Triple

T20509149
Position Surface form Disambiguated ID Type / Status
Subject intuitionism E503512 entity
Predicate associatedWith P37 FINISHED
Object Brouwerian continuity principle
The Brouwerian continuity principle is a key axiom in intuitionistic mathematics asserting that every total function from the real numbers to the real numbers is continuous, reflecting L.E.J. Brouwer’s constructive view of analysis.
E1436429 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: Brouwerian continuity principle | Statement: [intuitionism, associatedWith, Brouwerian continuity principle]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Brouwerian continuity principle
Context triple: [intuitionism, associatedWith, Brouwerian continuity principle]
  • A. Brouwer–Heyting–Kolmogorov interpretation
    The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
  • B. Brouwer’s intuitionism
    Brouwer’s intuitionism is a philosophy of mathematics that views mathematical objects as mental constructions and rejects classical logic principles like the law of excluded middle for infinite totalities.
  • C. Recursive Functions and Intuitionistic Mathematics
    Recursive Functions and Intuitionistic Mathematics is a seminal work by Stephen Kleene that develops the theory of recursive (computable) functions within the framework of intuitionistic logic and mathematics.
  • D. Brouwer fixed-point theorem
    The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
  • E. Curry–Howard correspondence
    The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
  • 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: Brouwerian continuity principle
Triple: [intuitionism, associatedWith, Brouwerian continuity principle]
Generated description
The Brouwerian continuity principle is a key axiom in intuitionistic mathematics asserting that every total function from the real numbers to the real numbers is continuous, reflecting L.E.J. Brouwer’s constructive view of analysis.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Brouwerian continuity principle
Target entity description: The Brouwerian continuity principle is a key axiom in intuitionistic mathematics asserting that every total function from the real numbers to the real numbers is continuous, reflecting L.E.J. Brouwer’s constructive view of analysis.
  • A. Brouwer–Heyting–Kolmogorov interpretation
    The Brouwer–Heyting–Kolmogorov interpretation is a foundational explanation of intuitionistic logic that interprets logical connectives and proofs in terms of explicit constructions and algorithms rather than classical truth values.
  • B. Brouwer’s intuitionism
    Brouwer’s intuitionism is a philosophy of mathematics that views mathematical objects as mental constructions and rejects classical logic principles like the law of excluded middle for infinite totalities.
  • C. Recursive Functions and Intuitionistic Mathematics
    Recursive Functions and Intuitionistic Mathematics is a seminal work by Stephen Kleene that develops the theory of recursive (computable) functions within the framework of intuitionistic logic and mathematics.
  • D. Brouwer fixed-point theorem
    The Brouwer fixed-point theorem is a fundamental result in topology stating that any continuous function from a compact convex set (such as a closed disk) to itself has at least one fixed point.
  • E. Curry–Howard correspondence
    The Curry–Howard correspondence is a foundational principle in logic and computer science that establishes a deep analogy between proofs and programs, and between logical propositions and types in programming languages.
  • 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_69e0b4b1e52c8190894281cf7e3283ab completed April 16, 2026, 10:06 a.m.
NER Named-entity recognition batch_69e69dc9de788190882ce471966ef2b4 completed April 20, 2026, 9:42 p.m.
NED1 Entity disambiguation (via context triple) batch_6a089d34c4ac8190a4ff8d8442dac927 completed May 16, 2026, 4:37 p.m.
NEDg Description generation batch_6a089dc1a5688190ba700d78fb1b1940 completed May 16, 2026, 4:39 p.m.
NED2 Entity disambiguation (via description) batch_6a08a16aa21c8190aa7d79578aca0698 completed May 16, 2026, 4:55 p.m.
Created at: April 16, 2026, 11:36 a.m.