Triple

T7338608
Position Surface form Disambiguated ID Type / Status
Subject PSL(2,ℤ) E169191 entity
Predicate generatorAction P77177 FINISHED
Object T:z ↦ z+1
T:z ↦ z+1 is the standard parabolic modular transformation acting on the upper half-plane, serving as one of the fundamental generators of the modular group PSL(2,ℤ).
E656690 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: T:z ↦ z+1 | Statement: [PSL(2,ℤ), generatorAction, T:z ↦ z+1]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: T:z ↦ z+1
Context triple: [PSL(2,ℤ), generatorAction, T:z ↦ z+1]
  • A. FnZ
    FnZ is a hip-hop production duo known for crafting atmospheric, hard-hitting beats for prominent rap artists.
  • B. Ackermann function
    The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
  • C. Riemann zeta function
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • D. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • E. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • 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: T:z ↦ z+1
Triple: [PSL(2,ℤ), generatorAction, T:z ↦ z+1]
Generated description
T:z ↦ z+1 is the standard parabolic modular transformation acting on the upper half-plane, serving as one of the fundamental generators of the modular group PSL(2,ℤ).
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: T:z ↦ z+1
Target entity description: T:z ↦ z+1 is the standard parabolic modular transformation acting on the upper half-plane, serving as one of the fundamental generators of the modular group PSL(2,ℤ).
  • A. FnZ
    FnZ is a hip-hop production duo known for crafting atmospheric, hard-hitting beats for prominent rap artists.
  • B. Ackermann function
    The Ackermann function is a classic example of a computable function that grows faster than any primitive recursive function, often used in theoretical computer science to illustrate extreme computational complexity.
  • C. Riemann zeta function
    The Riemann zeta function is a complex-valued function central to analytic number theory, whose properties—especially the distribution of its zeros—are deeply connected to the distribution of prime numbers.
  • D. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • E. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • 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_69c68a57710481909f0c1f3c6ebdb6f2 completed March 27, 2026, 1:47 p.m.
NER Named-entity recognition batch_69c6f4eb5c808190ba08956bcf297ea8 completed March 27, 2026, 9:21 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7ef266fd0819096cf3ece3fff6b90 completed March 28, 2026, 3:09 p.m.
NEDg Description generation batch_69c7efa4f5148190842f30988cbea94c completed March 28, 2026, 3:11 p.m.
NED2 Entity disambiguation (via description) batch_69c7f0092bac819080ded1863f99290a completed March 28, 2026, 3:13 p.m.
Created at: March 27, 2026, 3:04 p.m.