PureOne/Nhairun-Exact-Complexity

Nhaïrūn–Δ

Exact Complexity, Observable Compression, and One-Split Scheduling
Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Conceptual direction: Maciej Nowicki
Research Revision 3 · 13 November 2026

This is a theoretical research and synthetic verification dataset. It contains a complete proposed resolution of exact ordering complexity under fixed contraction, constructive approximation results, an exact algorithm for an enlarged scalar scheduling policy, and reproducible verification artifacts.

Read the 26-page manuscript · Editable source · Claim ledger · Data guide

Scientific content

Result	Scope and guarantee
Balanced scalar exact hardness	For every fixed rational contraction strictly between zero and one, exact zero-terminal-state ordering is NP-complete even in one dimension with zero-mean centers. The initial state, target, and minimizer of the summed task quadratics are zero; all Hessians are one.
Observable variation rank	Under the stated bounded rational endpoint assumptions, fixed observed variation rank admits a randomized fully polynomial additive scheme while hidden and readout dimensions may grow.
Robust observable quotients	A certified common low-dimensional quotient permits request-dependent hidden responses and gives regret at most epsilon + 8*q_N, with an explicit accumulated mismatch radius.
One interrupted request	Preserving each scalar request's target and retention product, one request split into two pieces suffices for exact squared-target optimization over all finite admissible fragmentations, using at most N+1 updates. This enlarges the feasible policy and charges the extra update.
Additional boundaries	Opposite-pair hardness in growing dimension; a three-state reversible stochastic boundary; a continuous-time reversible realization of the rational stochastic hard instances.

The manuscript supplies full ordinary mathematical proofs. Internal adversarial audits found no substantive gap. Independent external verification, proof-assistant formalization, and worldwide priority certification remain outstanding.

Dataset configurations

Configuration	Rows	Contents
cases (default)	78	Normalized case summaries from the scientific verification records, including exact rational values inside the original case_json payload.
claims	10	Theorem claims, assumptions, limitations, code references, and their original ledger records.
verification_suites	6	Suite-level counts, arithmetic, scope, verifier paths, and diagnostic summaries.

Every configuration uses a single validation split. This is a packaging label for a disclosed finite verification corpus; it is not a held-out neural-model evaluation set. The 78 rows summarize reported cases, not all individual permutations or assertions.

The five assertion-counted suites report 711,899 exact assertions. A separate marker sweep reports 192,780 ordered placements across 45 rational contractions and 405 configurations. Marker placements are kept separate from assertion totals.

Some original reports include floating logarithmic gap diagnostics. Those diagnostics are preserved inside JSON strings and identified by contains_float_diagnostics; mathematical decision checks and rational construction values use exact arithmetic.

Load the data

After publication, replace YOUR_ACCOUNT/Nhairun-Delta with this dataset's actual repository ID:

from datasets import load_dataset

cases = load_dataset("YOUR_ACCOUNT/Nhairun-Delta", "cases", split="validation")
claims = load_dataset("YOUR_ACCOUNT/Nhairun-Delta", "claims", split="validation")
audits = load_dataset("YOUR_ACCOUNT/Nhairun-Delta", "verification_suites", split="validation")

import json
original_case = json.loads(cases[0]["case_json"])

Without the datasets library, read the JSONL directly:

import json
from pathlib import Path

cases = [json.loads(line) for line in Path("data/cases.jsonl").read_text().splitlines()]

Run the exact construction

From this repository's root, Python 3.10+ and its standard library suffice:

python code/quickstart.py
python code/reproduce.py

The quickstart demonstrates zero-error one-interruption scheduling and a zero-mean scalar hardness instance. The reproduction runner executes all six scientific verifiers in a temporary working directory and compares their JSON records with this release. It leaves the repository files unchanged.

The scalar matching optimizer and one-interruption algorithm are executable. observable_certificates.py implements compression, rounding, and quotient certificate utilities. The full multivariate optimizer is specified constructively in the mathematical proof; it is not implemented as a production solver here.

Intended use and limits

Use these artifacts for mathematical review, exact-arithmetic regression tests, studying scheduling policies, and inspecting approximation certificates. The dataset is small, synthetic, fully disclosed, and produced by its own constructions. It does not measure real-world model performance or generalization.

The exact hardness reductions allow exponentially small gaps. No strong NP-hardness, constant-noise hardness, empirical neural speedup, or unrestricted autonomous recursive self-improvement is established. The one-interruption result changes the feasible policy; it preserves retention products rather than the sum of gradient step sizes or the number of gradient evaluations. The quotient guarantee requires its stated norm and mismatch certificates.

Provenance and reproducibility

The manuscript, original code, claim ledger, and six source reports are copied from the complete Revision 3 research package. The three JSONL files are deterministic normalized views of those records. See release provenance, dataset counts, and SHA-256 integrity manifest.

python code/export_dataset.py regenerates the JSONL views deterministically. The archived research README describes the original flat archive; the paths on this card describe the Hugging Face layout.

This packaging introduces no new license grant. No license metadata is asserted on behalf of the author.

Citation and related work

See CITATION.bib. The author label above is the requested authorial persona; the release is AI-generated research prepared for Maciej Nowicki.

The chosen fixed-contraction boundary is described in Wang et al., arXiv:2610.01149, Section 4.4. Randomized algebraic matching and monotone affine-composition sorting are established ingredients credited in the manuscript. The proof claims and scope in this release should be assessed on their explicit constructions.