Triple

T8926741
Position Surface form Disambiguated ID Type / Status
Subject complete class theorem in decision theory E212554 entity
Predicate isRelatedTo P37 FINISHED
Object admissibility theorem
The admissibility theorem is a result in statistical decision theory that characterizes when a decision rule cannot be uniformly improved upon, linking admissible rules to optimality concepts such as those in complete class theorems.
E766786 NE FINISHED

How this triple was built (4 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: admissibility theorem | Statement: [complete class theorem in decision theory, isRelatedTo, admissibility theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: admissibility theorem
Context triple: [complete class theorem in decision theory, isRelatedTo, admissibility theorem]
  • A. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • B. Halász theorem
    Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
  • C. Subspace theorem
    The Subspace theorem is a fundamental result in Diophantine approximation that describes how solutions to certain inequalities involving linear forms over algebraic numbers must lie in a finite union of proper subspaces.
  • D. Page theorem
    The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
  • E. Fitting lemma
    The Fitting lemma is a result in group theory and module theory that characterizes how certain algebraic structures decompose into direct sums of invariant subcomponents, often involving nilpotent and invertible parts.
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: admissibility theorem
Triple: [complete class theorem in decision theory, isRelatedTo, admissibility theorem]
Generated description
The admissibility theorem is a result in statistical decision theory that characterizes when a decision rule cannot be uniformly improved upon, linking admissible rules to optimality concepts such as those in complete class theorems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: admissibility theorem
Target entity description: The admissibility theorem is a result in statistical decision theory that characterizes when a decision rule cannot be uniformly improved upon, linking admissible rules to optimality concepts such as those in complete class theorems.
  • A. Szekeres–Lindström theorem
    The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
  • B. Halász theorem
    Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
  • C. Subspace theorem
    The Subspace theorem is a fundamental result in Diophantine approximation that describes how solutions to certain inequalities involving linear forms over algebraic numbers must lie in a finite union of proper subspaces.
  • D. Page theorem
    The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
  • E. Fitting lemma
    The Fitting lemma is a result in group theory and module theory that characterizes how certain algebraic structures decompose into direct sums of invariant subcomponents, often involving nilpotent and invertible parts.
  • F. None of above. chosen

Provenance (5 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_69ca839481d48190b42b037e0d0f636c completed March 30, 2026, 2:07 p.m.
NER Named-entity recognition batch_69cc6671557c81909f3837ffd6a15ffe completed April 1, 2026, 12:27 a.m.
NED1 Entity disambiguation (via context triple) batch_69cfba58e9ec81909141c516d05ac790 completed April 3, 2026, 1:02 p.m.
NEDg Description generation batch_69cfbade9330819096d4b0eeacdad6da completed April 3, 2026, 1:04 p.m.
NED2 Entity disambiguation (via description) batch_69cfbec2b8888190a0390168fdcef05f completed April 3, 2026, 1:21 p.m.
Created at: March 30, 2026, 6:57 p.m.