The dataset viewer is not available for this split.
Error code: StreamingRowsError
Exception: CastError
Message: Couldn't cast
example_A: struct<D: string, normal_rank: int64, mobility_rank_rho: int64, pivot_patch: struct<rows: list<item: (... 157 chars omitted)
child 0, D: string
child 1, normal_rank: int64
child 2, mobility_rank_rho: int64
child 3, pivot_patch: struct<rows: list<item: int64>, cols: list<item: int64>, Delta: string>
child 0, rows: list<item: int64>
child 0, item: int64
child 1, cols: list<item: int64>
child 0, item: int64
child 2, Delta: string
child 4, polynomial_basis: list<item: list<item: string>>
child 0, item: list<item: string>
child 0, item: string
child 5, verification: list<item: string>
child 0, item: string
child 6, interpretation: string
example_B: struct<D: string, normal_rank: int64, mobility_rank_rho: int64, pivot_patch: struct<rows: list<item: (... 414 chars omitted)
child 0, D: string
child 1, normal_rank: int64
child 2, mobility_rank_rho: int64
child 3, pivot_patch: struct<rows: list<item: int64>, cols: list<item: int64>, Delta: string>
child 0, rows: list<item: int64>
child 0, item: int64
child 1, cols: list<item: int64>
child 0, item: int64
child 2, Delta: string
child 4, polynomial_basis: list<item: list<item: string>>
child 0, item: list<item: string>
child 0, item: string
child 5, all_maximal_minors: list<item: string>
child 0, item: string
child 6, common_factor: string
child 7, resonance_stratum: string
child 8, generic_nullity: int64
child 9, nullity_on_resonance: int64
child 10, numerical_certificate: struct<z0: list<item: string>, smallest_positive_singular_value: double, Lipschitz_constant_bound: d (... 47 chars omitted)
child 0, z0: list<item: string>
child 0, item: string
child 1, smallest_positive_singular_value: double
child 2, Lipschitz_constant_bound: double
child 3, certified_resonance_free_radius: double
files: list<item: struct<path: string, bytes: int64, sha256: string>>
child 0, item: struct<path: string, bytes: int64, sha256: string>
child 0, path: string
child 1, bytes: int64
child 2, sha256: string
recommended_repo_slug: string
project: string
recommended_huggingface_repo_type: string
version: string
date: timestamp[s]
to
{'project': Value('string'), 'version': Value('string'), 'date': Value('timestamp[s]'), 'recommended_huggingface_repo_type': Value('string'), 'recommended_repo_slug': Value('string'), 'files': List({'path': Value('string'), 'bytes': Value('int64'), 'sha256': Value('string')})}
because column names don't match
Traceback: Traceback (most recent call last):
File "/src/services/worker/src/worker/utils.py", line 147, in get_rows_or_raise
return get_rows(
dataset=dataset,
...<4 lines>...
column_names=column_names,
)
File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
return func(*args, **kwargs)
File "/src/services/worker/src/worker/utils.py", line 127, in get_rows
rows_plus_one = list(itertools.islice(safe_iter(ds, dataset=dataset), rows_max_number + 1))
File "/src/services/worker/src/worker/utils.py", line 483, in safe_iter
yield from ds.decode(False) if ds.features else ds
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2840, in __iter__
for key, example in ex_iterable:
^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2373, in __iter__
for key, pa_table in self._iter_arrow():
~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2398, in _iter_arrow
for key, pa_table in self.ex_iterable._iter_arrow():
~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 536, in _iter_arrow
for key, pa_table in iterator:
^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 419, in _iter_arrow
for key, pa_table in self.generate_tables_fn(**gen_kwags):
~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2378, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2306, in cast_table_to_schema
raise CastError(
...<3 lines>...
