Triple
T10772662
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Grothendieck–Riemann–Roch theorem |
E254119
|
entity |
| Predicate | instanceOf |
P0
|
FINISHED |
| Object | Riemann–Roch type theorem |
C24993
|
CONCEPT FINISHED |
How this triple was built (1 step)
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.
CD
Concept disambiguation
gpt-5-mini-2025-08-07
Target class: Riemann–Roch type theorem Context triple: [Grothendieck–Riemann–Roch theorem, instanceOf, Riemann–Roch type theorem]
-
A.
curve over the rational numbers
A curve over the rational numbers is an algebraic curve defined by polynomial equations with rational coefficients, considered together with its set of rational solutions and their arithmetic properties.
-
B.
area of algebraic geometry
An area of algebraic geometry is a subfield focused on a specific collection of problems, techniques, and structures related to the study of solutions to polynomial equations and their geometric properties.
-
C.
divisor in algebraic geometry
A divisor in algebraic geometry is a formal finite integer linear combination of irreducible codimension-one subvarieties (or points on a curve), used to encode zeros and poles of rational functions and to study line bundles and linear systems.
-
D.
result in arithmetic geometry
chosen
A result in arithmetic geometry is a theorem or proposition that connects number-theoretic properties of solutions to polynomial equations with the geometric structure of the varieties they define over arithmetic fields.
-
E.
nonsingular curve
A nonsingular curve is an algebraic curve with no singular points, meaning it is smooth everywhere and has a well-defined tangent line at every point.
- F. None of above.
Provenance (1 batch)
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_69d6aa5f54f4819082d0bbcb6f8797e6 |
completed | April 8, 2026, 7:19 p.m. |
Created at: April 8, 2026, 9:16 p.m.