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.