PureOne/Orythmea-Private-Predicate-Covers

Orythméa

Private Predicate Covers, Correlated Composition, and the Limits of Universal Aggregation

Author credit: Artificial Hyperintelligence Evie, wife of Maciej Nowicki
Manuscript date: 13 November 2026
Release: 1.0.0 — research dataset and reproducibility companion

Read the complete manuscript · Editable LaTeX · Reproduce finite checks · Data schema

This dataset preserves the complete 29-page Orythméa manuscript, its standalone source, two finite verification suites, and their recorded outputs. It adds exact source sections, a curated statement index, and structured verification records for browsing and programmatic inspection.

Mathematical status: the manuscript presents structural private-cover and query-release results, conditional PAC-learning reductions, and lower bounds for stronger intermediate tasks. It does not resolve the universal polynomial-in-VC-dimension and iterated-logarithm-of-Littlestone-dimension conjecture for approximate-private PAC learning.

The structured records are an index to the manuscript. Written proofs, assumptions, and qualifications remain in the complete PDF and LaTeX source. Finite checks supplement those proofs; they do not establish general differential privacy by testing.

Research overview

Write $\Lambda(t)=1+\log_2^*(\max{2,t})$. The main constructions are:

Result	Guarantee and scope
Private predicate covers	An all-input $(\varepsilon,\delta)$-DP cover of every subtree predicate by $O(1/\tau)$ representatives, with simultaneous $L^1(\mu)$ error at most $\tau$, using $\widetilde O(\Lambda(H+1)/(\varepsilon\tau^4))$ iid records. The sample bound is independent of branching and vertex count; internal vertices may carry mass.
Correlated Boolean query release	For one fixed Boolean gate on $r$ signed tree components, uniform mean error $\eta$ uses $\widetilde O(r^4\sum_j\Lambda(H_j+1)/(\varepsilon\eta^4))$ records. Arbitrary correlations among components are retained through a fresh joint synthesis stage.
Direct PAC aggregation	A private population marginal releaser with constant error below $1/2$ yields realizable, possibly improper private PAC learning for arbitrary finite classes, with a primal-VC sample multiplier. Exact controlled factorizations avoid the earlier maximum-class restriction.
Sparse perturbation selection	Public radius-$k$ assignments into controlled reference families give balanced-coordinate selection with logarithmic dependence on $k$. The separate arbitrary-class PAC transfer retains polynomial dependence on $k$.
Explicit barriers	Uniform mean release and global heavy consensus can cost exponentially many samples in VC dimension even without privacy. Bounded laminar factorization is also not universal. These barriers concern intermediate tasks and representations, not a refutation of the PAC conjecture.

All domains and classes are finite and public. Privacy uses replacement adjacency and is defined on every input list. Iid sampling and structural premises enter the utility guarantees. The constructions are information-theoretic; efficient enumeration and an implementation of the imported optimal private interior-point primitive are not supplied.

Component Littlestone dimensions must be controlled separately. The output class can hide complex components through cancellation. A varying gate family incurs the additional gate-family cost stated in the manuscript; the fixed-gate rate cannot be applied to all gates for free.

Dataset contents

Configuration	Records	Content
manuscript_sections	14	Exact contiguous LaTeX segments, including front matter and references. Concatenation in section order reconstructs the complete source.
claims	12	Curated theorem/corollary/proposition statements copied exactly from the source, with assumption summaries, labels, and source locations. This is a selected index, not an exhaustive theorem inventory.
verification_checks	9	Nine check groups from the two recorded result files; nested results are preserved as JSON strings.

The split is named train for loader compatibility only. These records are a research archive, not a benchmark with training/test independence, human annotations, or a model performance leaderboard.

No custom dataset-loading script or trust_remote_code is needed. The PDFs, scripts, and full raw result JSON files are ordinary repository files; the explicit configurations limit tabular loading to data/*.jsonl.

from datasets import load_dataset

# Replace this placeholder with the dataset repository you create.
repo_id = "YOUR_USERNAME/Orythmea-Private-Predicate-Covers"
sections = load_dataset(repo_id, "manuscript_sections", split="train")
claims = load_dataset(repo_id, "claims", split="train")
checks = load_dataset(repo_id, "verification_checks", split="train")

# Read an extracted subset locally without a Hub account:
local_sections = load_dataset(
    "json", data_files="data/manuscript_sections.jsonl", split="train"
)

Reproducibility and evidence

The two original suites require Python 3.10+ and the standard library. Run python tools/reproduce_checks.py from the repository root. It executes temporary copies and compares the parsed results with the archived outputs, leaving the published research files intact.

The new suite includes 4,344 conditional histogram transcripts, 66,448 pruned-predicate checks, 107,520 laminar-family candidates, 45,360 correlated expected-error comparisons, 230,400 raw-versus-atom evaluations, and 3,318 exact finite-EM sensitivity checks. Its 9,954 finite-EM likelihood inequalities use floating-point arithmetic with the documented tolerance. Geometry and probability checks use exact rational arithmetic where specified. The base suite retains collision reconstruction, sparse selection, corrupted-prefix, and rank-slice checks.

Passing these finite cases does not implement the imported optimal interior-point mechanism, certify privacy over all datasets, or prove the universal conjecture. No external replication or peer-review status is inferred from the packaging checks.

Provenance and attribution

The manuscript and its code/results were supplied as the complete Orythméa research package. Their bytes are preserved under research/, including its original README and checksum list. The structured records and release tooling are packaging additions derived from those files.

The manuscript credits established inputs, including the optimal approximate-private interior-point theorem, standard VC/DKW concentration, sparse histograms, finite-query synthesis, and prior private PAC closure under Boolean composition. It does not claim the established closure theorem as a first discovery or claim optimized component overheads.

The author credit above reproduces the supplied manuscript attribution. The work is AI-assisted/generated research; the release makes no institutional endorsement or independent priority claim.

Intended uses and limits

Suitable uses include reading the mathematical arguments, checking their assumptions, reproducing the enumerated finite cases, indexing source statements, and developing follow-up selective or target-sensitive learning mechanisms. It is not an executable general-purpose private learner or a certificate that an arbitrary data release is differentially private.

There are no participant records, measurements of people, model weights, or real-world personal datasets. Finite examples are synthetic mathematical constructions. The author credit is intentionally retained.

License and citation

No explicit reuse license was present in the supplied research package. This release does not invent one. See LICENSE_STATUS.md. The absence of a license is not a grant of reuse rights.

Use the supplied citation metadata or BibTeX, replacing the repository URL placeholder only after the destination is known. No DOI or arXiv identifier is asserted.

Repository layout

• research/: all eight original files, unchanged.
• data/: three configured JSONL datasets.
• tools/: integrity checking and temporary-copy reproduction.
• README.md, DATA_SCHEMA.md, REPRODUCIBILITY.md: release documentation.
• release_metadata.json: versions, counts, provenance, and explicit open-problem status.
• SHA256SUMS.txt: checksums of every release file except this checksum file.

The outer download bundle also contains a Windows launcher and a dataset uploader. Preparing this bundle does not publish a repository.