TEMPORAL PROXIMITIES. SELF-SIMILAR, TEMPORALLY CLOSE SHAPES
Bibliographic record
Abstract
This article introduces temporal proximity spaces as a framework to observe surface shapes as well as geometric shapes that change over time. A surface shape has a boundary and a non-empty interior, which is approximated by a geometric shape that lies within the boundary of a surface shape recorded in a video frame. Temporally close shapes (briefly, δ ∆t shapes) persist over the some temporal interval. Those surface shapes that appear withing the same video frame are strongly self-similar as well as temporally close. The rate of change of self-similar shapes shE, shE ′ is represented by ∇(shE), ∇(shE ′) pairs. Temporally close shapes that appear during the same temporal interval may or may not be spatially or descriptively close to each other. Persistent as well as spatially close shapes share belong to the same era and also overlap along their boundaries or withing their interiors. Overlapping appearances of shapes such as vortexes occur within temporal CW (Closurefinite Weak) spaces (briefly, tCW spaces), which are an extension of the CW spaces introduced by J.H.C. Whitehead during the 1940s. Because of their simplicity, tCW space provide a workable setting for the study of δ ∆t surface as well as geometric shapes in sequences of video frames. Contents 14 Appendix D.Čech Proximity Spaces 15 References 16
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.000 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.010 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), 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".