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.