Triple

T5570724
Position Surface form Disambiguated ID Type / Status
Subject Fermat point E146192 entity
Predicate relatedTo P37 FINISHED
Object Fermat’s minimal path problem E146192 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: Fermat’s minimal path problem | Statement: [Fermat point, relatedTo, Fermat’s minimal path problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Fermat’s minimal path problem
Context triple: [Fermat point, relatedTo, Fermat’s minimal path problem]
  • A. Fermat’s principle of least time
    Fermat’s principle of least time is a fundamental variational principle in optics stating that light follows the path that takes the least time, from which many laws of geometrical optics can be derived.
  • B. brachistochrone problem
    The brachistochrone problem is a famous challenge in the calculus of variations that asks for the curve along which a particle will descend between two points in the shortest time under gravity, whose solution is a cycloid.
  • C. Elementa curvarum linearum
    Elementa curvarum linearum is a 17th-century mathematical treatise by Johan de Witt that systematically studies the geometry and properties of linear curves.
  • D. "Invariante Variationsprobleme"
    "Invariante Variationsprobleme" is Emmy Noether’s landmark 1918 paper that founded the deep connection between symmetries and conservation laws in physics and the calculus of variations.
  • E. Fermat point chosen
    The Fermat point is a special point inside a triangle that minimizes the total distance to the triangle’s three vertices.
  • 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_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_69c0284bb71881908c0ac4ea2a302327 completed March 22, 2026, 5:35 p.m.
Created at: March 22, 2026, 3:37 p.m.