Triple
T2364495
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Riemann surface |
E47348
|
entity |
| Predicate | hasTheorem |
P38252
|
FINISHED |
| Object | Riemann–Hurwitz formula |
E47610
|
NE FINISHED |
How this triple was built (2 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: Riemann–Hurwitz formula | Statement: [Riemann surface, hasTheorem, Riemann–Hurwitz formula]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Riemann–Hurwitz formula Context triple: [Riemann surface, hasTheorem, Riemann–Hurwitz formula]
-
A.
Riemann–Hurwitz formula
chosen
The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
-
B.
Riemann–Roch theorem
The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
-
C.
Hirzebruch–Riemann–Roch theorem
The Hirzebruch–Riemann–Roch theorem is a fundamental result in algebraic geometry and topology that expresses the holomorphic Euler characteristic of a complex manifold in terms of characteristic classes, unifying and extending classical Riemann–Roch type formulas.
-
D.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
-
E.
Grothendieck–Riemann–Roch theorem
The Grothendieck–Riemann–Roch theorem is a fundamental result in algebraic geometry that generalizes the classical Riemann–Roch theorem by relating pushforwards in K-theory to pushforwards in cohomology via characteristic classes.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69a88a1a4a6081908645b0f2914521ab |
completed | March 4, 2026, 7:38 p.m. |
| NER | Named-entity recognition | batch_69abd0d813dc8190aa331cdca0b75eca |
completed | March 7, 2026, 7:16 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69aeb3c5c4b881909ad3223206fb2940 |
completed | March 9, 2026, 11:49 a.m. |
Created at: March 4, 2026, 7:55 p.m.