Triple

T10388496
Position Surface form Disambiguated ID Type / Status
Subject Vladimir Voevodsky E244828 entity
Predicate notableIdea P4 FINISHED
Object univalent foundations program
The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
E860090 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: univalent foundations program | Statement: [Vladimir Voevodsky, notableIdea, univalent foundations program]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: univalent foundations program
Context triple: [Vladimir Voevodsky, notableIdea, univalent foundations program]
  • A. Archive of Formal Proofs
    The Archive of Formal Proofs is an online, peer-reviewed collection of machine-checked mathematical and computer science proofs formalized primarily in the Isabelle proof assistant.
  • B. Isabelle proof assistant
    Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
  • C. Grothendieck universe
    A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
  • D. Recent Synthetic Differential Geometry
    "Recent Synthetic Differential Geometry" is a mathematical work by Herbert Busemann that develops differential geometry using synthetic, axiomatic methods rather than traditional analytic techniques.
  • E. Grothendieck toposes
    Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
  • 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: univalent foundations program
Triple: [Vladimir Voevodsky, notableIdea, univalent foundations program]
Generated description
The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: univalent foundations program
Target entity description: The univalent foundations program is a research initiative that redefines the foundations of mathematics using homotopy type theory, emphasizing computationally verifiable proofs and new connections between logic, topology, and category theory.
  • A. Archive of Formal Proofs
    The Archive of Formal Proofs is an online, peer-reviewed collection of machine-checked mathematical and computer science proofs formalized primarily in the Isabelle proof assistant.
  • B. Isabelle proof assistant
    Isabelle proof assistant is a widely used interactive theorem prover and generic proof assistant designed for formal verification and mathematical logic, particularly known for its support of higher-order logic.
  • C. Grothendieck universe
    A Grothendieck universe is a set-theoretic construct large enough to contain all the usual objects and operations of mathematics, used to rigorously handle "large" categories while avoiding paradoxes.
  • D. Recent Synthetic Differential Geometry
    "Recent Synthetic Differential Geometry" is a mathematical work by Herbert Busemann that develops differential geometry using synthetic, axiomatic methods rather than traditional analytic techniques.
  • E. Grothendieck toposes
    Grothendieck toposes are highly structured categories that generalize topological spaces and serve as a unifying framework for geometry, logic, and cohomology in modern mathematics.
  • 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_69d381b5116081908d85227bab6d3c0c completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4e9a59d688190b1da1ea0ed48fafa completed April 7, 2026, 11:25 a.m.
NED1 Entity disambiguation (via context triple) batch_69d795b2423c8190a7c0e9b6fcbcc6db completed April 9, 2026, 12:04 p.m.
NEDg Description generation batch_69d7998acbf881909b6f063c4bf2d0a6 completed April 9, 2026, 12:20 p.m.
NED2 Entity disambiguation (via description) batch_69d79aa0cc5481908bc14cda8fb6e8b1 completed April 9, 2026, 12:25 p.m.
Created at: April 6, 2026, 12:05 p.m.