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.