Triple
T2815394
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler’s totient function φ(n) |
E54269
|
entity |
| Predicate | minimumOnInterval |
P4229
|
FINISHED |
| Object | For n ≥ 3, φ(n) attains its minimum at prime powers |
—
|
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: For n ≥ 3, φ(n) attains its minimum at prime powers | Statement: [Euler’s totient function φ(n), minimumOnInterval, For n ≥ 3, φ(n) attains its minimum at prime powers]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: minimumOnInterval Context triple: [Euler’s totient function φ(n), minimumOnInterval, For n ≥ 3, φ(n) attains its minimum at prime powers]
-
A.
isMinimumWhen
chosen
Indicates that a value or state is at its smallest or least level precisely under certain specified conditions or circumstances.
-
B.
minimumNumber
Indicates that the associated value is the smallest or least quantity allowed, required, or observed within a given set or context.
-
C.
lowerLimit
Indicates that one value serves as the minimum or smallest allowable bound or threshold for another value or range.
-
D.
minimumWidth
Indicates that there is a specified smallest allowable or required width for something in the relationship.
-
E.
lowestPoint
Indicates that one entity is the point with the minimum vertical position or value relative to another entity or within a specified context.
- 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_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. |
Created at: March 6, 2026, 9:59 p.m.