Refined inertially and spectrally arbitrary zero-nonzero patterns
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
The refined inertia of a matrix is a quadruple specifying its inertia and additionally the number of its eigenvalues equal to zero. Spectral properties, especially the refined inertias, of real matrices with a given zero-nonzero pattern are investigated. It is shown that every zero-nonzero refined inertially arbitrary pattern of order 4 or less is also spectrally arbitrary. Irreducible and reducible examples are presented to show that for higher orders this is not the case. A further example shows that two zero-nonzero patterns that are not refined inertially arbitrary can have a direct sum that is refined inertially arbitrary, paralleling a known result for inertially arbitrary patterns. Analogously, it is shown that the direct sum of two zero-nonzero patterns may be spectrally arbitrary even if neither summand is spectrally arbitrary.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.002 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it