Triple
T1483825
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Conway group Co1 |
E29418
|
entity |
| Predicate | isSubgroupOf |
P1244
|
FINISHED |
| Object |
automorphism group of the Leech lattice
The automorphism group of the Leech lattice is the large sporadic simple-related group of symmetries preserving the structure of the 24-dimensional Leech lattice, central to the theory of finite simple groups and lattice sphere packings.
|
E29418
|
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: automorphism group of the Leech lattice | Statement: [Conway group Co1, isSubgroupOf, automorphism group of the Leech lattice]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: automorphism group of the Leech lattice Context triple: [Conway group Co1, isSubgroupOf, automorphism group of the Leech lattice]
-
A.
Leech lattice
The Leech lattice is a highly symmetric 24-dimensional lattice in Euclidean space, notable for its dense sphere packing and deep connections to sporadic simple groups and modular forms.
-
B.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
-
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.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
- 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: automorphism group of the Leech lattice Triple: [Conway group Co1, isSubgroupOf, automorphism group of the Leech lattice]
Generated description
The automorphism group of the Leech lattice is the large sporadic simple-related group of symmetries preserving the structure of the 24-dimensional Leech lattice, central to the theory of finite simple groups and lattice sphere packings.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: automorphism group of the Leech lattice Target entity description: The automorphism group of the Leech lattice is the large sporadic simple-related group of symmetries preserving the structure of the 24-dimensional Leech lattice, central to the theory of finite simple groups and lattice sphere packings.
-
A.
Leech lattice
The Leech lattice is a highly symmetric 24-dimensional lattice in Euclidean space, notable for its dense sphere packing and deep connections to sporadic simple groups and modular forms.
-
B.
Conway–Norton collaboration
The Conway–Norton collaboration was a joint mathematical effort, led by John Conway and Simon Norton, that played a key role in developing the theory of monstrous moonshine and the construction of the Monster group.
-
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
chosen
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.
The Classical Groups: Their Invariants and Representations
The Classical Groups: Their Invariants and Representations is a foundational mathematical monograph by Hermann Weyl that systematically develops the theory of classical Lie groups, their invariants, and their representation theory.
- F. None of above.
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_69ad1ca4c4e481909ea0ca76841454b1 |
completed | March 8, 2026, 6:52 a.m. |
| NEDg | Description generation | batch_69ad1d28d8708190b284676ff407c3ec |
completed | March 8, 2026, 6:54 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69ad1ea291448190ba1c8593d11f86ee |
completed | March 8, 2026, 7 a.m. |
Created at: March 1, 2026, 8:12 p.m.