Triple

T5570626
Position Surface form Disambiguated ID Type / Status
Subject Fermat's theorem on sums of two squares E146190 entity
Predicate hasAlternativeProofBy P21917 FINISHED
Object Joseph-Louis Lagrange E29045 NE FINISHED

How this triple was built (3 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: Joseph-Louis Lagrange | Statement: [Fermat's theorem on sums of two squares, hasAlternativeProofBy, Joseph-Louis Lagrange]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Joseph-Louis Lagrange
Context triple: [Fermat's theorem on sums of two squares, hasAlternativeProofBy, Joseph-Louis Lagrange]
  • A. Joseph-Louis Lagrange chosen
    Joseph-Louis Lagrange was an 18th-century mathematician and astronomer renowned for his foundational contributions to analysis, number theory, and classical mechanics, including the formulation of Lagrangian mechanics.
  • B. Marie-Joseph Lagrange
    Marie-Joseph Lagrange was a French Dominican priest and pioneering biblical scholar known for advancing historical-critical study of Scripture within the Catholic Church.
  • C. Adrien-Marie Legendre
    Adrien-Marie Legendre was an influential 18th–19th century French mathematician known for major contributions to number theory, analysis, and mathematical statistics.
  • D. Pierre-Simon Laplace
    Pierre-Simon Laplace was a French mathematician, physicist, and astronomer whose work laid the foundations of celestial mechanics, probability theory, and statistics.
  • E. Jean d’Alembert
    Jean d’Alembert was an 18th-century French mathematician, physicist, and philosopher best known for his foundational work in calculus, mechanics (including d’Alembert’s principle), and co-editing the Encyclopédie.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07 
Target predicate: hasAlternativeProofBy
Context triple: [Fermat's theorem on sums of two squares, hasAlternativeProofBy, Joseph-Louis Lagrange]
  • A. hasCorollary
    Indicates that one statement, result, or proposition follows as a corollary from another, typically more general, statement.
  • B. attestedBy
    Indicates that the existence, occurrence, or validity of something is supported, confirmed, or documented by a specified source or authority.
  • C. hasProofMethod
    Indicates that there exists a specific method or technique used to establish or demonstrate the validity of something (such as a statement, claim, or theorem).
  • D. providesEvidenceFor
    Indicates that one entity serves as support, justification, or proof for the validity or truth of another entity.
  • E. proved chosen
    Indicates that one entity has demonstrated the truth or validity of another entity (such as a statement, theorem, or claim) through logical or evidential means.
  • F. None of above.

Provenance (4 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_69c008ffed108190a084602227af6157 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c020502a288190af37f9ebb88fccae completed March 22, 2026, 5:01 p.m.
NED1 Entity disambiguation (via context triple) batch_69c04d177d18819090018371d22c66a3 completed March 22, 2026, 8:12 p.m.
PD Predicate disambiguation batch_69c01b12826c8190969a584d0f53aa44 completed March 22, 2026, 4:38 p.m.
Created at: March 22, 2026, 3:37 p.m.