Triple

T5896701
Position Surface form Disambiguated ID Type / Status
Subject Pál Erdős E131117 entity
Predicate knownFor P22 FINISHED
Object Erdős number concept
The Erdős number concept is a measure of collaborative distance in mathematical research, indicating how many coauthorship links separate a given author from the prolific Hungarian mathematician Pál Erdős.
E554296 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 number concept | Statement: [Pál Erdős, knownFor, Erdős number concept]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Erdős number concept
Context triple: [Pál Erdős, knownFor, Erdős number concept]
  • A. Pál Erdős
    Pál Erdős was a highly prolific 20th-century Hungarian mathematician renowned for his extensive contributions to number theory, combinatorics, and discrete mathematics, as well as his famously collaborative working style.
  • B. Eddington number
    The Eddington number is a dimensionless quantity in astrophysics that represents the maximum luminosity a star can have before radiation pressure overcomes gravitational attraction, leading to mass loss.
  • C. 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.
  • D. 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.
  • E. Mertens’ theorems
    Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
  • 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 number concept
Triple: [Pál Erdős, knownFor, Erdős number concept]
Generated description
The Erdős number concept is a measure of collaborative distance in mathematical research, indicating how many coauthorship links separate a given author from the prolific Hungarian mathematician Pál Erdős.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Erdős number concept
Target entity description: The Erdős number concept is a measure of collaborative distance in mathematical research, indicating how many coauthorship links separate a given author from the prolific Hungarian mathematician Pál Erdős.
  • A. Pál Erdős
    Pál Erdős was a highly prolific 20th-century Hungarian mathematician renowned for his extensive contributions to number theory, combinatorics, and discrete mathematics, as well as his famously collaborative working style.
  • B. Eddington number
    The Eddington number is a dimensionless quantity in astrophysics that represents the maximum luminosity a star can have before radiation pressure overcomes gravitational attraction, leading to mass loss.
  • C. 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.
  • D. 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.
  • E. Mertens’ theorems
    Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
  • 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.