Triple

T7338359
Position Surface form Disambiguated ID Type / Status
Subject Leech lattice E169185 entity
Predicate relatedTo P37 FINISHED
Object E8 lattice
The E8 lattice is an eight-dimensional, highly symmetric even unimodular lattice that plays a central role in Lie theory, sphere packing, and string theory.
E656669 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: E8 lattice | Statement: [Leech lattice, relatedTo, E8 lattice]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: E8 lattice
Context triple: [Leech lattice, relatedTo, E8 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. Clebsch
    Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
  • C. 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.
  • D. Regular Polytopes
    "Regular Polytopes" is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the theory and classification of highly symmetric polytopes in various dimensions.
  • E. 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.
  • 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: E8 lattice
Triple: [Leech lattice, relatedTo, E8 lattice]
Generated description
The E8 lattice is an eight-dimensional, highly symmetric even unimodular lattice that plays a central role in Lie theory, sphere packing, and string theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: E8 lattice
Target entity description: The E8 lattice is an eight-dimensional, highly symmetric even unimodular lattice that plays a central role in Lie theory, sphere packing, and string theory.
  • 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. Clebsch
    Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
  • C. 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.
  • D. Regular Polytopes
    "Regular Polytopes" is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the theory and classification of highly symmetric polytopes in various dimensions.
  • E. 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.
  • 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_69c68a57710481909f0c1f3c6ebdb6f2 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f0d599c88190875514eae7084f8d completed March 27, 2026, 9:04 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7ef266fd0819096cf3ece3fff6b90 completed March 28, 2026, 3:09 p.m.
NEDg Description generation batch_69c7efa4f5148190842f30988cbea94c completed March 28, 2026, 3:11 p.m.
NED2 Entity disambiguation (via description) batch_69c7f0092bac819080ded1863f99290a completed March 28, 2026, 3:13 p.m.
Created at: March 27, 2026, 3:04 p.m.