Triple
T2815402
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler’s totient function φ(n) |
E54269
|
entity |
| Predicate | groupTheoryInterpretation |
P43792
|
FINISHED |
| Object | φ(n) equals the order of the multiplicative group (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: φ(n) equals the order of the multiplicative group (ℤ/nℤ)× | Statement: [Euler’s totient function φ(n), groupTheoryInterpretation, φ(n) equals the order of the multiplicative group (ℤ/nℤ)×]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: groupTheoryInterpretation Context triple: [Euler’s totient function φ(n), groupTheoryInterpretation, φ(n) equals the order of the multiplicative group (ℤ/nℤ)×]
-
A.
associatedCayleyGraph
Indicates that there is a Cayley graph constructed from, or corresponding to, the given algebraic structure or group.
-
B.
usesSymmetryGroup
Indicates that one entity employs or is based on a particular symmetry group in its structure, behavior, or formulation.
-
C.
hasRepresentationTheoryDevelopedBy
Indicates that the representation theory of one mathematical object or structure was developed or formulated by a particular person or group.
-
D.
automorphismGroupOrder
Indicates the size of the group of all structure-preserving bijections (automorphisms) of an object under composition.
-
E.
isSemidirectProductOf
Indicates that a group is constructed as a semidirect product of two subgroups, where one subgroup acts on the other via automorphisms in a way that generalizes the direct product.
- 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_69ab49de0af08190b3da69683be1e728 |
completed | March 6, 2026, 9:40 p.m. |
| NER | Named-entity recognition | batch_69abde4d29488190a32461906dd9ea7e |
completed | March 7, 2026, 8:14 a.m. |
| PD | Predicate disambiguation | batch_69abdd0740208190911dc9c9546a79ae |
completed | March 7, 2026, 8:08 a.m. |
| PDg | Predicate description generation | batch_69abde0f4c648190b9812e64f30c39da |
completed | March 7, 2026, 8:13 a.m. |
Created at: March 6, 2026, 9:59 p.m.