Triple

T1835353
Position Surface form Disambiguated ID Type / Status
Subject Raymond Smullyan E41052 entity
Predicate notableWork P4 FINISHED
Object Satan, Cantor, and Infinity
"Satan, Cantor, and Infinity" is a popular logic and mathematics book by Raymond Smullyan that presents puzzles and paradoxes through playful dialogues and stories.
E206685 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: Satan, Cantor, and Infinity | Statement: [Raymond Smullyan, notableWork, Satan, Cantor, and Infinity]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Satan, Cantor, and Infinity
Context triple: [Raymond Smullyan, notableWork, Satan, Cantor, and Infinity]
  • A. Orders of Infinity
    "Orders of Infinity" is a mathematical treatise by G. H. Hardy that systematically develops the theory of divergent series and the comparative growth rates of functions in analysis.
  • B. Cantor’s paradox
    Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
  • C. Cantor’s theorem
    Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
  • D. von Neumann paradox in set theory
    The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
  • E. Surreal numbers
    Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
  • 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: Satan, Cantor, and Infinity
Triple: [Raymond Smullyan, notableWork, Satan, Cantor, and Infinity]
Generated description
"Satan, Cantor, and Infinity" is a popular logic and mathematics book by Raymond Smullyan that presents puzzles and paradoxes through playful dialogues and stories.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Satan, Cantor, and Infinity
Target entity description: "Satan, Cantor, and Infinity" is a popular logic and mathematics book by Raymond Smullyan that presents puzzles and paradoxes through playful dialogues and stories.
  • A. Orders of Infinity
    "Orders of Infinity" is a mathematical treatise by G. H. Hardy that systematically develops the theory of divergent series and the comparative growth rates of functions in analysis.
  • B. Cantor’s paradox
    Cantor’s paradox is a foundational result in set theory showing that the “set of all sets” cannot exist because its power set would have a strictly larger cardinality, leading to a contradiction.
  • C. Cantor’s theorem
    Cantor’s theorem is a fundamental result in set theory stating that the power set of any set has a strictly greater cardinality than the set itself, implying there is no largest infinity.
  • D. von Neumann paradox in set theory
    The von Neumann paradox in set theory is a foundational result showing that, under certain group-theoretic conditions, a set can be decomposed and reassembled into paradoxical subsets of equal “size,” illustrating the counterintuitive consequences of the axiom of choice.
  • E. Surreal numbers
    Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
  • 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_69a88647f9388190909bc36e795bdaec completed March 4, 2026, 7:21 p.m.
NER Named-entity recognition batch_69abb026aa7c8190bc988d3ee0fd9f41 completed March 7, 2026, 4:57 a.m.
NED1 Entity disambiguation (via context triple) batch_69adc9b4b4f08190a0e5ad50de5c0ba8 completed March 8, 2026, 7:10 p.m.
NEDg Description generation batch_69adcd9359b88190ad312ff0389ff1a6 completed March 8, 2026, 7:27 p.m.
NED2 Entity disambiguation (via description) batch_69adce11558c8190bd8c6341837eb792 completed March 8, 2026, 7:29 p.m.
Created at: March 4, 2026, 7:33 p.m.