Triple
T12597139
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebyshev function θ(x) |
E300761
|
entity |
| Predicate | monotonicity |
P10675
|
FINISHED |
| Object | non-decreasing in x |
—
|
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: non-decreasing in x | Statement: [Chebyshev function θ(x), monotonicity, non-decreasing in x]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: monotonicity Context triple: [Chebyshev function θ(x), monotonicity, non-decreasing in x]
-
A.
monotoneIn
chosen
Indicates that the relationship or function preserves a specified order when one of its arguments increases, meaning larger inputs (in that argument) do not lead to smaller outputs with respect to the given ordering.
-
B.
arity
Indicates the number of arguments or participants that a relation or function takes.
-
C.
monogeneric
Indicates that a taxonomic group (such as a family or subfamily) contains only a single genus.
-
D.
linearity
Indicates that a relationship between quantities preserves addition and scalar multiplication, so outputs change in direct proportion to inputs.
-
E.
hasMonodromy
Indicates that one mathematical object exhibits a monodromy action or structure with respect to another (typically along loops in a parameter or base space).
- 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_69d7bdea2ca881908f379526c13b1145 |
completed | April 9, 2026, 2:55 p.m. |
| NER | Named-entity recognition | batch_69d954e6e20481908bca684c4b497c48 |
completed | April 10, 2026, 7:52 p.m. |
| PD | Predicate disambiguation | batch_69d95416cbd88190b2c65196162349bc |
completed | April 10, 2026, 7:48 p.m. |
Created at: April 9, 2026, 5:08 p.m.