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.