Triple

T9838806
Position Surface form Disambiguated ID Type / Status
Subject de Bruijn–Newman constant E239168 entity
Predicate conjecturedRelationToRiemannHypothesis P38260 FINISHED
Object Riemann Hypothesis is equivalent to Λ ≤ 0 E47346 NE FINISHED

How this triple was built (3 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: Riemann Hypothesis is equivalent to Λ ≤ 0 | Statement: [de Bruijn–Newman constant, conjecturedRelationToRiemannHypothesis, Riemann Hypothesis is equivalent to Λ ≤ 0]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Riemann Hypothesis is equivalent to Λ ≤ 0
Context triple: [de Bruijn–Newman constant, conjecturedRelationToRiemannHypothesis, Riemann Hypothesis is equivalent to Λ ≤ 0]
  • A. Riemann hypothesis chosen
    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.
  • B. Lindelöf hypothesis
    The Lindelöf hypothesis is an unproven conjecture in analytic number theory about the growth rate of the Riemann zeta function along the critical line, with deep implications for the distribution of prime numbers.
  • C. Euler product formula for the Riemann zeta function
    The Euler product formula for the Riemann zeta function is a fundamental identity in analytic number theory that expresses the zeta function as an infinite product over all prime numbers, revealing a deep connection between primes and the distribution of integers.
  • D. 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.
  • E. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
PD Predicate disambiguation gpt-5-mini-2025-08-07
Target predicate: conjecturedRelationToRiemannHypothesis
Context triple: [de Bruijn–Newman constant, conjecturedRelationToRiemannHypothesis, Riemann Hypothesis is equivalent to Λ ≤ 0]
  • A. relatedConjecture
    Indicates that one conjecture is connected or associated with another conjecture, such as by similarity, dependency, or thematic relation.
  • B. associatedConjecture chosen
    Indicates that one entity is linked or connected to a particular conjecture, typically as its subject, source, or relevant context.
  • C. primeNumberTheoremRelation
    Indicates the asymptotic relationship between the distribution of prime numbers and the logarithmic growth of integers, as formalized by the prime number theorem.
  • D. VoroninUniversality
    Indicates that a function or object exhibits Voronin universality, meaning its values approximate those of a wide class of analytic functions arbitrarily well on certain domains.
  • E. zetaRelation
    Indicates a specialized, context-dependent association between entities whose exact nature is defined by the specific system or theory using the term "zetaRelation".
  • F. None of above.

Provenance (4 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_69ca84e314108190978324a4bdb959f8 completed March 30, 2026, 2:12 p.m.
NER Named-entity recognition batch_69cdb34921b881909836ba0f5b42a27b completed April 2, 2026, 12:07 a.m.
NED1 Entity disambiguation (via context triple) batch_69d1d5d145ac8190ad10a4328216ef54 completed April 5, 2026, 3:24 a.m.
PD Predicate disambiguation batch_69cd03e30bc08190816c0a6d29c21b0f completed April 1, 2026, 11:39 a.m.
Created at: March 30, 2026, 8:33 p.m.