Triple

T10617353
Position Surface form Disambiguated ID Type / Status
Subject Alexander Beilinson E276155 entity
Predicate knownFor P22 FINISHED
Object Beilinson regulator
The Beilinson regulator is a deep arithmetic-geometric map connecting algebraic K-theory of varieties to their Deligne or absolute Hodge cohomology, playing a central role in conjectural formulas for special values of L-functions.
E876106 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 regulator | Statement: [Alexander Beilinson, knownFor, Beilinson regulator]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Beilinson regulator
Context triple: [Alexander Beilinson, knownFor, Beilinson regulator]
  • A. 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.
  • 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. Hodge–Riemann bilinear relations
    The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
  • D. Standard Conjectures on Algebraic Cycles
    The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
  • E. Arakelov theory
    Arakelov theory is a framework in arithmetic geometry that extends intersection theory to arithmetic surfaces by incorporating both finite and infinite places, enabling analytic tools to study Diophantine problems.
  • 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 regulator
Triple: [Alexander Beilinson, knownFor, Beilinson regulator]
Generated description
The Beilinson regulator is a deep arithmetic-geometric map connecting algebraic K-theory of varieties to their Deligne or absolute Hodge cohomology, playing a central role in conjectural formulas for special values of L-functions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Beilinson regulator
Target entity description: The Beilinson regulator is a deep arithmetic-geometric map connecting algebraic K-theory of varieties to their Deligne or absolute Hodge cohomology, playing a central role in conjectural formulas for special values of L-functions.
  • A. 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.
  • 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. Hodge–Riemann bilinear relations
    The Hodge–Riemann bilinear relations are fundamental positivity and orthogonality conditions on the intersection form in Hodge theory that underpin results such as the hard Lefschetz theorem and the Hodge index theorem.
  • D. Standard Conjectures on Algebraic Cycles
    The Standard Conjectures on Algebraic Cycles are a set of deep, still unproven hypotheses in algebraic geometry that aim to provide a foundational theory of algebraic cycles and their cohomological properties, underpinning much of the modern theory of motives.
  • E. Arakelov theory
    Arakelov theory is a framework in arithmetic geometry that extends intersection theory to arithmetic surfaces by incorporating both finite and infinite places, enabling analytic tools to study Diophantine problems.
  • 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.