Triple

T14265335
Position Surface form Disambiguated ID Type / Status
Subject Tarski’s fixed point theorem E353628 entity
Predicate relatedTo P37 FINISHED
Object Kleene fixed-point theorem E607898 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: Kleene fixed-point theorem | Statement: [Tarski’s fixed point theorem, relatedTo, Kleene fixed-point theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Kleene fixed-point theorem
Context triple: [Tarski’s fixed point theorem, relatedTo, Kleene fixed-point theorem]
  • A. Kleene’s recursion theorem chosen
    Kleene’s recursion theorem is a fundamental result in computability theory that guarantees the existence of self-referential programs, allowing a program to effectively obtain and use its own description.
  • B. Tarski’s fixed point theorem
    Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
  • C. Kleene’s normal form theorem
    Kleene’s normal form theorem is a fundamental result in computability theory that characterizes all partial recursive (effectively computable) functions using a universal primitive recursive function and the μ-operator.
  • 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. Glicksberg fixed-point theorem
    The Glicksberg fixed-point theorem is a result in functional analysis that extends Kakutani’s fixed-point theorem to certain infinite-dimensional or compact convex subsets of locally convex topological vector spaces.
  • 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_69d8278c43e08190824146f4632b89a5 completed April 9, 2026, 10:26 p.m.
NER Named-entity recognition batch_69de6357a8188190ba518a486521052b completed April 14, 2026, 3:55 p.m.
NED1 Entity disambiguation (via context triple) batch_69fd3d150b188190a0858ab94f81d9a8 completed May 8, 2026, 1:32 a.m.
Created at: April 10, 2026, 1:09 a.m.