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.