Triple
T12597008
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Jordan’s totient functions |
E300758
|
entity |
| Predicate | multiplicativeGroupInterpretation |
P105603
|
FINISHED |
| Object | J_k(n) counts k-tuples that generate (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: J_k(n) counts k-tuples that generate (Z/nZ,+) | Statement: [Jordan’s totient functions, multiplicativeGroupInterpretation, J_k(n) counts k-tuples that generate (Z/nZ,+)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: multiplicativeGroupInterpretation Context triple: [Jordan’s totient functions, multiplicativeGroupInterpretation, J_k(n) counts k-tuples that generate (Z/nZ,+)]
-
A.
groupTheoryInterpretation
Indicates a mapping that interprets abstract group-theoretic expressions or structures in terms of a specific group and its operations.
-
B.
multiplicativeInverse
Indicates that one quantity is the multiplicative inverse of another, meaning their product equals the multiplicative identity (typically 1).
-
C.
hasAdditiveGroupIsomorphicTo
Indicates that the additive group structure of one algebraic object is isomorphic (structure-preserving bijection exists) to the additive group structure of another.
-
D.
hasAdditiveGroup
Indicates that something possesses an associated additive group structure, typically meaning its elements form a group under an addition-like operation.
-
E.
isAutomorphismGroupOf
Indicates that a group is the full automorphism group consisting of all structure-preserving bijections (automorphisms) of a given mathematical object.
- F. None of above. chosen
Provenance (4 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_69d7bdea2ca881908f379526c13b1145 |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d954e6e20481908bca684c4b497c48 |
completed | April 10, 2026, 7:52 p.m. |
| PD | Predicate disambiguation | batch_69d95416cbd88190b2c65196162349bc |
completed | April 10, 2026, 7:48 p.m. |
| PDg | Predicate description generation | batch_69d954e351f88190869220d46e0ce282 |
completed | April 10, 2026, 7:52 p.m. |
Created at: April 9, 2026, 5:08 p.m.