Triple
T11098643
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | (2,3,7) triangle group |
E262443
|
entity |
| Predicate | isRelatedTo |
P37
|
FINISHED |
| Object | Klein quartic |
E50328
|
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: Klein quartic | Statement: [(2,3,7) triangle group, isRelatedTo, Klein quartic]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Klein quartic Context triple: [(2,3,7) triangle group, isRelatedTo, Klein quartic]
-
A.
Klein quartic
chosen
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.
-
B.
Clebsch
Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
-
C.
Hurwitz group
A Hurwitz group is a finite group that attains the maximal possible order of the automorphism group of a compact Riemann surface of given genus, as specified by Hurwitz's bound.
-
D.
Kummer surfaces
Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
-
E.
Riemann–Hurwitz formula
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.
- 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_69d6aa9a40d88190a373e2c7e48285db |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d79a0c46308190889b94c23ebaca62 |
completed | April 9, 2026, 12:22 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e441bb14d08190ac01bf3daa34ae43 |
completed | April 19, 2026, 2:45 a.m. |
Created at: April 8, 2026, 9:27 p.m.