Triple

T34418890
Position Surface form Disambiguated ID Type / Status
Subject Serre vanishing theorem E883473 entity
Predicate typicalFormulation P12789 FINISHED
Object If X is projective over a Noetherian ring and L is ample, then for any coherent sheaf F on X there exists n_0 such that H^i(X, F \otimes L^{\otimes n}) = 0 for all i > 0 and n \ge n_0 — LITERAL FINISHED

How this triple was built (1 step)

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: If X is projective over a Noetherian ring and L is ample, then for any coherent sheaf F on X there exists n_0 such that H^i(X, F \otimes L^{\otimes n}) = 0 for all i > 0 and n \ge n_0 | Statement: [Serre vanishing theorem, typicalFormulation, If X is projective over a Noetherian ring and L is ample, then for any coherent sheaf F on X there exists n_0 such that H^i(X, F \otimes L^{\otimes n}) = 0 for all i > 0 and n \ge n_0]

Provenance (2 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_69f349c2e3b88190a67834eb5bcffeaf completed April 30, 2026, 12:23 p.m.
NER Named-entity recognition batch_69f718d9ae648190a4d4bffaa8a5c606 completed May 3, 2026, 9:43 a.m.
Created at: May 1, 2026, 2 a.m.