Triple

T30501047

Position	Surface form	Disambiguated ID	Type / Status
Subject	van der Corput method for estimating exponential sums	`E776136`	entity
Predicate	relatedTo	`P37`	FINISHED
Object	Weyl sums Weyl sums are exponential sums of polynomial phases that play a central role in analytic number theory, particularly in estimating error terms and studying equidistribution and Diophantine approximation.	`E776136`	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 sums | Statement: [van der Corput method for estimating exponential sums, relatedTo, Weyl sums]

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: Weyl sums
Triple: [van der Corput method for estimating exponential sums, relatedTo, Weyl sums]

Generated description

Weyl sums are exponential sums of polynomial phases that play a central role in analytic number theory, particularly in estimating error terms and studying equidistribution and Diophantine approximation.

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_69f22498c5d481908aaea89e6fab8280`	completed	April 29, 2026, 3:32 p.m.
NER	Named-entity recognition	`batch_69f687805b048190824b5c0bc8d09bab`	completed	May 2, 2026, 11:23 p.m.
NED1	Entity disambiguation (via context triple)	`batch_6a27ac34e2cc81908b00ea172a52137e`	completed	June 9, 2026, 6:01 a.m.
NEDg	Description generation	`batch_6a27ad12e04881909ed3d8bc5f38b65d`	completed	June 9, 2026, 6:05 a.m.
NED2	Entity disambiguation (via description)	`batch_6a27ae0e5be0819080fd9538605b65b7`	completed	June 9, 2026, 6:09 a.m.

Created at: April 29, 2026, 8:14 p.m.