Triple
T11098652
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | (2,3,7) triangle group |
E262443
|
entity |
| Predicate | isAssociatedWith |
P2830
|
FINISHED |
| Object |
Hurwitz surfaces
Hurwitz surfaces are compact Riemann surfaces of maximal possible automorphism group size for their genus, achieving the Hurwitz bound of 84(g−1) symmetries.
|
E907201
|
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: Hurwitz surfaces | Statement: [(2,3,7) triangle group, isAssociatedWith, Hurwitz surfaces]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hurwitz surfaces Context triple: [(2,3,7) triangle group, isAssociatedWith, Hurwitz surfaces]
-
A.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
-
B.
Hurwitz space
A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
-
C.
Hurwitz numbers
Hurwitz numbers are algebraic invariants that count branched coverings of the Riemann sphere (or other curves) with specified ramification data, playing a key role in enumerative geometry and mathematical physics.
-
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.
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.
- 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: Hurwitz surfaces Triple: [(2,3,7) triangle group, isAssociatedWith, Hurwitz surfaces]
Generated description
Hurwitz surfaces are compact Riemann surfaces of maximal possible automorphism group size for their genus, achieving the Hurwitz bound of 84(g−1) symmetries.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hurwitz surfaces Target entity description: Hurwitz surfaces are compact Riemann surfaces of maximal possible automorphism group size for their genus, achieving the Hurwitz bound of 84(g−1) symmetries.
-
A.
Hurwitz bound on automorphism groups of curves
The Hurwitz bound on automorphism groups of curves is a classical result in algebraic geometry stating that a compact Riemann surface of genus at least 2 has at most 84(g − 1) automorphisms.
-
B.
Hurwitz space
A Hurwitz space is a moduli space that parametrizes branched covers of Riemann surfaces (or algebraic curves) with specified branching data.
-
C.
Hurwitz numbers
Hurwitz numbers are algebraic invariants that count branched coverings of the Riemann sphere (or other curves) with specified ramification data, playing a key role in enumerative geometry and mathematical physics.
-
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.
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.
- 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_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. |
| NEDg | Description generation | batch_69e44c0606408190819b9d3fd58f818f |
completed | April 19, 2026, 3:29 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69e4510dc55081908f89aab15726b2a8 |
completed | April 19, 2026, 3:50 a.m. |
Created at: April 8, 2026, 9:27 p.m.