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.