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.