Triple

T10991304
Position Surface form Disambiguated ID Type / Status
Subject Montgomery's pair correlation conjecture E259758 entity
Predicate relatedTo P37 FINISHED
Object GUE conjecture for zeta zeros
The GUE conjecture for zeta zeros posits that the statistical distribution of the nontrivial zeros of the Riemann zeta function matches the eigenvalue statistics of large random Hermitian matrices from the Gaussian Unitary Ensemble.
E259758 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: GUE conjecture for zeta zeros | Statement: [Montgomery's pair correlation conjecture, relatedTo, GUE conjecture for zeta zeros]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: GUE conjecture for zeta zeros
Context triple: [Montgomery's pair correlation conjecture, relatedTo, GUE conjecture for zeta zeros]
  • A. Hilbert–Pólya conjecture
    The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
  • B. Montgomery's pair correlation conjecture
    Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
  • C. Siegel’s theorem on zeros of L-functions
    Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
  • D. Riemann hypothesis
    The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
  • E. Voronin universality theorem
    The Voronin universality theorem is a result in analytic number theory stating that, in a precise sense, the Riemann zeta function can approximate any non-vanishing analytic function arbitrarily well on certain regions of the complex plane.
  • 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: GUE conjecture for zeta zeros
Triple: [Montgomery's pair correlation conjecture, relatedTo, GUE conjecture for zeta zeros]
Generated description
The GUE conjecture for zeta zeros posits that the statistical distribution of the nontrivial zeros of the Riemann zeta function matches the eigenvalue statistics of large random Hermitian matrices from the Gaussian Unitary Ensemble.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: GUE conjecture for zeta zeros
Target entity description: The GUE conjecture for zeta zeros posits that the statistical distribution of the nontrivial zeros of the Riemann zeta function matches the eigenvalue statistics of large random Hermitian matrices from the Gaussian Unitary Ensemble.
  • A. Hilbert–Pólya conjecture
    The Hilbert–Pólya conjecture is an unproven idea in number theory suggesting that the nontrivial zeros of the Riemann zeta function correspond to eigenvalues of a suitable self-adjoint operator, offering a potential spectral approach to proving the Riemann hypothesis.
  • B. Montgomery's pair correlation conjecture chosen
    Montgomery's pair correlation conjecture is a deep number-theoretic prediction about the statistical spacing of the nontrivial zeros of the Riemann zeta function, linking them to eigenvalues of random matrices and suggesting profound connections between number theory and quantum physics.
  • C. Siegel’s theorem on zeros of L-functions
    Siegel’s theorem on zeros of L-functions is a result in analytic number theory that gives strong bounds on how close nontrivial zeros of Dirichlet L-functions can approach 1, with deep implications for the distribution of primes in arithmetic progressions.
  • D. Riemann hypothesis
    The Riemann hypothesis is a famous unsolved conjecture in number theory asserting that all nontrivial zeros of the Riemann zeta function lie on a critical line in the complex plane, with deep implications for the distribution of prime numbers.
  • E. Voronin universality theorem
    The Voronin universality theorem is a result in analytic number theory stating that, in a precise sense, the Riemann zeta function can approximate any non-vanishing analytic function arbitrarily well on certain regions of the complex plane.
  • F. None of above.

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_69d6aa8a6a548190a750f944ccdc8064 completed April 8, 2026, 7:20 p.m.
NER Named-entity recognition batch_69d795d1e918819090c71f5a077fa15a completed April 9, 2026, 12:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69e34504ebec8190a78e4795765b0c24 completed April 18, 2026, 8:47 a.m.
NEDg Description generation batch_69e3556fd3548190a33f04604be947cf completed April 18, 2026, 9:57 a.m.
NED2 Entity disambiguation (via description) batch_69e3593b0f8481909ed7a90f8bb9839d completed April 18, 2026, 10:13 a.m.
Created at: April 8, 2026, 9:24 p.m.