Triple

T5896709
Position Surface form Disambiguated ID Type / Status
Subject Pál Erdős E131117 entity
Predicate knownFor P22 FINISHED
Object Erdős discrepancy problem
The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
E554302 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: Erdős discrepancy problem | Statement: [Pál Erdős, knownFor, Erdős discrepancy problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Erdős discrepancy problem
Context triple: [Pál Erdős, knownFor, Erdős discrepancy problem]
  • A. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • B. 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.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • D. Conway's 99-graph problem
    Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
  • E. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • 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: Erdős discrepancy problem
Triple: [Pál Erdős, knownFor, Erdős discrepancy problem]
Generated description
The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Erdős discrepancy problem
Target entity description: The Erdős discrepancy problem is a famous question in combinatorial number theory that asks whether every infinite ±1 sequence has arbitrarily large discrepancy along some homogeneous arithmetic progression.
  • A. Green–Tao theorem
    The Green–Tao theorem is a landmark result in number theory proving that the sequence of prime numbers contains arbitrarily long arithmetic progressions.
  • B. 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.
  • C. Dyson’s transform in number theory
    Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
  • D. Conway's 99-graph problem
    Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
  • E. Grothendieck inequality
    The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
  • 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_69c00857439c819095950754176aa58a completed March 22, 2026, 3:18 p.m.
NER Named-entity recognition batch_69c036f4b56c8190aa52c9460eae8fbe completed March 22, 2026, 6:37 p.m.
NED1 Entity disambiguation (via context triple) batch_69c0b159cb908190b78b78d1e854212b completed March 23, 2026, 3:19 a.m.
NEDg Description generation batch_69c0b22d661c8190a055abd3ca6fa92f completed March 23, 2026, 3:23 a.m.
NED2 Entity disambiguation (via description) batch_69c0b608a10881908c9bca7d09a99b05 completed March 23, 2026, 3:39 a.m.
Created at: March 22, 2026, 3:58 p.m.