Triple
T10617354
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Alexander Beilinson |
E276155
|
entity |
| Predicate | knownFor |
P22
|
FINISHED |
| Object |
Beilinson spectral sequence
The Beilinson spectral sequence is a powerful tool in algebraic geometry that reconstructs coherent sheaves on projective space from their cohomology via a resolution by exceptional collections.
|
E876107
|
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: Beilinson spectral sequence | Statement: [Alexander Beilinson, knownFor, Beilinson spectral sequence]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Beilinson spectral sequence Context triple: [Alexander Beilinson, knownFor, Beilinson spectral sequence]
-
A.
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.
-
B.
Deligne cohomology
Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
-
C.
Weil cohomology
Weil cohomology is a type of cohomology theory for algebraic varieties that satisfies specific axioms enabling the proof of the Weil conjectures and the development of modern algebraic geometry.
-
D.
Beilinson conjectures
Beilinson conjectures are a set of deep conjectures in arithmetic geometry that relate special values of L-functions to algebraic K-theory and motivic cohomology, generalizing phenomena seen in cases like the Birch and Swinnerton-Dyer conjecture.
-
E.
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.
- 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: Beilinson spectral sequence Triple: [Alexander Beilinson, knownFor, Beilinson spectral sequence]
Generated description
The Beilinson spectral sequence is a powerful tool in algebraic geometry that reconstructs coherent sheaves on projective space from their cohomology via a resolution by exceptional collections.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Beilinson spectral sequence Target entity description: The Beilinson spectral sequence is a powerful tool in algebraic geometry that reconstructs coherent sheaves on projective space from their cohomology via a resolution by exceptional collections.
-
A.
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.
-
B.
Deligne cohomology
Deligne cohomology is a refined cohomology theory in algebraic geometry that combines singular cohomology and differential forms to capture both topological and arithmetic information about complex algebraic varieties.
-
C.
Weil cohomology
Weil cohomology is a type of cohomology theory for algebraic varieties that satisfies specific axioms enabling the proof of the Weil conjectures and the development of modern algebraic geometry.
-
D.
Beilinson conjectures
Beilinson conjectures are a set of deep conjectures in arithmetic geometry that relate special values of L-functions to algebraic K-theory and motivic cohomology, generalizing phenomena seen in cases like the Birch and Swinnerton-Dyer conjecture.
-
E.
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.
- 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_69d6aaf948d88190806cc3a8c47a3fb2 |
completed | April 8, 2026, 7:22 p.m. |
| NER | Named-entity recognition | batch_69d6df6e2df4819099a19b59d90d0dd1 |
completed | April 8, 2026, 11:06 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d96b7bb7108190b0f1cbe4117abec0 |
completed | April 10, 2026, 9:28 p.m. |
| NEDg | Description generation | batch_69d96dee84f48190bf5b0cb1115a8bba |
completed | April 10, 2026, 9:38 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69d9708824208190acf75933962d690f |
completed | April 10, 2026, 9:50 p.m. |
Created at: April 8, 2026, 7:33 p.m.