Triple
T1484054
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Conway’s topograph |
E29423
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
modular group PSL(2,Z)
The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
|
E169191
|
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: modular group PSL(2,Z) | Statement: [Conway’s topograph, relatedTo, modular group PSL(2,Z)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: modular group PSL(2,Z) Context triple: [Conway’s topograph, relatedTo, modular group PSL(2,Z)]
-
A.
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.
-
B.
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.
-
C.
Conway’s topograph
Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
-
D.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
-
E.
Weierstrass elliptic functions
Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
- 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: modular group PSL(2,Z) Triple: [Conway’s topograph, relatedTo, modular group PSL(2,Z)]
Generated description
The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: modular group PSL(2,Z) Target entity description: The modular group PSL(2,ℤ) is a fundamental discrete group of 2×2 integer matrices modulo sign, acting by fractional linear transformations on the upper half-plane and playing a central role in number theory, geometry, and the theory of modular forms.
-
A.
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.
-
B.
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.
-
C.
Conway’s topograph
Conway’s topograph is a geometric visualization tool introduced by mathematician John H. Conway to study binary quadratic forms and their arithmetic properties using a planar graph of curves and regions.
-
D.
Conway groups
Conway groups are a set of three closely related sporadic simple groups discovered by John H. Conway in the study of symmetries of the Leech lattice in group theory.
-
E.
Weierstrass elliptic functions
Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
- 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_69a498da82e08190ba833330d05f380f |
completed | March 1, 2026, 7:51 p.m. |
| NER | Named-entity recognition | batch_69a4c679714c8190ac53630fb49e19c5 |
completed | March 1, 2026, 11:06 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ad15b3a8548190b484a15757aee7b1 |
completed | March 8, 2026, 6:22 a.m. |
| NEDg | Description generation | batch_69ad16bc23808190ba26aa98764f3186 |
completed | March 8, 2026, 6:27 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ad172912488190b77c77e4e61e0183 |
completed | March 8, 2026, 6:28 a.m. |
Created at: March 1, 2026, 8:12 p.m.