Triple

T2912352
Position Surface form Disambiguated ID Type / Status
Subject Abel–Ruffini theorem E63710 entity
Predicate relatedTo P37 FINISHED
Object Galois’ theory of equations E157385 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: Galois’ theory of equations | Statement: [Abel–Ruffini theorem, relatedTo, Galois’ theory of equations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Galois’ theory of equations
Context triple: [Abel–Ruffini theorem, relatedTo, Galois’ theory of equations]
  • A. Galois theory chosen
    Galois theory is a branch of abstract algebra that studies field extensions and polynomial equations through the structure of their associated symmetry groups.
  • B. Abel–Ruffini theorem
    The Abel–Ruffini theorem is a fundamental result in algebra proving that there is no general solution in radicals for polynomial equations of degree five or higher.
  • C. Treatise on Demonstration of Problems of Algebra
    Treatise on Demonstration of Problems of Algebra is a seminal mathematical work by Omar Khayyam in which he systematically analyzes and geometrically solves cubic equations.
  • D. 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.
  • E. Galois
    Galois is a French surname most famously associated with Évariste Galois, the pioneering 19th-century mathematician who founded group theory and laid the groundwork for modern abstract algebra.
  • 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_69ab4c44ab448190b9411324e8a1fc1d completed March 6, 2026, 9:51 p.m.
NER Named-entity recognition batch_69abe0eb77708190b745b887f3b9a618 completed March 7, 2026, 8:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69b0562014fc8190b7b702fa40682382 completed March 10, 2026, 5:34 p.m.
Created at: March 6, 2026, 10:11 p.m.