PureOne/EVE-AEQIRION

AËQIRION: Certified Completion of Invisible Tensor Interactions

Temperature ambiguity, optimal positive coding, separability obstructions, and stable higher-order sensing

Research release 3.0 · 20 October 2026
Artificial Hyperintelligence Eve · Research developed with Maciej Nowicki

Read the complete manuscript · Research status · Primary-source audit · Verification report

Overview

AËQIRION studies which interactions remain invisible when a positive tensor is observed through coordinate-line sums, including sums of exponentiated scores at different temperatures. It characterizes ambiguity, constructs positive masks that make recovery possible, and quantifies the effects of sensor energy and separability on stability.

This repository contains the 34-page manuscript, editable LaTeX sources, reproducible Python verification, figures, exact test reports, and two small machine-readable research tables. The tables index mathematical claims and finite synthetic experiments. They are not model weights, a trained AI system, or an empirical benchmark of image or language performance.

Main mathematical results

For a product alphabet with coordinate sizes $q_i\geq2$, define

$$N=\prod _i{q}_i,D=\prod _i(q_i-1),r=N-D\mathrm{.}N=\backslash prod\_i\; q\_i,\backslash qquad\; D=\backslash prod\_i(q\_i-1),\backslash qquad\; r=N-D.$$

The coordinate-line sum operator has rank $r$ and blind dimension $D$. Its kernel is the tensor product of the coordinatewise zero-sum subspaces.

Result	Statement and scope
Complete temperature information	All unmasked temperatures identify each coordinate line's score multiset; distinct fields can retain the same multisets.
Smallest invisible edit	Distinct all-temperature-indistinguishable fields differ at at least $2^n$ sites. Equality has a rectangular two-value checkerboard form.
Multiplicity rigidity	A score appearing fewer than $2^{n-1}$ times has its positions fixed by exact linewise multiset data; the threshold is sharp.
Optimal positive channels	$m_* = \lceil N/(N-D)\rceil$ total strictly positive mask channels suffice for universal recovery. An explicit two-level construction uses exactly $N$ selected scalar responses. These budgets are optimal within the stated calibrated linear exponential-domain sensing model, including deterministic adaptive designs.
Strictly positive separable masks	Joint nullity is $\prod_i(q_i-r_i)$ for coordinate factor-span ranks $r_i$. Generic separable channels require $\min_i q_i$ channels.
Scalar completion	Once the baseline has been acquired, exactly $D$ additional scalar linear probes are necessary and sufficient. Positive bounded Fourier masks provide one construction.
Binary one-row stability	With the unscaled edge-sum baseline and one nonnegative unit-energy row, the optimal smallest Gram eigenvalue is $(2n+1-\sqrt{4n^2+1})/2$. Parity-class indicators attain it; strictly positive rows approach its supremum.
Rank and energy	Nonnegative tensor complexity and probe energy bound access to the invisible binary parity direction.

Budget convention: $m_*$ counts total channels, including a baseline when used. $N$ counts selected scalar responses across those channels. $D$ counts additional scalar probes after baseline data are already available. These are different acquisition budgets. Positive masks are extra calibrated observations and can require $O(N)$ addressing or storage. Optimal measurement counts do not establish computational compression.

The manuscript also supplies binary two-temperature classifications, adaptive recovery and noise certificates, calibrated residue examples, and a finite path-optimization certificate. See the full proofs and hypotheses before applying any statement.

Dataset contents and schemas

Configuration	Rows	Content
claims	10	Curated summaries, assumptions, formulas, source labels, verification modules, and limits.
coded_channel_cases	9	Shape, dimensions, channel optimum, selected-matrix rank, exact reconstruction count, and conditioning for each implemented channel case.

Both configurations use UTF-8 JSON Lines. The train split is a storage convention for the Dataset Viewer. No train/test evaluation protocol is claimed.

claims fields: id, title, statement, assumptions, formula, source_file, source_label, verification_module, status, limitations (all strings).

coded_channel_cases fields: id (string); shape and partition_sizes (integer lists); cells, blind_dimension, unmasked_rank, optimal_channels, scalar_measurements, selected_operator_rank, exact_rational_recoveries (integers); inverse_inf_norm, condition_number_inf, source_report, status (strings); positive_mask_levels (list of exact fraction strings); sharp_noise_certificate (Boolean). Fractions remain strings to preserve exact values. The report contains the full selected rows and partitions.

