Triple

T8644707
Position Surface form Disambiguated ID Type / Status
Subject Deuring–Heilbronn phenomenon E204744 entity
Predicate involves P1256 FINISHED
Object Siegel zero
A Siegel zero is a hypothetical exceptional real zero of certain Dirichlet L-functions that would lie unusually close to 1 and have deep implications for the distribution of prime numbers in arithmetic progressions.
E747887 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: Siegel zero | Statement: [Deuring–Heilbronn phenomenon, involves, Siegel zero]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Siegel zero
Context triple: [Deuring–Heilbronn phenomenon, involves, Siegel zero]
  • A. Bombieri–Vinogradov theorem
    The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
  • 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. 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.
  • D. Ramanujan–Petersson conjecture
    The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
  • E. Bateman–Horn conjecture
    The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
  • 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: Siegel zero
Triple: [Deuring–Heilbronn phenomenon, involves, Siegel zero]
Generated description
A Siegel zero is a hypothetical exceptional real zero of certain Dirichlet L-functions that would lie unusually close to 1 and have deep implications for the distribution of prime numbers in arithmetic progressions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Siegel zero
Target entity description: A Siegel zero is a hypothetical exceptional real zero of certain Dirichlet L-functions that would lie unusually close to 1 and have deep implications for the distribution of prime numbers in arithmetic progressions.
  • A. Bombieri–Vinogradov theorem
    The Bombieri–Vinogradov theorem is a major result in analytic number theory that gives strong average estimates for the distribution of prime numbers in arithmetic progressions, approaching what is predicted by the Generalized Riemann Hypothesis.
  • 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. 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.
  • D. Ramanujan–Petersson conjecture
    The Ramanujan–Petersson conjecture is a fundamental statement in number theory and the theory of modular forms that predicts strong bounds on the Fourier coefficients of modular cusp forms, with deep connections to automorphic forms and the Langlands program.
  • E. Bateman–Horn conjecture
    The Bateman–Horn conjecture is a far-reaching unproven statement in number theory that predicts how often sets of polynomial expressions simultaneously take prime values, generalizing several earlier conjectures about the distribution of prime numbers.
  • 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_69ca834ca1c88190a11ffb0200342fac completed March 30, 2026, 2:06 p.m.
NER Named-entity recognition batch_69cc479999c881908c0c4e01c07d02d4 completed March 31, 2026, 10:15 p.m.
NED1 Entity disambiguation (via context triple) batch_69cebc42922c819099a464d2e347dec4 completed April 2, 2026, 6:58 p.m.
NEDg Description generation batch_69cec03fa5dc8190bbfe40aa1a3b27c1 completed April 2, 2026, 7:15 p.m.
NED2 Entity disambiguation (via description) batch_69cec0cac51c8190962a23d53c1fb48b completed April 2, 2026, 7:17 p.m.
Created at: March 30, 2026, 6:28 p.m.