Triple
T5212094
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weyl law |
E117656
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Weyl’s law for the Laplacian on a compact surface |
E117656
|
NE FINISHED |
How this triple was built (2 steps)
Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.
NER
Named-entity recognition
gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Weyl’s law for the Laplacian on a compact surface | Statement: [Weyl law, relatedTo, Weyl’s law for the Laplacian on a compact surface]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weyl’s law for the Laplacian on a compact surface Context triple: [Weyl law, relatedTo, Weyl’s law for the Laplacian on a compact surface]
-
A.
Weyl law
chosen
The Weyl law is a fundamental result in spectral theory that describes the asymptotic distribution of eigenvalues of the Laplacian (or similar operators) in terms of the volume of the underlying domain or manifold.
-
B.
Can one hear the shape of a drum?
"Can one hear the shape of a drum?" is a famous 1966 paper by mathematician Mark Kac that explores whether the geometric shape of a domain can be uniquely determined from the spectrum of its Laplacian, encapsulated in the question of whether one can infer a drum’s shape from the sound it makes.
-
C.
Perelman’s entropy functionals
Perelman’s entropy functionals are analytic quantities introduced by Grigori Perelman to study the behavior and singularities of the Ricci flow, playing a central role in his proof of the Poincaré and geometrization conjectures.
-
D.
Milnor–Wood inequality
The Milnor–Wood inequality is a result in differential geometry and topology that bounds the Euler class of flat circle bundles over surfaces, with important implications for foliations and group actions on the circle.
-
E.
Israel–Carter–Robinson uniqueness theorems
The Israel–Carter–Robinson uniqueness theorems are a set of results in general relativity showing that stationary, asymptotically flat black holes in four-dimensional spacetime are completely characterized by just their mass, charge, and angular momentum.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 batches)
The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.
| Step | Stage | Batch ID | Status | When |
|---|---|---|---|---|
| creating | Elicitation | batch_69bd4464ba3c8190bc16b2ebbe42ddb0 |
completed | March 20, 2026, 12:58 p.m. |
| NER | Named-entity recognition | batch_69bd7a7166848190805152142e184529 |
completed | March 20, 2026, 4:48 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69beefdee940819098e397ab50f57411 |
completed | March 21, 2026, 7:22 p.m. |
Created at: March 20, 2026, 1:47 p.m.