Triple

T6475544
Position Surface form Disambiguated ID Type / Status
Subject Dennis Sullivan E146060 entity
Predicate hasWork P6260 FINISHED
Object Sullivan minimal model in rational homotopy theory
The Sullivan minimal model in rational homotopy theory is a canonical commutative differential graded algebra that encodes the rational homotopy type of a topological space in an algebraic form.
E596068 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: Sullivan minimal model in rational homotopy theory | Statement: [Dennis Sullivan, hasWork, Sullivan minimal model in rational homotopy theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Sullivan minimal model in rational homotopy theory
Context triple: [Dennis Sullivan, hasWork, Sullivan minimal model in rational homotopy theory]
  • A. L’Analysis Situs et la Géométrie Algébrique
    L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
  • B. 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.
  • 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. Cartan theorems A and B
    Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
  • E. Serre spectral sequence
    The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
  • 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: Sullivan minimal model in rational homotopy theory
Triple: [Dennis Sullivan, hasWork, Sullivan minimal model in rational homotopy theory]
Generated description
The Sullivan minimal model in rational homotopy theory is a canonical commutative differential graded algebra that encodes the rational homotopy type of a topological space in an algebraic form.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Sullivan minimal model in rational homotopy theory
Target entity description: The Sullivan minimal model in rational homotopy theory is a canonical commutative differential graded algebra that encodes the rational homotopy type of a topological space in an algebraic form.
  • A. L’Analysis Situs et la Géométrie Algébrique
    L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
  • B. 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.
  • 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. Cartan theorems A and B
    Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
  • E. Serre spectral sequence
    The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
  • 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_69c008fec7408190af7b146dc63d9750 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c06a49b3bc8190ad80c6ca2dd15c68 completed March 22, 2026, 10:16 p.m.
NED1 Entity disambiguation (via context triple) batch_69c653a595b881909e5d3cb781ad5ad4 completed March 27, 2026, 9:53 a.m.
NEDg Description generation batch_69c6553c17bc81908719ecc7db9e3960 completed March 27, 2026, 10 a.m.
NED2 Entity disambiguation (via description) batch_69c655f4ee5c81909620e732b72ee694 completed March 27, 2026, 10:03 a.m.
Created at: March 22, 2026, 4:50 p.m.