Triple

T5040498
Position Surface form Disambiguated ID Type / Status
Subject Lindemann–Weierstrass theorem precursor E113531 entity
Predicate precedes P97 FINISHED
Object Lindemann–Weierstrass theorem E113531 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: Lindemann–Weierstrass theorem | Statement: [Lindemann–Weierstrass theorem precursor, precedes, Lindemann–Weierstrass theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Lindemann–Weierstrass theorem
Context triple: [Lindemann–Weierstrass theorem precursor, precedes, Lindemann–Weierstrass theorem]
  • A. Lindemann–Weierstrass theorem precursor chosen
    The Lindemann–Weierstrass theorem precursor is an early foundational result in transcendental number theory developed by Ferdinand von Lindemann that paved the way for the full Lindemann–Weierstrass theorem on the algebraic independence of exponentials of algebraic numbers.
  • B. Bateman–Horn conjecture
    The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
  • C. Picard theorem
    Picard theorem is a fundamental result in complex analysis stating that entire non-constant functions take on all possible complex values, with at most one exception.
  • D. Dirichlet's theorem on arithmetic progressions
    Dirichlet's theorem on arithmetic progressions is a fundamental result in number theory stating that any arithmetic progression with first term and difference coprime contains infinitely many prime numbers.
  • E. Hilbert’s irreducibility theorem
    Hilbert’s irreducibility theorem is a fundamental result in number theory and algebraic geometry that ensures many polynomial equations with parameterized coefficients retain irreducibility for infinitely many specializations of those parameters.
  • 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_69bd44384298819089c49e7c330ec7b8 completed March 20, 2026, 12:57 p.m.
NER Named-entity recognition batch_69bd73dd27fc8190817e53311ea3f706 completed March 20, 2026, 4:20 p.m.
NED1 Entity disambiguation (via context triple) batch_69bea47c5f808190821d7f708003a07d completed March 21, 2026, 2 p.m.
Created at: March 20, 2026, 1:37 p.m.