Laplace spectrum for exponential decomposition and pole–zero estimation
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
A novel Laplace transform power spectrum is proposed as a basic tool for complex-exponential decomposition of finite-duration continuous functions. The weighted spectrum leads to a direct decomposition in terms of exponential damping function content in addition to the usual decomposition in terms of sinusoidal circular content produced by Fourier and Laplace transforms. The weighting results in a two-dimensional spectral peak on the Laplace s-plane identifying the exponential and frequency content of finite-duration functions. An algorithm for two-dimensional generalised spectral analysis of finite duration functions is described. It is shown that the proposed spectral weighting eliminates the exponential divergence of spectra of usual transforms which masks poles along one dimension of the complex plane. As an application, an algorithm for mathematical modelling pole–zero estimation through a direct two-dimensional localisation of pole–zero peaks of weighted spectra is described.
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 | 0.000 | 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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