Triple

T4996539
Position Surface form Disambiguated ID Type / Status
Subject Weierstrass preparation theorem E112259 entity
Predicate hasVariant P455 FINISHED
Object formal Weierstrass preparation theorem E112259 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: formal Weierstrass preparation theorem | Statement: [Weierstrass preparation theorem, hasVariant, formal Weierstrass preparation theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: formal Weierstrass preparation theorem
Context triple: [Weierstrass preparation theorem, hasVariant, formal Weierstrass preparation theorem]
  • A. Weierstrass preparation theorem chosen
    The Weierstrass preparation theorem is a fundamental result in complex analysis and analytic geometry that locally expresses analytic functions near a zero as a product of a polynomial and a unit, enabling a power-series analogue of factorization.
  • B. Weierstrass factorization theorem
    The Weierstrass factorization theorem is a fundamental result in complex analysis that expresses any entire function as an infinite product determined by its zeros, generalizing the factorization of polynomials.
  • C. Hilbert’s Nullstellensatz
    Hilbert’s Nullstellensatz is a foundational theorem in algebraic geometry that establishes a deep correspondence between ideals in polynomial rings and algebraic sets, linking algebra and geometry.
  • D. Mittag-Leffler theorem
    The Mittag-Leffler theorem is a fundamental result in complex analysis that characterizes meromorphic functions by allowing the construction of such functions with prescribed principal parts at given poles.
  • E. Hilbert’s fourteenth problem
    Hilbert’s fourteenth problem is one of David Hilbert’s famous list of 23 problems, concerning the finite generation of certain algebras of invariants in algebraic geometry and invariant theory.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69bd4432b32c81909f3b3c6bd10f0653 completed March 20, 2026, 12:57 p.m.
NER Named-entity recognition batch_69bd72a130708190b9bc1393ba78bfb1 completed March 20, 2026, 4:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69be8a3489f08190a338de8d8be09813 completed March 21, 2026, 12:08 p.m.
Created at: March 20, 2026, 1:34 p.m.