Triple
T11971691
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Ilya Piatetski-Shapiro |
E284934
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Piatetski-Shapiro measure
The Piatetski-Shapiro measure is a probability measure in harmonic analysis and representation theory introduced by Ilya Piatetski-Shapiro, used to study automorphic forms and related number-theoretic structures.
|
E957158
|
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: Piatetski-Shapiro measure | Statement: [Ilya Piatetski-Shapiro, knownFor, Piatetski-Shapiro measure]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Piatetski-Shapiro measure Context triple: [Ilya Piatetski-Shapiro, knownFor, Piatetski-Shapiro measure]
-
A.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
-
B.
Khintchine theorem
Khintchine theorem is a fundamental result in metric Diophantine approximation that characterizes, via a simple convergence–divergence criterion, when almost all real numbers admit infinitely many rational approximations of a prescribed quality.
-
C.
Liouville measure
Liouville measure is a canonical volume measure on phase space in Hamiltonian mechanics and symplectic geometry that remains invariant under the system’s time evolution.
-
D.
Erdős–Wintner theorem
The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
-
E.
Liouville's inequality in Diophantine approximation
Liouville's inequality in Diophantine approximation is a foundational result that gives explicit lower bounds on how closely algebraic numbers can be approximated by rationals, leading to the first examples of transcendental 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: Piatetski-Shapiro measure Triple: [Ilya Piatetski-Shapiro, knownFor, Piatetski-Shapiro measure]
Generated description
The Piatetski-Shapiro measure is a probability measure in harmonic analysis and representation theory introduced by Ilya Piatetski-Shapiro, used to study automorphic forms and related number-theoretic structures.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Piatetski-Shapiro measure Target entity description: The Piatetski-Shapiro measure is a probability measure in harmonic analysis and representation theory introduced by Ilya Piatetski-Shapiro, used to study automorphic forms and related number-theoretic structures.
-
A.
Deuring–Heilbronn phenomenon
The Deuring–Heilbronn phenomenon is a result in analytic number theory describing how the presence of an exceptional (Siegel) zero of a Dirichlet L-function forces other zeros away from the real axis, sharpening zero-free regions and affecting the distribution of primes in arithmetic progressions.
-
B.
Khintchine theorem
Khintchine theorem is a fundamental result in metric Diophantine approximation that characterizes, via a simple convergence–divergence criterion, when almost all real numbers admit infinitely many rational approximations of a prescribed quality.
-
C.
Liouville measure
Liouville measure is a canonical volume measure on phase space in Hamiltonian mechanics and symplectic geometry that remains invariant under the system’s time evolution.
-
D.
Erdős–Wintner theorem
The Erdős–Wintner theorem is a fundamental result in probabilistic number theory that characterizes when an additive arithmetic function has a limiting distribution.
-
E.
Liouville's inequality in Diophantine approximation
Liouville's inequality in Diophantine approximation is a foundational result that gives explicit lower bounds on how closely algebraic numbers can be approximated by rationals, leading to the first examples of transcendental 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_69d6ab2eaeb881909f7914758f859413 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d9037d32e88190b1509285dc907d29 |
completed | April 10, 2026, 2:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f4597cf818819089b0d897c236b87b |
completed | May 1, 2026, 7:42 a.m. |
| NEDg | Description generation | batch_69f45f89d5b08190a87312d96e61898a |
completed | May 1, 2026, 8:08 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f464a5191881908e291943996169cb |
completed | May 1, 2026, 8:30 a.m. |
Created at: April 8, 2026, 9:46 p.m.