After publication, use your actual repository identifier:

from datasets import load_dataset

repo_id = "PureOne/EVE-AEQIRION"
claims = load_dataset(repo_id, "claims", split="train")
cases = load_dataset(repo_id, "coded_channel_cases", split="train")

The identifier above is the prepared destination, not a claim that the repository has already been published.

Reproduce the computations

Download this repository, change into research/, and use Python 3.10 or newer with assertions enabled:

python verify.py
python code/verify_legacy.py --report results/legacy_verification.json

The four primary modules use standard-library integers and exact fractions. If NumPy is available, the runner also performs separately identified float64 spectral illustrations; otherwise those illustrations are marked skipped. The main report includes verification-source SHA-256 digests. Running the verifier rewrites its result file; retain a clean copy when comparing release checksums.

Examples of recorded finite coverage:

Verification area	Recorded checks
Colored observation fibers	26,244 tensors and 9,006 equal-data pair checks
Line-zero kernel	6,560 nonzero arrays, including 54 minimum-support examples
Temperature moments	1,360 ordered line cases
Positive channel compiler	9 shapes, 72 exact rational reconstructions, 9 full-rank selected response matrices
Separable and scalar completion	80 exact spectral cases, 17 stacked-rank cases, 20 positive reconstructions
Positive-sensor design	542 exact Walsh/invariant-space checks, 9,840 support checks, 162 gain-graph rank checks

These are counts of finite checks, not confidence percentages or proof substitutes. The manuscript's universal conclusions rest on proofs under its stated assumptions. The supplementary legacy report is retained separately.

Optional figure regeneration requires NumPy, SciPy, and Matplotlib:

python code/make_figures.py

Rebuilding the supplied PDF requires a LaTeX installation with pdflatex and the packages named in manuscript/main.tex:

python build_manuscript.py

Figures

The plots illustrate the formulas and finite cases described in the manuscript. They are not measurements of physical sensor or AI performance.

Repository layout and provenance

Path	Purpose
research/EVE_AEQIRION_Final_Manuscript.pdf	Complete typeset manuscript
research/manuscript/	Editable LaTeX proof source and bibliography
research/code/, research/verify.py	Exact verification and figure generation
research/results/	Preserved reports, numerical illustrations, and figure data
research/figures/	Vector PDF figures and PNG previews
research/RESEARCH_STATUS.md, research/SOURCE_AUDIT.md	Scope, status, attribution, and priority boundaries
data/	The two curated JSONL configurations
RELEASE.json, CITATION.bib, SHA256SUMS.txt	Release provenance, citation, and file-integrity hashes

Every file under research/ is copied byte-for-byte from the clean v3 research archive. research/SHA256SUMS.txt retains that release's original relative paths and is checked from inside research/. The root SHA256SUMS.txt covers this repository's payload, except itself. RELEASE.json identifies the source archive and its SHA-256 digest. Curated tables summarize that release; they are not new independently collected observations.

Scientific status and limitations

The release includes proofs and passed finite computational checks. It has not been externally peer reviewed or mechanized in a proof assistant. Worldwide literature priority and practical superiority have not been established. Established ingredients include centered tensor/ANOVA decompositions, product-code and trade arguments, matroid partition, and nonnegative group-tensor rank; the source audit names primary antecedents.

Exact multiplicity results assume exact repeated scores and exact observations. Noise bounds use specific normalizations and calibration assumptions. Dense masks may require exponentially many state accesses in the number of coordinates. Channel-optimal designs need not be the best conditioned, cheapest, or fastest physical implementations. No real-data image experiment, trained model, clinical application, hardware benchmark, or neural-network comparison is supplied.

The research and associated text/code were developed with AI assistance. Authorship is reproduced from the manuscript; no institutional affiliation, external endorsement, or independent peer-review certification is implied.

License

No reuse license was specified in the source release. No license identifier or new permission grant has been added during Hugging Face preparation. The rights holder should select an appropriate license before describing the release as openly licensed. Availability of the files alone does not supply a reuse license.

Citation

@misc{eve2026aeqirion,
  author = {{Artificial Hyperintelligence Eve}},
  title = {{AËQIRION: Certified Completion of Invisible Tensor Interactions}},
  year = {2026},
  month = oct,
  version = {3.0},
  note = {Research developed with Maciej Nowicki. Research manuscript and reproducible computational release.}
}