[ARTICLE] Structure of Molecular Water and the 3D Pythagoras Theorem (Canadian Journal of Applied Physics Research / 2024)
Bibliographic record
Abstract
Water ice crystals inherently embed in their shape complex hexagonal structures, emerging mostly due to the O-H bond angle 104.5 degrees being close to the 120 degrees found in hexagons. This article explores the possible integration of water molecules into a recently published mathematical architecture called the Universal Gear model. Already published in a mathematics peer-reviewed journal, the Universal Gear is an orthogonally-intertwined construct of Pythagoras theorem driven planes, that all together provide a perfect balance in terms of the three main equations governing three-dimensional existence: zero net sum of lengths, zero net sum of areas and zero net sum of volumes. Computer-aided Design shows how a group of (simplified and realistic) water molecules successfully integrate into the (regular and irregular) version of the Universal Gear. Interestingly the geometric pattern that emerges from the projected field of water molecules integrated into the Universal Gear is a structure already observed in monuments of ancient civilizations. The ambient conditions, in terms of pressure and temperature, where such a structure could appear is not yet known, requiring further research preferably using computational molecular dynamics.3D CAD available here: https://figshare.com/articles/dataset/_CAD_3D_Model_of_Water_Molecules_x_y_Grouped_as_per_Geometrical_Theorem/26767678?file=48629065Canadian Journal of Applied Physics Research link: https://ccsenet.org/journal/index.php/apr/article/view/0/50127Universal Gear Article link: https://figshare.com/articles/journal_contribution/_ARTICLE_Universal_Gear_and_the_Pythagorean_Theorem_Australian_Mathematics_Education_Journal_2019_/21618003-------------------------------------------------------------------------For more public data, please visit my Figshare profile: https://figshare.com/authors/Luis_Teia/10811244
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.003 | 0.006 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.003 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.071 | 0.019 |
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".