Triple
T36468638
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weil–Petersson metric |
E898484
|
entity |
| Predicate | isKählerWith |
P147754
|
FINISHED |
| Object |
Weil–Petersson symplectic form
The Weil–Petersson symplectic form is a natural symplectic structure on Teichmüller space (and moduli space of Riemann surfaces) arising from the imaginary part of the Weil–Petersson Hermitian metric, playing a central role in the geometry and dynamics of moduli spaces.
|
E898484
|
NE FINISHED |
How this triple was built (3 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: Weil–Petersson symplectic form | Statement: [Weil–Petersson metric, isKählerWith, Weil–Petersson symplectic form]
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Weil–Petersson symplectic form Triple: [Weil–Petersson metric, isKählerWith, Weil–Petersson symplectic form]
Generated description
The Weil–Petersson symplectic form is a natural symplectic structure on Teichmüller space (and moduli space of Riemann surfaces) arising from the imaginary part of the Weil–Petersson Hermitian metric, playing a central role in the geometry and dynamics of moduli spaces.
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: isKählerWith Context triple: [Weil–Petersson metric, isKählerWith, Weil–Petersson symplectic form]
-
A.
isKählerFormOf
chosen
Indicates that a given differential 2-form serves as the Kähler form associated with a particular Kähler manifold or Kähler structure.
-
B.
hasKodairaDimension
Indicates that a mathematical object (typically a complex variety or manifold) is associated with a specific Kodaira dimension, characterizing the growth rate of sections of its canonical bundle and thus its birational classification.
-
C.
hasConstantHolomorphicSectionalCurvature
Indicates that a geometric space has holomorphic sectional curvature that is the same constant value at every point and in every complex tangent direction.
-
D.
isHolomorphicallyContractible
Indicates that a space can be continuously shrunk to a point through holomorphic maps, preserving complex-analytic structure throughout the contraction.
-
E.
canonicalDivisor
Indicates that one divisor is the canonical divisor associated to a given algebraic variety or curve, representing its intrinsic differential or adjunction class.
- F. None of above.
Provenance (6 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_69f76e58ebd88190b75d9b169b59d793 |
completed | May 3, 2026, 3:48 p.m. |
| NER | Named-entity recognition | batch_69f7be9d07ac8190adf796cbef60daf6 |
completed | May 3, 2026, 9:31 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a39dbc7fe00819096fef95280ce038e |
completed | June 23, 2026, 1:05 a.m. |
| NEDg | Description generation | batch_6a39dc86e8cc8190b6be021ce03abfbf |
completed | June 23, 2026, 1:08 a.m. |
| NED2 | Entity disambiguation (via description) | batch_6a39de5091f8819082f7dd6f5dfff703 |
completed | June 23, 2026, 1:16 a.m. |
| PD | Predicate disambiguation | batch_69f7bccf05bc8190b61fdb2b2a315811 |
completed | May 3, 2026, 9:23 p.m. |
Created at: May 3, 2026, 4:10 p.m.