Triple
T1249043
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | multinomial theorem |
E26831
|
entity |
| Predicate | connectedTo |
P37
|
FINISHED |
| Object |
stars and bars method
The stars and bars method is a classic combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinct bins, often applied to problems involving nonnegative integer solutions to equations.
|
E141902
|
NE FINISHED |
How this triple was built (4 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: stars and bars method | Statement: [multinomial theorem, connectedTo, stars and bars method]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: stars and bars method Context triple: [multinomial theorem, connectedTo, stars and bars method]
-
A.
Pascal's identity
Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
-
B.
binomial theorem
The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
-
C.
multinomial theorem
The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
-
D.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
E.
Bernoulli trials
Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg
Description generation
gpt-5.1
Instruction
Generate a one-sentence description of the target entity. You are given a context triple in the form (subject, predicate, object), where the object is the target entity. # Instructions Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. Avoid repeating the information from the triple, unless really essential. # Response Format Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: stars and bars method Triple: [multinomial theorem, connectedTo, stars and bars method]
Generated description
The stars and bars method is a classic combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinct bins, often applied to problems involving nonnegative integer solutions to equations.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: stars and bars method Target entity description: The stars and bars method is a classic combinatorial technique used to count the number of ways to distribute indistinguishable objects into distinct bins, often applied to problems involving nonnegative integer solutions to equations.
-
A.
Pascal's identity
Pascal's identity is a fundamental combinatorial formula that relates adjacent binomial coefficients and underlies many proofs and properties of binomial expansions.
-
B.
binomial theorem
The binomial theorem is a fundamental algebraic formula that provides a systematic way to expand powers of binomial expressions, playing a key role in combinatorics and mathematical analysis.
-
C.
multinomial theorem
The multinomial theorem is a fundamental algebraic formula that generalizes the binomial theorem to express powers of sums with any number of terms using multinomial coefficients.
-
D.
Pascal's triangle
Pascal's triangle is a triangular array of numbers in which each entry is the sum of the two directly above it, widely used in combinatorics, algebra, and probability.
-
E.
Bernoulli trials
Bernoulli trials are a sequence of independent experiments, each with exactly two possible outcomes (often called success and failure) and the same probability of success on every trial, forming the basis of the binomial distribution in probability theory.
- F. None of above. chosen
Provenance (5 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_69a49487a9c48190ba9b05348fd1b53f |
completed | March 1, 2026, 7:33 p.m. |
| NER | Named-entity recognition | batch_69a4bf83b32c81908648e5748b897247 |
completed | March 1, 2026, 10:36 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69ac8f7f59148190a9f1cbd4af8a115e |
completed | March 7, 2026, 8:50 p.m. |
| NEDg | Description generation | batch_69ac8ff7ae0c81908ca8ace1f4159383 |
completed | March 7, 2026, 8:52 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69ac905e121c819093c9d960b53a45b7 |
completed | March 7, 2026, 8:53 p.m. |
Created at: March 1, 2026, 7:47 p.m.