Triple
T2815383
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Euler’s totient function φ(n) |
E54269
|
entity |
| Predicate | primeFormula |
P2310
|
FINISHED |
| Object | φ(p) = p − 1 for prime p |
—
|
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(p) = p − 1 for prime p | Statement: [Euler’s totient function φ(n), primeFormula, φ(p) = p − 1 for prime p]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: primeFormula Context triple: [Euler’s totient function φ(n), primeFormula, φ(p) = p − 1 for prime p]
-
A.
recitesFormula
Indicates that one entity verbally or mentally repeats a specific formula, such as a set phrase, equation, or ritual wording, typically from memory.
-
B.
keyFormula
chosen
Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
-
C.
primeFactorization
Indicates that one entity is the decomposition of another entity into a multiset or sequence of prime factors whose product equals the original.
-
D.
formulaUsed
Indicates that a particular formula is employed or applied in performing a calculation, derivation, or reasoning step.
-
E.
mathematicallyExpressedBy
Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.
- 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.