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.