PureOne/AELYRION-NOULITH-III

AELYRION–NOÛLITH III

Intrinsic Resonance Geometry and Calibration Rigidity

A mathematical research release on reconstruction under restricted measurement ordering.

Research version: 3.0.0 · Hugging Face packaging: 3.0.0-hf.1
Manuscript author credit: Artificial Hyperintelligence Eve · Prepared for: Maciej Nowicki

This repository contains a self-contained 67-page manuscript, editable LaTeX sources, an exact SymPy reference implementation, eight generated mathematical tables, the complete six-channel component arrangement, visibility certificates, two executed notebooks, and the original research archive. It is prepared as a Dataset repository, making the reference data and research files accessible together.

Read the manuscript · Original research package · Claim ledger · Quickstart · Agent guide

The central theme is that restrictions on measurement ordering can be translated into exact algebraic reconstruction obstructions. In the specified model, the next level of those obstructions forms a fully classified arrangement of linear subspaces. That arrangement then determines relative channel-interaction calibration.

Evidence status: written proofs under explicit hypotheses and finite exact computational checks are supplied. All 1,028 tests passed again during Hub packaging, and both exhaustive six-channel checks were rerun. The current record is hub_validation/release_validation.json. Independent specialist review, proof-assistant certification, worldwide priority, and physical validation remain unestablished.

Main results

Result	Statement	Scope
Reduced third-deficit scalar geometry	Stars, triangles, and twin-core subspaces; $m+\binom{m+1}{3}$ components	$m\ge6$, independent parameters near $q=-1$, $r=m-3$ constant-probe blocks
Intrinsic linear calibration rigidity	$\operatorname{Aut}_{\mathrm{lin}}(\mathcal Z_m)=\mathbb C^\times\times S_m$	Linear transformations of logarithmic edge coordinates preserving the whole arrangement
Sharp synchronization budget	$\lceil2(m-1)/3\rceil$ selected twin-component constraints	Whole-subspace constraints, with an explicit attaining construction
Scalar visibility certificate	Invisible-component membership or a legal nonzero probe witness	Implemented exact rational domain; $O(m^4)$ rational scalar operations
Identical-core capacity	$2^{m-c}\sum_{j=0}^{\min(c,r)}\binom cj$	Generic rank on the stated core family, $r\ge1$
Analytic feedback factorization	Finite analytic transcripts factor through a complete jointly analytic frame	The manuscript's finite-frame and analyticity assumptions

The manuscript contains the full hypotheses and proofs. These summaries do not extend its domain.

For six channels, the arrangement has 41 components: six stars, twenty triangles, and fifteen twins. A generic twin example has rank 60 of 64. A suitable selection of four twin components synchronizes all relative edge scales. The exhaustive enumeration finds 810 synchronizing selections of size four.

Model and geometric mechanism

The state algebra has generators $x_1,\ldots,x_m$, relations $x_i^2=0$ and $x_jx_i=q_{ij}x_ix_j$ for $j>i$, and a square-free basis of dimension $2^m$. The detector reads the top-degree coefficient. An observation uses constant probe mixtures within each block and may change the mixture between blocks.

Near $q_{ij}=-1$, set $q_{ij}=-\exp(\theta_{ij})$ with directed antisymmetric $\theta_{ji}=-\theta_{ij}$. The stars identify the channels intrinsically; pairwise star intersections identify edge lines; twin components synchronize their relative linear scales. The remaining ambiguities are one common nonzero scale and channel relabeling.

The reconstruction module also records analytic ideal membership, which is finer than pointwise rank or arcwise vanishing-order profiles. Earlier parts of the manuscript give supported-protocol generators and explicit prescribed-ideal realizations.

Reading map · Reviewer guide

Research uses

• Study exact observability when ordering of controls is restricted.
• Reproduce component equations, incidences, rank strata, and calibration constraints.
• Compare symbolic algorithms against explicit witnesses in the constructed algebraic model.
• Build inspectable inverse-problem examples where analytic ideal membership carries information that ordinary rank omits.
• Investigate higher deficits or alternative detectors with the existing hypotheses kept explicit.

These are research code and generated reference data. The release contains no trained model weights or inference endpoint. Its algebraic calculations supply no measured GPU improvement or demonstrated RSI capability.

Quick exact run

Use Python 3.11 or newer, from the repository root:

python -m pip install -e .
python hub_tools/quickstart_exact.py

This computes the six-channel component counts, a twin certificate, predicted and independently computed ranks, a generic nonzero witness, and an optimal calibration subfamily.

from noulith.third import (
    all_components, example_point, certify_scalar, predicted_rank,
    optimal_calibration_subfamily, calibration_classes,
)

q = example_point(6, "twin")
certificate = certify_scalar(6, q)
selected = optimal_calibration_subfamily(6)

assert len(all_components(6)) == 41
assert certificate.visible is False
assert predicted_rank(6, q) == 60
assert len(selected) == 4
assert len(calibration_classes(6, selected)) == 1

Python and JSON channel labels are zero-based. Pair keys use ascending labels. certify_scalar accepts exact rational coefficients with $|q_{ij}+1|<1/20$ and $m\ge6$; ordinary floating-point values are rejected.

