Triple
T26255033
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | SL(2,ℤ) |
E656692
|
entity |
| Predicate | principalCongruenceSubgroupDefinition |
P160157
|
FINISHED |
| Object | kernel of reduction mod N homomorphism SL(2,ℤ) → SL(2,ℤ/Nℤ) |
—
|
LITERAL FINISHED |
How this triple was built (2 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: kernel of reduction mod N homomorphism SL(2,ℤ) → SL(2,ℤ/Nℤ) | Statement: [SL(2,ℤ), principalCongruenceSubgroupDefinition, kernel of reduction mod N homomorphism SL(2,ℤ) → SL(2,ℤ/Nℤ)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: principalCongruenceSubgroupDefinition Context triple: [SL(2,ℤ), principalCongruenceSubgroupDefinition, kernel of reduction mod N homomorphism SL(2,ℤ) → SL(2,ℤ/Nℤ)]
-
A.
congruenceSubgroups
chosen
Indicates that there is a relationship between groups where one is a congruence subgroup of the other, typically defined by congruence conditions modulo some integer or ideal.
-
B.
thirdCongruenceModulus
Indicates that the third argument serves as the modulus with respect to which two other quantities are congruent.
-
C.
secondCongruence
Indicates that one entity is congruent to another with respect to a second, distinct congruence relation or modular equivalence condition.
-
D.
firstCongruenceModulus
Indicates that the specified value is the modulus used in the first congruence of a system of modular equations or congruence relations.
-
E.
firstCongruence
Indicates that one entity is the initial or primary instance in a set of congruent (equivalent in form or measure) entities or relationships.
- F. None of above.
Provenance (3 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_69ee5b4d25ac819086acb51184602576 |
completed | April 26, 2026, 6:37 p.m. |
| NER | Named-entity recognition | batch_69f6430a93a48190854ce71df680b2fa |
completed | May 2, 2026, 6:31 p.m. |
| PD | Predicate disambiguation | batch_69f641da05b881909f6283c988639c53 |
completed | May 2, 2026, 6:26 p.m. |
Created at: April 26, 2026, 9:08 p.m.