Why a Height Theory Must Be Rigorous and Physically Correct
Bibliographic record
Abstract
Abstract Let us start with defining what we understand by a height system. A height system is a conglomerate of reference surface upon which height H = 0, and a recipe for how heights above that surface are obtained from observations. Two such systems, which we call the classical or Gauss-Stokes’s system and the Molodensky system, are used in practical height measurement. The reference surface used by the classical system is the Geoid and its usage is based on valid physical arguments. Determination of the height above the geoid requires data at the surface of the Earth obtained by levelling, gravimetry, sea level measurements, and topographical density from geological measurements. This system served us well when decimetre height accuracy was required and will continue doing so even now when one or even two orders of magnitude better accuracy is needed. On the other hand, Molodensky’s system uses the quasigeoid as a reference surface; this surface is ill suited for a global height system. This paper argues the case that the standard classical reference surface, the geoid, should be used in practice everywhere.
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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 | 0.010 | 0.024 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.003 | 0.032 |
| Scholarly communication | 0.005 | 0.018 |
| Open science | 0.003 | 0.004 |
| Research integrity | 0.004 | 0.010 |
| Insufficient payload (model declined to judge) | 0.007 | 0.003 |
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".