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.