Triple
T1285997
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | generalized binomial theorem |
E27434
|
entity |
| Predicate | mainFormula |
P2310
|
FINISHED |
| Object | (1+z)^α = Σ_{k=0}^{∞} (α choose k) z^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: (1+z)^α = Σ_{k=0}^{∞} (α choose k) z^k | Statement: [generalized binomial theorem, mainFormula, (1+z)^α = Σ_{k=0}^{∞} (α choose k) z^k]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: mainFormula
Context triple: [generalized binomial theorem, mainFormula, (1+z)^α = Σ_{k=0}^{∞} (α choose k) z^k]
-
A.
formulaUsed
Indicates that a particular formula is employed or applied in performing a calculation, derivation, or reasoning step.
-
B.
keyFormula
chosen
Indicates that a formula serves as the primary or defining expression associated with an entity or relationship.
-
C.
recitesFormula
Indicates that one entity verbally or mentally repeats a specific formula, such as a set phrase, equation, or ritual wording, typically from memory.
-
D.
mathematicallyExpressedBy
Indicates that something (such as a concept, quantity, or relationship) is represented or captured using a specific mathematical expression or formulation.
-
E.
mathematicallyFormulatedBy
Indicates that something (such as a concept, model, or theory) is expressed or defined using mathematical formulations created by a particular agent.
- 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_69a496d4ec448190ad653b2590c46711 |
completed | March 1, 2026, 7:43 p.m. |
| NER | Named-entity recognition | batch_69a4c0b85eb48190a8b61dc397fa6390 |
completed | March 1, 2026, 10:42 p.m. |
| PD | Predicate disambiguation | batch_69a4bee276d8819092f71c5a1140bb61 |
completed | March 1, 2026, 10:34 p.m. |
Created at: March 1, 2026, 7:51 p.m.