Triple

T16571019
Position Surface form Disambiguated ID Type / Status
Subject Bronisław Knaster E402583 entity
Predicate notableWork P4 FINISHED
Object Knaster–Kuratowski–Mazurkiewicz theorem E518469 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: Knaster–Kuratowski–Mazurkiewicz theorem | Statement: [Bronisław Knaster, notableWork, Knaster–Kuratowski–Mazurkiewicz theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Knaster–Kuratowski–Mazurkiewicz theorem
Context triple: [Bronisław Knaster, notableWork, Knaster–Kuratowski–Mazurkiewicz theorem]
  • 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. Sperner's lemma
    Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
  • C. 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.
  • D. Brouwer fixed-point theorem
    The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
  • E. Tucker’s lemma
    Tucker’s lemma is a combinatorial analog of the Borsuk–Ulam theorem that provides conditions guaranteeing the existence of certain complementary edge labels in triangulated spheres.
  • 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_69d8838648088190acf97ef11fc3f61b completed April 10, 2026, 4:58 a.m.
NER Named-entity recognition batch_69e35958d49c8190b995188240fb355b completed April 18, 2026, 10:13 a.m.
NED1 Entity disambiguation (via context triple) batch_6a006ee8812c81908ef74636bf39d44a completed May 10, 2026, 11:41 a.m.
Created at: April 10, 2026, 5:16 a.m.