Triple

T2364375
Position Surface form Disambiguated ID Type / Status
Subject Riemann hypothesis E47346 entity
Predicate relatedTo P37 FINISHED
Object random matrix theory
Random matrix theory is a branch of mathematics and mathematical physics that studies the statistical properties of matrices with randomly chosen entries, with deep applications to fields such as number theory, quantum chaos, and statistical mechanics.
E259756 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: random matrix theory | Statement: [Riemann hypothesis, relatedTo, random matrix theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: random matrix theory
Context triple: [Riemann hypothesis, relatedTo, random matrix theory]
  • A. Wigner surmise
    The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
  • B. Selberg integral
    The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
  • C. Anderson localization
    Anderson localization is a quantum mechanical phenomenon in which disorder in a material causes electrons or waves to become spatially localized, preventing them from diffusing freely.
  • D. Cauchy interlacing theorem
    The Cauchy interlacing theorem is a fundamental result in linear algebra that relates the eigenvalues of a symmetric matrix to those of its principal submatrices, showing how they "interlace" on the real line.
  • E. Wick’s theorem
    Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
  • 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: random matrix theory
Triple: [Riemann hypothesis, relatedTo, random matrix theory]
Generated description
Random matrix theory is a branch of mathematics and mathematical physics that studies the statistical properties of matrices with randomly chosen entries, with deep applications to fields such as number theory, quantum chaos, and statistical mechanics.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: random matrix theory
Target entity description: Random matrix theory is a branch of mathematics and mathematical physics that studies the statistical properties of matrices with randomly chosen entries, with deep applications to fields such as number theory, quantum chaos, and statistical mechanics.
  • A. Wigner surmise
    The Wigner surmise is an approximate formula in random matrix theory that describes the statistical distribution of spacings between neighboring energy levels in complex quantum systems.
  • B. Selberg integral
    The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
  • C. Anderson localization
    Anderson localization is a quantum mechanical phenomenon in which disorder in a material causes electrons or waves to become spatially localized, preventing them from diffusing freely.
  • D. Cauchy interlacing theorem
    The Cauchy interlacing theorem is a fundamental result in linear algebra that relates the eigenvalues of a symmetric matrix to those of its principal submatrices, showing how they "interlace" on the real line.
  • E. Wick’s theorem
    Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
  • 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_69a88a1a4a6081908645b0f2914521ab completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc7486cb48190acef1891cc87bdb1 completed March 7, 2026, 6:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69aea896e0388190aabff2d70787dc43 completed March 9, 2026, 11:01 a.m.
NEDg Description generation batch_69aea91ce164819091aa24b287f9fb8e completed March 9, 2026, 11:03 a.m.
NED2 Entity disambiguation (via description) batch_69aea999b864819084134c670e7c5d9c completed March 9, 2026, 11:06 a.m.
Created at: March 4, 2026, 7:55 p.m.