Triple

T11219611
Position Surface form Disambiguated ID Type / Status
Subject Characteristic Classes E265523 entity
Predicate hasSubject P450 FINISHED
Object CW complexes
CW complexes are topological spaces built by inductively attaching cells of increasing dimension, providing a flexible and combinatorially tractable framework for algebraic topology.
E911364 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: CW complexes | Statement: [Characteristic Classes, hasSubject, CW complexes]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: CW complexes
Context triple: [Characteristic Classes, hasSubject, CW complexes]
  • A. Eilenberg–MacLane spaces
    Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
  • B. Eilenberg–Steenrod axioms
    The Eilenberg–Steenrod axioms are a foundational set of conditions that formally characterize homology theories in algebraic topology.
  • C. Alexandrov–Čech cohomology
    Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
  • D. 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.
  • E. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • 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: CW complexes
Triple: [Characteristic Classes, hasSubject, CW complexes]
Generated description
CW complexes are topological spaces built by inductively attaching cells of increasing dimension, providing a flexible and combinatorially tractable framework for algebraic topology.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: CW complexes
Target entity description: CW complexes are topological spaces built by inductively attaching cells of increasing dimension, providing a flexible and combinatorially tractable framework for algebraic topology.
  • A. Eilenberg–MacLane spaces
    Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
  • B. Eilenberg–Steenrod axioms
    The Eilenberg–Steenrod axioms are a foundational set of conditions that formally characterize homology theories in algebraic topology.
  • C. Alexandrov–Čech cohomology
    Alexandrov–Čech cohomology is a topological cohomology theory that computes invariants of spaces using inverse limits over open covers, closely related to and often coinciding with sheaf cohomology.
  • D. 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.
  • E. Alexander–Spanier cohomology
    Alexander–Spanier cohomology is a cohomology theory in algebraic topology defined using cochains on all finite subsets of a space, notable for its generality and close relationship to Čech and singular cohomology.
  • 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_69d6aac59460819089b9848b27f57848 completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d7e8eb84c48190b4f3bede254afde2 completed April 9, 2026, 5:59 p.m.
NED1 Entity disambiguation (via context triple) batch_69e4976f38788190855aed6338d819b7 completed April 19, 2026, 8:50 a.m.
NEDg Description generation batch_69e49d37989881909c7e75ddfff06726 completed April 19, 2026, 9:15 a.m.
NED2 Entity disambiguation (via description) batch_69e49f41a1f8819087cc15527dc7ff63 completed April 19, 2026, 9:24 a.m.
Created at: April 8, 2026, 9:30 p.m.