Bibliographic record
Abstract
In mathematics, space encompasses various structured sets such as Euclidean, metric, or vector space. This article introduces temporal space—a novel concept independent of traditional spatial dimensions and frames of reference, accommodating multiple object-oriented durations in a dynamical system. The novelty of building temporal space using finite geometry is rooted in recent advancements in the theory of relationalism which utilizes Euclidean geometry, set theory, dimensional analysis, and a causal signal system. Multiple independent and co-existing cyclic durations are measurable as a network of finite one-dimensional timelines. The work aligns with Leibniz’s comments on relational measures of duration with the addition of using discrete cyclic relational events that define these finite temporal spaces, applicable to quantum and classical physics. Ancient formulas have symmetry along with divisional and subdivisional orders of operations that create discrete and ordered temporal geometric elements. Elements have cyclically conserved symmetry but unique cyclic dimensional quantities applicable for anchoring temporal equivalence relations in linear time. We present both fixed equivalences and expanded periods of temporal space offering a non-Greek calendar methodology consistent with ancient global timekeeping descriptions. Novel applications of Euclid’s division algorithm and Cantor’s pairing function introduce a novel paired function equation. The mathematical description of finite temporal space within relationalism theory offers an alternative discrete geometric methodology for examining ancient timekeeping with new hypotheses for Egyptian calendars.
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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 | 0.002 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.010 |
| Scholarly communication | 0.005 | 0.008 |
| Open science | 0.001 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 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".