Triple
T3214205
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Fibonacci sequence |
E67350
|
entity |
| Predicate | moduloPatternName |
P46247
|
FINISHED |
| Object |
Pisano period
The Pisano period is the repeating cycle length of Fibonacci numbers when taken modulo a given integer.
|
E337574
|
NE FINISHED |
How this triple was built (5 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: Pisano period | Statement: [Fibonacci sequence, moduloPatternName, Pisano period]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Pisano period Context triple: [Fibonacci sequence, moduloPatternName, Pisano period]
-
A.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
B.
Euler’s totient function φ(n)
Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
-
C.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
-
D.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
E.
Fermat's little theorem
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
- 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: Pisano period Triple: [Fibonacci sequence, moduloPatternName, Pisano period]
Generated description
The Pisano period is the repeating cycle length of Fibonacci numbers when taken modulo a given integer.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Pisano period Target entity description: The Pisano period is the repeating cycle length of Fibonacci numbers when taken modulo a given integer.
-
A.
Fibonacci sequence
The Fibonacci sequence is an infinite series of numbers where each term is the sum of the two preceding ones, widely used in mathematics, art, and design due to its connection with the golden ratio and natural growth patterns.
-
B.
Euler’s totient function φ(n)
Euler’s totient function φ(n) is a fundamental arithmetic function in number theory that counts the positive integers up to n that are relatively prime to n and plays a key role in topics such as modular arithmetic and cryptography.
-
C.
Ulam sequence
The Ulam sequence is an integer sequence starting with 1 and 2 in which each subsequent term is the smallest integer that can be written uniquely as the sum of two distinct earlier terms.
-
D.
Look-and-say sequence
The look-and-say sequence is a famous integer sequence where each term is generated by verbally describing the digits of the previous term, studied for its surprising combinatorial and growth properties.
-
E.
Fermat's little theorem
Fermat's little theorem is a fundamental result in number theory that characterizes how prime numbers interact with integer powers modulo that prime, forming the basis for many modern cryptographic algorithms.
- F. None of above. chosen
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: moduloPatternName Context triple: [Fibonacci sequence, moduloPatternName, Pisano period]
-
A.
notationPattern
Indicates a recurring way in which something is symbolically represented or written, such as a consistent style or structure of notation used for an entity or concept.
-
B.
famousPattern
Indicates that one entity is widely recognized or renowned for a particular style, design, or recurring configuration associated with it.
-
C.
kitPattern
Indicates the design or visual pattern featured on a team's kit or uniform.
-
D.
commandModuleName
Indicates the name assigned to a specific command module within a system or application.
-
E.
pattern
Indicates that one entity exhibits, follows, or is characterized by a particular recurring form, structure, or arrangement associated with another entity.
- F. None of above. chosen
Provenance (7 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_69ad858ac36c81909962589cd277d6e2 |
completed | March 8, 2026, 2:19 p.m. |
| NER | Named-entity recognition | batch_69adaabd01d48190be0dc610b9987a25 |
completed | March 8, 2026, 4:58 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b26237211c81908cddc4e8d42e497e |
completed | March 12, 2026, 6:50 a.m. |
| NEDg | Description generation | batch_69b264c54c508190be85da879935e7f4 |
completed | March 12, 2026, 7:01 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69b268d60bd0819097194da2e9065947 |
completed | March 12, 2026, 7:18 a.m. |
| PD | Predicate disambiguation | batch_69ad9e09b83881908801d79c3d9254f9 |
completed | March 8, 2026, 4:04 p.m. |
| PDg | Predicate description generation | batch_69ada0f9259c8190afbc5ad0fa55436b |
completed | March 8, 2026, 4:16 p.m. |
Created at: March 8, 2026, 3:07 p.m.