Triple
T7030752
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Multiplicative Number Theory |
E163262
|
entity |
| Predicate | hasClassicResult |
P74560
|
FINISHED |
| Object |
Halász theorem
Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
|
E637298
|
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: Halász theorem | Statement: [Multiplicative Number Theory, hasClassicResult, Halász theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Halász theorem Context triple: [Multiplicative Number Theory, hasClassicResult, Halász theorem]
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
C.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
E.
Steinhaus theorem
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
- 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: Halász theorem Triple: [Multiplicative Number Theory, hasClassicResult, Halász theorem]
Generated description
Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Halász theorem Target entity description: Halász theorem is a fundamental result in analytic number theory that provides sharp bounds on the mean values of multiplicative functions, playing a key role in understanding their average behavior.
-
A.
Szekeres–Lindström theorem
The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
-
B.
de Bruijn–van Aardenne–Ehrenfest theorem
The de Bruijn–van Aardenne–Ehrenfest theorem is a fundamental result in combinatorics that characterizes the number of Eulerian circuits in directed graphs, particularly de Bruijn graphs, and underpins constructions in coding theory and discrete mathematics.
-
C.
Page theorem
The Page theorem is a result in quantum information theory and black hole physics that predicts how the entanglement entropy of a subsystem typically evolves, underpinning the characteristic "Page curve" behavior in discussions of the black hole information paradox.
-
D.
Bogoliubov–Parasyuk theorem
The Bogoliubov–Parasyuk theorem is a fundamental result in quantum field theory that rigorously establishes a systematic procedure for renormalizing divergent Feynman diagrams.
-
E.
Steinhaus theorem
The Steinhaus theorem is a fundamental result in measure theory stating that the difference set of any subset of the real numbers with positive Lebesgue measure contains an open interval around zero.
- 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_69c6885d691c81908cf7d31083113886 |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6e77415e88190ab65137382f1b155 |
completed | March 27, 2026, 8:24 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c775980920819081d31b8d2843fb3d |
completed | March 28, 2026, 6:30 a.m. |
| NEDg | Description generation | batch_69c77aa1c704819088a9561ac55f9037 |
completed | March 28, 2026, 6:52 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c77b082f3c8190a649297ce0f816bb |
completed | March 28, 2026, 6:54 a.m. |
Created at: March 27, 2026, 2:35 p.m.