Triple
T2815391
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler’s totient function φ(n) |
E54269
|
entity |
| Predicate | asymptoticBehavior |
P6112
|
FINISHED |
| Object | φ(n) is typically of size ≈ n · 6/π² |
—
|
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) is typically of size ≈ n · 6/π² | Statement: [Euler’s totient function φ(n), asymptoticBehavior, φ(n) is typically of size ≈ n · 6/π²]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: asymptoticBehavior Context triple: [Euler’s totient function φ(n), asymptoticBehavior, φ(n) is typically of size ≈ n · 6/π²]
-
A.
divergesAt
Indicates that a process, function, or behavior fails to converge or terminate at a specific point or under specific conditions.
-
B.
finiteAt
Indicates that a function, quantity, or value remains finite (not infinite or undefined) at a specified point or under a given condition.
-
C.
asymmetric
Indicates that the relationship between two entities never holds in both directions simultaneously, so if it holds from A to B it cannot also hold from B to A.
-
D.
canBeAnalyticallyContinuedTo
Indicates that one mathematical object (typically a function) can be extended beyond its original domain in a consistent, analytic way that preserves its defining properties.
-
E.
limitBehavior
chosen
Indicates how an entity behaves or changes as it approaches a specified limit or boundary condition.
- 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.