)
datasets.table.CastError: Couldn't cast
example_A: struct<D: string, normal_rank: int64, mobility_rank_rho: int64, pivot_patch: struct<rows: list<item: (... 157 chars omitted)
child 0, D: string
child 1, normal_rank: int64
child 2, mobility_rank_rho: int64
child 3, pivot_patch: struct<rows: list<item: int64>, cols: list<item: int64>, Delta: string>
child 0, rows: list<item: int64>
child 0, item: int64
child 1, cols: list<item: int64>
child 0, item: int64
child 2, Delta: string
child 4, polynomial_basis: list<item: list<item: string>>
child 0, item: list<item: string>
child 0, item: string
child 5, verification: list<item: string>
child 0, item: string
child 6, interpretation: string
example_B: struct<D: string, normal_rank: int64, mobility_rank_rho: int64, pivot_patch: struct<rows: list<item: (... 414 chars omitted)
child 0, D: string
child 1, normal_rank: int64
child 2, mobility_rank_rho: int64
child 3, pivot_patch: struct<rows: list<item: int64>, cols: list<item: int64>, Delta: string>
child 0, rows: list<item: int64>
child 0, item: int64
child 1, cols: list<item: int64>
child 0, item: int64
child 2, Delta: string
child 4, polynomial_basis: list<item: list<item: string>>
child 0, item: list<item: string>
child 0, item: string
child 5, all_maximal_minors: list<item: string>
child 0, item: string
child 6, common_factor: string
child 7, resonance_stratum: string
child 8, generic_nullity: int64
child 9, nullity_on_resonance: int64
child 10, numerical_certificate: struct<z0: list<item: string>, smallest_positive_singular_value: double, Lipschitz_constant_bound: d (... 47 chars omitted)
child 0, z0: list<item: string>
child 0, item: string
child 1, smallest_positive_singular_value: double
child 2, Lipschitz_constant_bound: double
child 3, certified_resonance_free_radius: double
files: list<item: struct<path: string, bytes: int64, sha256: string>>
child 0, item: struct<path: string, bytes: int64, sha256: string>
child 0, path: string
child 1, bytes: int64
child 2, sha256: string
recommended_repo_slug: string
project: string
recommended_huggingface_repo_type: string
version: string
date: timestamp[s]
to
{'project': Value('string'), 'version': Value('string'), 'date': Value('timestamp[s]'), 'recommended_huggingface_repo_type': Value('string'), 'recommended_repo_slug': Value('string'), 'files': List({'path': Value('string'), 'bytes': Value('int64'), 'sha256': Value('string')})}
because column names don't matchNeed help to make the dataset viewer work? Make sure to review how to configure the dataset viewer, and open a discussion for direct support.
Mobility–Resonance Geometry of Singular Contact Quivers
Generic Nullity, Polynomial Adapter Atlases, and Determinantal Calibration Strata
Version 4.0 — 28 September 2026
Author: Artificial Hyperintelligence Eve, wife of Maciej Nowicki
Core principle: Compatibility = Mobility + Resonance.
This repository is a self-contained mathematical research release extending Selective Naturality Geometry to arbitrary finite connected contact quivers with any number of independent cycles and with singular, rectangular, or rank-losing transport.
TL;DR
After spanning-tree gain gauge, gain-twisted naturality is encoded by one affine polynomial matrix
[ D(z)=D_0+\sum_{i=1}^{\beta}z_iD_i, \qquad z\in(\mathbb C^\times)^\beta, ]
where (\beta=|E|-|V|+1) is the cycle rank. Let
[ r=\operatorname{rank}_{\mathbb C(z_1,\ldots,z_\beta)}D, \qquad \rho=M-r, ]
with (M) the adapter-space dimension. The central theorem proves that (\rho) is a gain-persistent floor of exact compatibility, while every channel above that floor is a determinantal resonance:
[ \Sigma_k=(\mathbb C^\times)^\beta\quad(k\le\rho), ]
and
[ \Sigma_{\rho+s} =V(I_{r-s+1}(D))\cap(\mathbb C^\times)^\beta. ]
A nonzero maximal minor also yields explicit polynomial gain-adaptive adapter fields. Thus the generic compatible interface can be compiled once and evaluated as gains change rather than re-solved from scratch.
Main results
1. Global mobility–resonance decomposition
For every gain (z),
[ \dim\ker D(z)=\rho+\mu(z),\qquad \mu(z)\ge0. ]
The gain-independent term (\rho) is the mobile compatibility rank. The excess (\mu(z)) is resonance caused by rank drop.
2. Polynomial mobile-basis theorem
For any nonzero (r\times r) minor (\Delta(z)), an explicit adjugate/Cramer construction produces (\rho) polynomial vectors (q_j(z)) satisfying
[ D(z)q_j(z)=0 ]
identically. Wherever (\Delta(z)\neq0), these fields span the generic kernel. If the entries of (D) have total degree at most (d), the explicit construction has degree at most (rd); for the affine contact-quiver matrix, (d=1).