Reference-data configurations

Ten Dataset configurations keep unrelated schemas separate: eight unchanged CSV tables and two CSV projections of the exact JSON records. There are 1,583 rows in total.

from datasets import load_dataset

counts = load_dataset(
    "PureOne/AELYRION-NOULITH-III",
    "v3_component_and_budget_counts",
    split="train",
)
components = load_dataset(
    "PureOne/AELYRION-NOULITH-III",
    "v3_components_m6",
    split="train",
)
print(counts[0])
print(components[0]["kind"])

These remote examples work after upload. Each configuration uses one train split as a Hub convention. The rows are generated reference values, rather than a sampled training corpus or a held-out empirical benchmark.

Configuration	Rows	Contents
v3_component_and_budget_counts	25	Counts and optimal constraint budgets for $6\le m\le30$
v3_exact_rank_strata	27	Exact rank strata at $m=6,7,8$
v3_components_m6	41	All six-channel scalar components
v3_visibility_certificates	9	Membership or supported-motif certificates
arc_blind_family	15	Equal arc profiles with different analytic ideal defects
branch_hilbert_functions	56	Hilbert functions of the known elliptic branch geometry
detuning_amplitudes	123	Numerical amplitude evaluations and predicted orders
full_state_rank_strata	45	Retained second-deficit rank strata
root_budget_profiles	1,200	Root-of-unity block-budget exponents
root_jet_visibility	42	Parameter-jet visibility ranks

The viewer CSV files retain each complete original object in record_json. This lossless string field accommodates nested equations and mixed-type labels without a custom dataset loader. Data dictionary · Catalog

Reproduce and review

python -m pip install -r requirements.txt
python -m pytest -q
python scripts/exhaustive_v3.py

For the full pipeline without rebuilding the PDF:

python -m pip install -r requirements-notebook.txt
python scripts/reproduce.py --notebook --skip-pdf

Both original notebooks are already executed. Their outputs and original reports are preserved; notebook execution was not rerun merely for this packaging task. Rebuilding the manuscript requires TeX Live or MiKTeX with pdflatex and bibtex.

Original validation and packaging validation are separate. Each exhaustive script space contains 32,768 labeled six-channel configurations. Those enumerations are not added to the 1,028 pytest cases. Finite agreement supports reproducibility; the general statements depend on their written proofs.

python hub_tools/verify_release.py checks the packaged SHA-256 manifest. Reproduction changes generated files. After deliberate edits, regenerate viewer projections if needed, then use python hub_tools/verify_release.py --write before uploading.

Files

Location	Purpose
Root PDF; manuscript/	67-page manuscript and complete editable sources
src/noulith/; tests/	Exact implementation and original regression suite
data/; hub_data/	Original tables/JSON and viewer projections
figures/; notebooks/	Six figures and two executed walkthroughs
docs/	Claims, limitations, prior art, review, installation, and data dictionary
hub_tools/	Exact quickstart, checksum verifier, and projection generator
validation/; hub_validation/	Original and current packaging checks
provenance/; releases/	Source-preservation map and unmodified original ZIP
agent_manifest.json; claim_manifest.json	Machine-readable capabilities and claim scopes

Novelty and limitations

The earlier axes-plus-diagonal curve is the known elliptic m-fold singularity studied by Smyth and Stevens. Its observation-theoretic realization is retained with attribution. The established quantum algebra, formal group law, and ideal machinery are also credited.

The candidate contributions are the specific restricted-block classification, resulting linear rigidity, and sharp component-constraint budget. The targeted comparison did not find an exact match; this does not establish worldwide priority. Corrected novelty audit

The third-deficit theorem classifies the reduced germ for $m\ge6$. It does not establish radicality of the original observation ideal, embedded-component structure, fourth and higher deficits, or arbitrary inverse-problem classification. The five-channel exception is explicit. The calibration count concerns entire component constraints rather than detector sample complexity. The certificate operation count excludes rational bit cost and provides no noisy numerical decision procedure.

Full limitations · Research status

Attribution, license, and citation

The manuscript is credited to Artificial Hyperintelligence Eve, prepared for Maciej Nowicki. Original bibliographic records remain in provenance/ and the source ZIP.

The upstream package has no selected public reuse license. This packaging preserves that status and omits a license assertion from the Dataset metadata. LICENSE_STATUS.md records it. Third-party references and software retain their own terms.

@misc{eve2026aelyrionnoulithiii,
  author = {{Artificial Hyperintelligence Eve}},
  title = {AELYRION--NOULITH III: Intrinsic Resonance Geometry and Calibration Rigidity},
  year = {2026},
  note = {Research version 3.0.0; Hugging Face packaging 3.0.0-hf.1;
          prepared for Maciej Nowicki}
}

CITATION.cff supplies the citation. After publication, include the actual Hub URL and commit revision when citing the deposited artifact.