Bibliographic record
Abstract
Abstract This paper will solve problems using numerical tools from various branches of math, including linear algebra, analytical topology, and calculus. The main question is of how one can define an abstract algebraic group within a Hilbert space to describe an individual performing a specific movement. Several other questions arise from this, including the modeling of an axis of rotation. These are best resolved by an abstract representation of a motion of a body in space, then applying it to a specific material case. The abstract representation will be in the form of an algebraic group with a defined topology. The model maps the possible singular points in space the individual could occupy. The method of arriving at a solution for each step of the problem was the creation of a series of conclusions, linked by reasoning, expanding from an initial material example. This is known as divergent reasoning. Existent theories related to the concept at the root of the computational result were analyzed to identify any contradictions in lines of reasoning. The model was developed by means of an example case of a sport with elements of martial arts and gymnastics, called tricking. This was accomplished using four theorems: the Hilbert Basis theorem, the Nullstellensatz theorem, the weak Nullstellensatz theorem, and a new theorem, which describes the axis of rotation. The intended outcome is achieved by the end of the paper. The model was proved with a physical example, in which the algebraic group was translated into a vector function in R 3 between a limiting interval of time.
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.
How this classification was reachedexpand
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 | 0.003 | 0.003 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.003 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".