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.