Triple

T22328612
Position Surface form Disambiguated ID Type / Status
Subject Eugenio Calabi E551965 entity
Predicate knownFor P22 FINISHED
Object Calabi–Bernstein theorem
The Calabi–Bernstein theorem is a result in differential geometry that characterizes entire maximal spacelike hypersurfaces in Minkowski space as necessarily being affine hyperplanes.
E1531310 NE FINISHED

How this triple was built (4 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: Calabi–Bernstein theorem | Statement: [Eugenio Calabi, knownFor, Calabi–Bernstein theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Calabi–Bernstein theorem
Context triple: [Eugenio Calabi, knownFor, Calabi–Bernstein theorem]
  • A. Calabi conjecture
    The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.
  • B. Donaldson–Uhlenbeck–Yau theorem
    The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
  • C. Kodaira vanishing theorem
    The Kodaira vanishing theorem is a fundamental result in algebraic geometry that gives conditions under which certain cohomology groups of ample line bundles on smooth projective varieties vanish, with deep implications for the classification of complex manifolds.
  • D. Monge–Ampère equation
    The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
  • E. Christoffel–Minkowski problem
    The Christoffel–Minkowski problem is a classical question in convex geometry that seeks to reconstruct a convex body from prescribed curvature or area measure data on the unit sphere.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
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: Calabi–Bernstein theorem
Triple: [Eugenio Calabi, knownFor, Calabi–Bernstein theorem]
Generated description
The Calabi–Bernstein theorem is a result in differential geometry that characterizes entire maximal spacelike hypersurfaces in Minkowski space as necessarily being affine hyperplanes.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Calabi–Bernstein theorem
Target entity description: The Calabi–Bernstein theorem is a result in differential geometry that characterizes entire maximal spacelike hypersurfaces in Minkowski space as necessarily being affine hyperplanes.
  • A. Calabi conjecture
    The Calabi conjecture is a fundamental result in complex differential geometry, proved by Shing-Tung Yau, which characterizes when a compact Kähler manifold admits a unique Ricci-flat Kähler metric in a given Kähler class.
  • B. Donaldson–Uhlenbeck–Yau theorem
    The Donaldson–Uhlenbeck–Yau theorem is a fundamental result in differential and algebraic geometry that characterizes when a holomorphic vector bundle over a compact Kähler manifold admits a Hermitian–Einstein metric, linking geometric stability with the existence of such metrics.
  • C. Kodaira vanishing theorem
    The Kodaira vanishing theorem is a fundamental result in algebraic geometry that gives conditions under which certain cohomology groups of ample line bundles on smooth projective varieties vanish, with deep implications for the classification of complex manifolds.
  • D. Monge–Ampère equation
    The Monge–Ampère equation is a fully nonlinear partial differential equation central to differential geometry, optimal transport, and several complex variables, often used to study curvature and geometric structures.
  • E. Christoffel–Minkowski problem
    The Christoffel–Minkowski problem is a classical question in convex geometry that seeks to reconstruct a convex body from prescribed curvature or area measure data on the unit sphere.
  • F. None of above. chosen

Provenance (5 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_69e11e482f788190b78d1588fc26d606 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15769fdb48190b84e0c019ab63579 completed April 29, 2026, 12:57 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0ad523ecec8190a85eb932288965fb completed May 18, 2026, 9 a.m.
NEDg Description generation batch_6a0ad992b43c8190b0e409d64db83308 completed May 18, 2026, 9:19 a.m.
NED2 Entity disambiguation (via description) batch_6a0adac48bec8190989dd7c5e28d283a completed May 18, 2026, 9:24 a.m.
Created at: April 16, 2026, 8:43 p.m.