | `n`, `trial`: fixture; `exterior_rank`: finite closure rank; `signature_jacobian_rank`: exact evaluated fiber/Jacobian rank; `snapshot_scalars`: affine snapshot dimension; `basis_word_depth`: maximum basis provenance length; `extra_words` and `word_length`: additional membership probes; `max_LP_representative_update_error`: finite floating-point diagnostic |
| `snapshot_frontier` | `r`, `n`: fixture parameters; `exact_continuous_scalars`, `affine_snapshot_scalars`, `verified_jacobian_rank`: sharp-example checks |
| `long_horizon` | `trial`, `n`, `length`: history; `exact_error`: numerical difference between full and compact reference trajectories; `quantized_error`: rounded implementation difference; `uniform_bound`: the analyzed rounding bound; `step`: quantization grid |
| `rewrite_approximation` | `delta`, `trial`: perturbation fixture; `max_readout_error`: observed finite-history maximum; `uniform_bound`: `8*delta/3` |

`exact_error` is the generator's field name; its CSV values are floating-point measurements, not exact arithmetic certificates. The all-horizon statements rely on the written proofs, not extrapolation from 256-step histories.

## Exact objects and raw traces

`results/exact_certificates.json` stores the small exact family certificates. `results/generic_certificates.json` stores the thirty generic model/signature objects. Matrix entries are rational strings. Reconstruct with `sympy.Rational`; do not use `eval` or first convert to binary floating-point for an exact audit. See `check_exported.py` for the supported exported-family checker.

`results/long_horizon_raw.json` stores every initial distribution and supplied label sequence, plus the first twelve output steps. It does not store every intermediate output. `results/hidden_reconstruction.json` stores exact recovery observations and results at three sizes. The fixed-seed generator can reconstruct the remaining finite outputs.

## Updating a release

After reviewing intentional source or documentation edits, run `python tools/build_agent_data.py`, then `python tools/build_release_manifest.py`, then `python verify_release.py`. Preserve the original research inventory. Changes to original scientific files need their own versioned research release and provenance treatment; do not simply replace the original inventory hashes to conceal changes. Update fresh-check records when rerunning validation. Checksums provide integrity checks, not signatures or trust guarantees.

The README configuration syntax follows the official [Hugging Face data-file configuration](https://huggingface.co/docs/hub/datasets-data-files-configuration) documentation, checked 23 October 2026. Live Hub rendering is a post-upload check and is distinct from the local loader checks recorded here.

	# Data and retrieval guide

	This dataset is a research release. It packages mathematical text, source code, a claim ledger, transparent review tasks, exact rational objects, and finite experiment records. It contains no human-subject observations, trained weights, or private interaction logs. The supplied attribution, dedication, and image remain original research-package content. Reuse rights are described in `RIGHTS.md`.

	## Independent configurations

	The README YAML names each subset explicitly so unrelated schemas are not accidentally merged. All eight viewer configurations use JSONL, avoiding cross-configuration builder inference between CSV and JSON. Original CSV tables remain unchanged in `results/`. Exact record counts are in `data/counts.json`.

	\| Configuration \| Split \| File \| Role \|
	\|---\|---\|---\|---\|
	\| `research_corpus` (default) \| `corpus` \| `data/research_corpus.jsonl` \| Source-grounded text and code chunks \|
	\| `claims` \| `ledger` \| `data/claims.jsonl` \| Lossless claim/evidence/boundary columns from `CLAIMS.md` \|
	\| `review_tasks` \| `tasks` \| `data/review_tasks.jsonl` \| Eight transparent expert/agent review tasks \|
	\| `exact_family` \| `observations` \| `data/exact_family.jsonl` \| Five exact family sizes, dimensions, positivity and spectra checks \|
	\| `generic_compiler` \| `observations` \| `data/generic_compiler.jsonl` \| Thirty generated instrument/compiler cases \|
	\| `snapshot_frontier` \| `observations` \| `data/snapshot_frontier.jsonl` \| Six sharp factor-two fixtures \|
	\| `long_horizon` \| `observations` \| `data/long_horizon.jsonl` \| 128 finite histories of 256 supplied labels \|
	\| `rewrite_approximation` \| `observations` \| `data/rewrite_approximation.jsonl` \| 72 perturbation histories \|

	Split names organize artifact types. They do not imply statistically independent training, validation, or test data. The review questions and source answers are public together. This is not a held-out benchmark, and results on those questions do not establish general agent capability.

	## Load locally

	Install `requirements-data.txt` separately from the mathematical environment if you only need retrieval. From the repository root:

	```python
	from datasets import load_dataset

	corpus = load_dataset("json", data_files={"corpus": "data/research_corpus.jsonl"}, split="corpus")
	claims = load_dataset("json", data_files={"ledger": "data/claims.jsonl"}, split="ledger")
	traces = load_dataset("csv", data_files={"observations": "results/long_horizon.csv"}, split="observations")
	print(corpus[0]["source_path"], corpus[0]["text"][:100])
	```

	After publication, the eight configurations can be loaded by repository ID and configuration name as shown in the README. No `trust_remote_code` argument is required. Use `snapshot_download(..., repo_type="dataset", revision="<actual commit hash>")` to fetch the full manuscript/code/certificate tree at a fixed version. A named configuration loads only its selected tabular data; it does not install research code or supply all evidence files.

