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| pretty_name: "AELYRION–NOÛLITH III — Intrinsic Resonance Geometry and Calibration Rigidity" | |
| language: | |
| - en | |
| size_categories: | |
| - 1K<n<10K | |
| tags: | |
| - mathematics | |
| - inverse-problems | |
| - observability | |
| - noncommutative-algebra | |
| - symbolic-computation | |
| - calibration-rigidity | |
| - exact-computation | |
| - research-artifact | |
| - ai-assisted-research | |
| configs: | |
| - config_name: v3_component_and_budget_counts | |
| default: true | |
| data_files: | |
| - split: train | |
| path: data/v3_component_and_budget_counts.csv | |
| - config_name: arc_blind_family | |
| data_files: | |
| - split: train | |
| path: data/arc_blind_family.csv | |
| - config_name: branch_hilbert_functions | |
| data_files: | |
| - split: train | |
| path: data/branch_hilbert_functions.csv | |
| - config_name: detuning_amplitudes | |
| data_files: | |
| - split: train | |
| path: data/detuning_amplitudes.csv | |
| - config_name: full_state_rank_strata | |
| data_files: | |
| - split: train | |
| path: data/full_state_rank_strata.csv | |
| - config_name: root_budget_profiles | |
| data_files: | |
| - split: train | |
| path: data/root_budget_profiles.csv | |
| - config_name: root_jet_visibility | |
| data_files: | |
| - split: train | |
| path: data/root_jet_visibility.csv | |
| - config_name: v3_components_m6 | |
| data_files: | |
| - split: train | |
| path: hub_data/v3_components_m6.csv | |
| - config_name: v3_exact_rank_strata | |
| data_files: | |
| - split: train | |
| path: data/v3_exact_rank_strata.csv | |
| - config_name: v3_visibility_certificates | |
| data_files: | |
| - split: train | |
| path: hub_data/v3_visibility_certificates.csv | |
| # 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](Aelyrion_Noulith_III_Research_Manuscript_v3.0.0.pdf) · | |
| [Original research package](releases/Aelyrion_Noulith_III_v3.0.0_Research_Package.zip) · | |
| [Claim ledger](docs/CLAIMS.md) · [Quickstart](docs/HF_QUICKSTART.md) · | |
| [Agent guide](AGENTS.md) | |
| 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](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](docs/V3_NEW_RESULTS_GUIDE.md) · [Reviewer guide](docs/REVIEWER_GUIDE.md) | |
| ## 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: | |
| ```bash | |
| 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. | |
| ```python | |
| 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**. | |
| ```python | |
| 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](docs/DATA_DICTIONARY.md) · [Catalog](data_catalog.json) | |
| ## Reproduce and review | |
| ```bash | |
| python -m pip install -r requirements.txt | |
| python -m pytest -q | |
| python scripts/exhaustive_v3.py | |
| ``` | |
| For the full pipeline without rebuilding the PDF: | |
| ```bash | |
| 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](validation/validation_report.json) and | |
| [packaging validation](hub_validation/release_validation.json) 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](docs/NOVELTY_AUDIT.md) | |
| 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](docs/LIMITATIONS.md) · [Research status](docs/RESEARCH_STATUS.md) | |
| ## 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](LICENSE_STATUS.md) records it. Third-party references and software retain | |
| their own terms. | |
| ```bibtex | |
| @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](CITATION.cff) supplies the citation. After publication, include the actual | |
| Hub URL and commit revision when citing the deposited artifact. | |