Triple
T9844216
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cauchy residue theorem |
E239298
|
entity |
| Predicate | variantFormula |
P4680
|
FINISHED |
| Object | ∮_γ f(z) dz = 2πi Σ n(γ, a_k) Res(f, a_k) |
—
|
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: ∮_γ f(z) dz = 2πi Σ n(γ, a_k) Res(f, a_k) | Statement: [Cauchy residue theorem, variantFormula, ∮_γ f(z) dz = 2πi Σ n(γ, a_k) Res(f, a_k)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: variantFormula Context triple: [Cauchy residue theorem, variantFormula, ∮_γ f(z) dz = 2πi Σ n(γ, a_k) Res(f, a_k)]
-
A.
variant
chosen
Indicates that one entity is an alternative form, version, or variation of another entity.
-
B.
formulaUsed
Indicates that a particular formula is employed or applied in performing a calculation, derivation, or reasoning step.
-
C.
formulaType
Indicates the specific kind or category of formula associated with an entity or expression.
-
D.
mathematicallyExpressedBy
Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.
-
E.
keyFormula
Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
- 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_69ca84e3f0c48190ada72a65ebd50efd |
completed | March 30, 2026, 2:12 p.m. |
| NER | Named-entity recognition | batch_69cdb35dc29c819080203be5b904dc9d |
completed | April 2, 2026, 12:07 a.m. |
| PD | Predicate disambiguation | batch_69cd03e57cac8190914bb5ae608a6e0e |
completed | April 1, 2026, 11:39 a.m. |
Created at: March 30, 2026, 8:33 p.m.