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.