Triple

T21046761
Position Surface form Disambiguated ID Type / Status
Subject Knaster–Kuratowski–Mazurkiewicz lemma E518469 entity
Predicate alsoKnownAs P39 FINISHED
Object KKM lemma — NE NERFINISHED

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: KKM lemma | Statement: [Knaster–Kuratowski–Mazurkiewicz lemma, alsoKnownAs, KKM lemma]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: KKM lemma
Context triple: [Knaster–Kuratowski–Mazurkiewicz lemma, alsoKnownAs, KKM lemma]
  • A. Knaster–Kuratowski–Mazurkiewicz lemma chosen
    The Knaster–Kuratowski–Mazurkiewicz lemma is a fundamental result in combinatorial topology that guarantees the existence of a point common to a family of closed sets covering a simplex under certain intersection conditions, and underlies several fixed-point theorems.
  • B. Scarf’s lemma
    Scarf’s lemma is a fundamental result in combinatorial topology and game theory that guarantees the existence of approximate solutions to certain systems, underpinning proofs of equilibrium existence in economics and related fields.
  • C. Ky Fan’s lemma
    Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
  • D. Kakutani fixed-point theorem
    The Kakutani fixed-point theorem is a fundamental result in mathematical analysis and game theory that guarantees the existence of fixed points for certain set-valued (multivalued) functions, underpinning key existence proofs such as Nash equilibria.
  • E. Gale–Nikaidō–Debreu theorem
    The Gale–Nikaidō–Debreu theorem is a fundamental result in mathematical economics that provides conditions ensuring the existence (and sometimes uniqueness) of equilibrium in certain nonlinear and general equilibrium models.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69e0b50438e08190917e2538bb8bc034 completed April 16, 2026, 10:08 a.m.
NER Named-entity recognition batch_69e6fcf4d26481908b639996500a8319 completed April 21, 2026, 4:28 a.m.
Created at: April 16, 2026, 2:34 p.m.