Triple
T38260650
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kantorovich duality |
E1017918
|
entity |
| Predicate | hasDualFormulation |
P90301
|
FINISHED |
| Object | maximization over pairs of functions bounded by cost |
—
|
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: maximization over pairs of functions bounded by cost | Statement: [Kantorovich duality, hasDualFormulation, maximization over pairs of functions bounded by cost]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasDualFormulation Context triple: [Kantorovich duality, hasDualFormulation, maximization over pairs of functions bounded by cost]
-
A.
hasCanonicalFormulation
Indicates that one entity is the standard or officially accepted formulation or expression of another entity.
-
B.
hasEquivalentFormulation
chosen
Indicates that two representations, statements, or formulations express the same underlying meaning, condition, or effect, even if they differ in form.
-
C.
hasDualBasis
Indicates that one mathematical structure serves as the dual basis corresponding to another basis, typically in a dual vector space.
-
D.
haveDualityProperty
Indicates that an entity possesses a characteristic or state that inherently consists of two complementary, contrasting, or coexisting aspects.
-
E.
hasFormulation
Indicates that one entity is expressed, prepared, or configured in a particular form or composition defined by another entity.
- 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_69f76de33e4481909099fa812709bd42 |
completed | May 3, 2026, 3:46 p.m. |
| NER | Named-entity recognition | batch_69fcc3321ef081908023590ba70ba0cf |
completed | May 7, 2026, 4:52 p.m. |
| PD | Predicate disambiguation | batch_69fcb0fdc6e08190b05e894c59481a0d |
completed | May 7, 2026, 3:34 p.m. |
Created at: May 3, 2026, 4:30 p.m.