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
This thesis presents some results in spectral theory for bounded and unbounded linear operators, as well as results that are helpful in spectral analysis. \nThe key concepts are essential and discrete spectrum along with spectral measures, functions of operators and spectral projections. \nThe most important statements contained in this thesis are the spectral theorem about representing a self-adjoint operator as a simple L2 multiplication operator, and Weyl's essential spectrum theorem on the invariance of essential spectrum under suitable perturbations. \nThere are also a few results that can be used to immediately decide the finiteness or infiniteness of the discrete spectrum for quite general types of Hamiltonian operators, and similar qualitative results for the absolutely continuous and essential spectrum types. \nThe reader is assumed to have knowledge in functional analysis, real analysis, and elementary complex analysis.
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 | 0.002 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.001 |
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