Triple

T7011078
Position Surface form Disambiguated ID Type / Status
Subject Samuel Eilenberg E162580 entity
Predicate notableWork P4 FINISHED
Object 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.
E634842 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: Eilenberg–MacLane spaces | Statement: [Samuel Eilenberg, notableWork, Eilenberg–MacLane spaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Eilenberg–MacLane spaces
Context triple: [Samuel Eilenberg, notableWork, Eilenberg–MacLane spaces]
  • A. "Algebraic Topology"
    "Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
  • B. 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.
  • C. 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.
  • D. Atiyah–Segal axioms
    The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
  • E. Grothendieck spectral sequence
    The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of 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: Eilenberg–MacLane spaces
Triple: [Samuel Eilenberg, notableWork, Eilenberg–MacLane spaces]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Eilenberg–MacLane spaces
Target entity description: 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.
  • A. "Algebraic Topology"
    "Algebraic Topology" is a foundational mathematical text that develops topological concepts using algebraic methods such as homology and cohomology theories.
  • B. 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.
  • C. 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.
  • D. Atiyah–Segal axioms
    The Atiyah–Segal axioms are a set of mathematical conditions that rigorously define topological quantum field theories as functorial assignments from geometric data to algebraic structures.
  • E. Grothendieck spectral sequence
    The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of 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_69c6885a127c8190867b059bdccf13ff completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6dc5729448190af66dbd6f3e8936e completed March 27, 2026, 7:36 p.m.
NED1 Entity disambiguation (via context triple) batch_69c76a4bd424819097e1543ec59979ff completed March 28, 2026, 5:42 a.m.
NEDg Description generation batch_69c76b1ef6f481908f4c4f610328f633 completed March 28, 2026, 5:46 a.m.
NED2 Entity disambiguation (via description) batch_69c76c01679c8190b61f642c23c25ed5 completed March 28, 2026, 5:49 a.m.
Created at: March 27, 2026, 2:34 p.m.