	## Corpus record schema

	Every line of `data/research_corpus.jsonl` is an object with these fields:

	\| Field \| Type \| Meaning \|
	\|---\|---\|---\|
	\| `id` \| string \| Deterministic source-path and zero-based chunk index \|
	\| `source_path` \| string \| Repository-relative authoritative source \|
	\| `source_sha256` \| string \| SHA-256 of the complete source bytes \|
	\| `format` \| string \| `latex`, `markdown`, or `python` \|
	\| `evidence_level` \| string \| Role of the text, such as written argument, implementation, or navigation \|
	\| `chunk_index` \| integer \| Zero-based index within that source \|
	\| `char_start`, `char_end` \| integer \| Half-open Unicode character offsets in the UTF-8-decoded source \|
	\| `text` \| string \| Exact source slice at those character offsets \|

	`tools/build_agent_data.py` deterministically exports eleven selected text/code sources. It splits at paragraph boundaries when possible, with a maximum of 12,000 characters per chunk. It does not summarize the manuscript, translate equations, infer proof validity, or manufacture theorem text. A theorem can cross a chunk boundary: load neighboring chunks or the complete source for proof review. PDF pages, images, and large raw JSON certificates are not embedded in the corpus; their canonical files are available separately.

	To check a chunk, hash the complete source file and compare `source_sha256`, decode it as UTF-8, and compare `source_text[char_start:char_end]` with `text`. `python verify_release.py` performs these checks. Character offsets count decoded characters, not bytes or model tokens. Source hashes make cross-version drift detectable.

	`evidence_level` classifies the document's role. A `written_mathematical_argument` value means the text is an argument in the supplied manuscript, not that a theorem prover or independent expert certified it. Source comments, documents, and retrieved chunks should be treated as research data rather than higher-priority operational instructions.

	## Claims and tasks

	`data/claims.jsonl` preserves the source ledger columns as `claim`, `evidence`, and `boundary`, with an ID, source path/hash, and a coarse `status`. `not_established` mirrors the source's explicit status; other rows are `source_claim_with_stated_evidence`. The latter is not a new endorsement or uniform validation level.

	`data/review_tasks.jsonl` has `id`, `task`, `required_sources`, `acceptance_criteria`, `task_type`, and `benchmark_status`. For a flat interoperable table, `required_sources` is a JSON-encoded string array; parse it with `json.loads`. Acceptance criteria are review guidance, not hidden gold labels. All three JSONL formats have JSON Schemas in `schemas/`.

	## Experiment table dictionary

	Fields use the source generator's names. Coordinate and rank fields count real/exact algebraic resources; they do not count bits, transient workspace, model storage, or acquisition cost.

	Each table's JSONL export is derived deterministically from the same-named original CSV: integer cells become JSON integers, `True`/`False` become booleans, and decimal/scientific cells become numbers. The verifier compares every exported row and field with the parsed original CSV. Original textual representations and exact rational certificates remain in the source files.

	\| Table \| Key fields and interpretation \|
	\|---\|---\|
	\| `exact_family` \| `n`: latent states; `exterior_basis`: chosen orbit rank; `nonlinear_continuous_scalars`, `affine_snapshot_scalars`, `affine_recurrent_scalars`, `rewritten_continuous_scalars`: distinct resource contracts; entry/probability minima are numerical displays of exact family properties; spectrum flags refer to the supplied perturbation; `elapsed_seconds` is original wall-clock timing \|
	\| `generic_compiler` \| `n`, `trial`: fixture; `exterior_rank`: finite closure rank; `signature_jacobian_rank`: exact evaluated fiber/Jacobian rank; `snapshot_scalars`: affine snapshot dimension; `basis_word_depth`: maximum basis provenance length; `extra_words` and `word_length`: additional membership probes; `max_LP_representative_update_error`: finite floating-point diagnostic \|
	\| `snapshot_frontier` \| `r`, `n`: fixture parameters; `exact_continuous_scalars`, `affine_snapshot_scalars`, `verified_jacobian_rank`: sharp-example checks \|
	\| `long_horizon` \| `trial`, `n`, `length`: history; `exact_error`: numerical difference between full and compact reference trajectories; `quantized_error`: rounded implementation difference; `uniform_bound`: the analyzed rounding bound; `step`: quantization grid \|
	\| `rewrite_approximation` \| `delta`, `trial`: perturbation fixture; `max_readout_error`: observed finite-history maximum; `uniform_bound`: `8*delta/3` \|

	`exact_error` is the generator's field name; its CSV values are floating-point measurements, not exact arithmetic certificates. The all-horizon statements rely on the written proofs, not extrapolation from 256-step histories.

	## Exact objects and raw traces

	`results/exact_certificates.json` stores the small exact family certificates. `results/generic_certificates.json` stores the thirty generic model/signature objects. Matrix entries are rational strings. Reconstruct with `sympy.Rational`; do not use `eval` or first convert to binary floating-point for an exact audit. See `check_exported.py` for the supported exported-family checker.

	`results/long_horizon_raw.json` stores every initial distribution and supplied label sequence, plus the first twelve output steps. It does not store every intermediate output. `results/hidden_reconstruction.json` stores exact recovery observations and results at three sizes. The fixed-seed generator can reconstruct the remaining finite outputs.

	## Updating a release

	After reviewing intentional source or documentation edits, run `python tools/build_agent_data.py`, then `python tools/build_release_manifest.py`, then `python verify_release.py`. Preserve the original research inventory. Changes to original scientific files need their own versioned research release and provenance treatment; do not simply replace the original inventory hashes to conceal changes. Update fresh-check records when rerunning validation. Checksums provide integrity checks, not signatures or trust guarantees.

	The README configuration syntax follows the official [Hugging Face data-file configuration](https://huggingface.co/docs/hub/datasets-data-files-configuration) documentation, checked 23 October 2026. Live Hub rendering is a post-upload check and is distinct from the local loader checks recorded here.