Triple

T6901171
Position Surface form Disambiguated ID Type / Status
Subject René Thom E159495 entity
Predicate knownFor P22 FINISHED
Object Thom space construction
The Thom space construction is a fundamental operation in algebraic topology that associates a topological space to a vector bundle, playing a central role in cobordism theory and characteristic classes.
E627199 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: Thom space construction | Statement: [René Thom, knownFor, Thom space construction]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Thom space construction
Context triple: [René Thom, knownFor, Thom space construction]
  • A. Whitney approximation theorem
    The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
  • B. h-cobordism theorem
    The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
  • C. Thom–Mather stratification
    Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
  • D. Atiyah–Hirzebruch spectral sequence
    The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
  • E. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • 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: Thom space construction
Triple: [René Thom, knownFor, Thom space construction]
Generated description
The Thom space construction is a fundamental operation in algebraic topology that associates a topological space to a vector bundle, playing a central role in cobordism theory and characteristic classes.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Thom space construction
Target entity description: The Thom space construction is a fundamental operation in algebraic topology that associates a topological space to a vector bundle, playing a central role in cobordism theory and characteristic classes.
  • A. Whitney approximation theorem
    The Whitney approximation theorem is a fundamental result in differential topology stating that any continuous function between smooth manifolds can be uniformly approximated by smooth functions.
  • B. h-cobordism theorem
    The h-cobordism theorem is a fundamental result in differential topology that classifies when two high-dimensional manifolds are diffeomorphic by analyzing the structure of a cobordism between them.
  • C. Thom–Mather stratification
    Thom–Mather stratification is a refined notion of stratification in differential topology that imposes strong regularity and control conditions on how smooth strata fit together, generalizing and strengthening Whitney stratifications.
  • D. Atiyah–Hirzebruch spectral sequence
    The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
  • E. Hirzebruch signature theorem
    The Hirzebruch signature theorem is a fundamental result in differential topology that expresses the signature of a smooth, compact, oriented 4k-dimensional manifold as a polynomial in its Pontryagin classes.
  • 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_69c6883822e0819091e321526f20ae0a completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6d9603f448190bb9f963c17ca206d completed March 27, 2026, 7:24 p.m.
NED1 Entity disambiguation (via context triple) batch_69c748f0dc448190914e38d780644698 completed March 28, 2026, 3:20 a.m.
NEDg Description generation batch_69c749f7ab5c8190ab823fac27f7484d completed March 28, 2026, 3:24 a.m.
NED2 Entity disambiguation (via description) batch_69c74a6f828c8190bf0cc56227b1a5b2 completed March 28, 2026, 3:26 a.m.
Created at: March 27, 2026, 2:24 p.m.