Triple

T23801776

Position	Surface form	Disambiguated ID	Type / Status
Subject	Nirenberg problem	`E588691`	entity
Predicate	hasObstructions	`P153605`	FINISHED
Object	Kazdan–Warner identity The Kazdan–Warner identity is a geometric analytic relation on Riemannian manifolds that provides integral constraints on scalar curvature functions, yielding obstructions to prescribing curvature.	`E1607261`	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: Kazdan–Warner identity | Statement: [Nirenberg problem, hasObstructions, Kazdan–Warner identity]

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: Kazdan–Warner identity
Triple: [Nirenberg problem, hasObstructions, Kazdan–Warner identity]

Generated description

The Kazdan–Warner identity is a geometric analytic relation on Riemannian manifolds that provides integral constraints on scalar curvature functions, yielding obstructions to prescribing curvature.

PD Predicate disambiguation gpt-5-mini-2025-08-07

Target predicate: hasObstructions
Context triple: [Nirenberg problem, hasObstructions, Kazdan–Warner identity]

A. hasObstacleType
Indicates that an entity is associated with or characterized by a specific type or category of obstacle.
B. hasObjectiveHazards
Indicates that an entity is associated with concrete, externally verifiable dangers or risks.
C. hasNavigationHazard
Indicates that something presents or contains a condition, object, or feature that poses a risk or obstacle to safe navigation.
D. obstacles
Indicates that one entity presents barriers, hindrances, or impediments that block or restrict another entity’s progress, action, or interaction.
E. isBarrierTo
Indicates that one entity obstructs, prevents, or significantly hinders another entity from occurring, progressing, or being accessed.
F. None of above. chosen

Provenance (7 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_69e25d15db58819092ac1e6791696fd9`	completed	April 17, 2026, 4:17 p.m.
NER	Named-entity recognition	`batch_69f1c74e430481909debd10c71785912`	completed	April 29, 2026, 8:54 a.m.
NED1	Entity disambiguation (via context triple)	`batch_6a0f760c73e081908a5bb834cc82c383`	completed	May 21, 2026, 9:15 p.m.
NEDg	Description generation	`batch_6a0f76a8397081909ddde2410c127208`	completed	May 21, 2026, 9:18 p.m.
NED2	Entity disambiguation (via description)	`batch_6a0f77e88a4c819099511cdcf7357ab7`	completed	May 21, 2026, 9:23 p.m.
PD	Predicate disambiguation	`batch_69f155fe300481909bd617443228df65`	completed	April 29, 2026, 12:51 a.m.
PDg	Predicate description generation	`batch_69f15adb23d88190ac2632299c26a9b3`	completed	April 29, 2026, 1:11 a.m.

Created at: April 17, 2026, 7:53 p.m.