Triple
T2815403
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler’s totient function φ(n) |
E54269
|
entity |
| Predicate | EulerTheoremStatement |
P38252
|
FINISHED |
| Object | If gcd(a,n) = 1 then a^{φ(n)} ≡ 1 (mod n) |
—
|
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: If gcd(a,n) = 1 then a^{φ(n)} ≡ 1 (mod n) | Statement: [Euler’s totient function φ(n), EulerTheoremStatement, If gcd(a,n) = 1 then a^{φ(n)} ≡ 1 (mod n)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: EulerTheoremStatement
Context triple: [Euler’s totient function φ(n), EulerTheoremStatement, If gcd(a,n) = 1 then a^{φ(n)} ≡ 1 (mod n)]
-
A.
EuclideanFunction
Indicates a relationship defined by a Euclidean distance–based function, typically mapping entities or their attributes to values derived from Euclidean metric properties.
-
B.
hasTheorem
chosen
Indicates that one entity (typically a mathematical theory, field, or work) includes, establishes, or is associated with a particular theorem.
-
C.
hasTheoremNamedAfter
Indicates that a theorem is named in honor of or after a particular person or entity.
-
D.
primeNumberTheoremRelation
Indicates the asymptotic relationship between the distribution of prime numbers and the logarithmic growth of integers, as formalized by the prime number theorem.
-
E.
EulerCharacteristic
Indicates the topological invariant of a space that equals, in a suitable decomposition, the alternating sum of the counts of its cells (e.g., vertices − edges + faces).
- 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.