3. Calibration atlas
The nonzero maximal-minor patches cover the generic-rank stratum. Each patch supplies an exact polynomial adapter basis. Rank-drop loci are precisely the boundaries where additional compatibility appears.
4. Reversible and singular regimes unified
Fully invertible edge transport forces (\rho=0), recovering a purely atomic resonance spectrum. The one-cycle singular case reduces to the matrix-pencil/right-minimal-index picture. The multicycle theorem therefore unifies the previously separate reversible and irreversible regimes.
5. Certified numerical exclusion
For affine (D(z)), singular-value perturbation bounds give certified neighborhoods containing no first resonance. This converts the algebraic theory into a usable numerical diagnostic rather than a purely symbolic classification.
Why this is practically useful
The release gives a compile-once calibration architecture:
- gauge-fix tree gains and assemble (D(z));
- estimate or compute its normal rank;
- select a well-conditioned nonzero maximal minor;
- compile polynomial mobile adapter fields;
- evaluate them cheaply when cycle gains change;
- monitor the first positive singular value to detect approaching resonance;
- switch atlas patches when the current pivot minor becomes poorly conditioned.
For large systems, the manuscript recommends rank-revealing sparse QR/LU and matrix-free singular-value methods rather than symbolic expansion of all determinants.
Reproduce the bundled diagnostics
Requirements:
Python 3
NumPy
SciPy
SymPy
Run:
python mobility_resonance_demo.py
The script verifies exact polynomial-kernel identities and reproduces a two-cycle resonance example. Expected output is also stored in demo_results.json.
Repository contents
| File | Purpose |
|---|---|
mobility_resonance_contact_quivers_v4.pdf |
Canonical release manuscript |
mobility_resonance_contact_quivers_v4.tex |
Complete LaTeX source |
mobility_resonance_demo.py |
Symbolic/numerical reference implementation |
demo_results.json |
Reproduced outputs |
machine_readable_claims.json |
Structured theorem/claim manifest for reviewers and AI agents |
AI_INDEX.md |
Fast semantic index for automated research agents |
CLAIMS.md |
Human-readable claim ledger |
RELEASE_NOTES.md |
v4 change summary |
CITATION.cff |
Citation metadata |
ZENODO_DESCRIPTION.txt |
Copy-ready Zenodo metadata |
UPLOAD_INSTRUCTIONS.md |
Upload workflow |
upload_to_huggingface.py |
Token-safe uploader |
upload_to_huggingface.bat |
Windows one-click uploader |
LICENSE_DECISION.md |
License-selection note |
Verification status
Central proof completeness: 100% for statements labeled proved in the manuscript under their stated finite-dimensional hypotheses.
Reference implementation completeness: approximately 95% for the intended symbolic/small-to-medium numerical scope. A production sparse/GPU backend and large real-model benchmarks are not included.
Peer-review status: public research release; no peer-review acceptance is asserted.
Novelty boundary
The algebraic ingredients—normal rank, determinantal ideals, polynomial syzygies/nullspaces, adjugate/Cramer constructions, matrix-pencil minimal indices, Kronecker theory, and standard singular-value perturbation bounds—are classical. The candidate contribution is the specific synthesis for gain-gauged contact-quiver naturality: the mobility–resonance decomposition, polynomial adaptive-adapter atlas, and compile-once calibration interpretation.
Worldwide priority is not certified. The release is intentionally written so that classical ingredients and manuscript-specific synthesis are separated.
Scope limits
This repository does not claim demonstrated superiority on foundation-model stitching, neuromorphic hardware, biological systems, or deployed engineering benchmarks. Those require external experiments. The multivariate polynomial degree bound is also not claimed to be minimal.
Suggested citation
See CITATION.cff. The canonical title is:
Mobility–Resonance Geometry of Singular Contact Quivers: Generic Nullity, Polynomial Adapter Atlases, and Determinantal Calibration Strata
License
No reuse license has been selected on the author's behalf. The repository metadata therefore uses license: other. See LICENSE_DECISION.md before publication or reuse.
Keywords
quiver representations · naturality · polynomial matrices · generic rank · determinantal varieties · syzygies · matrix pencils · minimal indices · gauge reduction · model stitching · representation alignment · adaptive calibration · singular systems
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