Triple
T14506554
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | twistor space |
E340277
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object |
Penrose transform
The Penrose transform is a mathematical correspondence that relates geometric structures and fields on twistor space to solutions of certain differential equations, such as massless field equations, on space-time.
|
E340277
|
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: Penrose transform | Statement: [twistor space, relatedTo, Penrose transform]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Penrose transform Context triple: [twistor space, relatedTo, Penrose transform]
-
A.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
-
B.
Penrose spinor calculus
Penrose spinor calculus is a mathematical framework that reformulates tensor calculus and general relativity using two-component spinors to simplify and clarify the geometry of spacetime.
-
C.
Riemann–Hilbert correspondence
The Riemann–Hilbert correspondence is a fundamental result in mathematics that establishes an equivalence between certain differential equations (or flat connections) on complex manifolds and representations of their fundamental groups, linking analytic and topological data.
-
D.
twistor space
Twistor space is a geometric framework in mathematical physics that reformulates spacetime and field theories using complex geometry, introduced by Roger Penrose to study fundamental physics and gravitation.
-
E.
Fubini–Study form
The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
- 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: Penrose transform Triple: [twistor space, relatedTo, Penrose transform]
Generated description
The Penrose transform is a mathematical correspondence that relates geometric structures and fields on twistor space to solutions of certain differential equations, such as massless field equations, on space-time.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Penrose transform Target entity description: The Penrose transform is a mathematical correspondence that relates geometric structures and fields on twistor space to solutions of certain differential equations, such as massless field equations, on space-time.
-
A.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
-
B.
Penrose spinor calculus
Penrose spinor calculus is a mathematical framework that reformulates tensor calculus and general relativity using two-component spinors to simplify and clarify the geometry of spacetime.
-
C.
Riemann–Hilbert correspondence
The Riemann–Hilbert correspondence is a fundamental result in mathematics that establishes an equivalence between certain differential equations (or flat connections) on complex manifolds and representations of their fundamental groups, linking analytic and topological data.
-
D.
twistor space
chosen
Twistor space is a geometric framework in mathematical physics that reformulates spacetime and field theories using complex geometry, introduced by Roger Penrose to study fundamental physics and gravitation.
-
E.
Fubini–Study form
The Fubini–Study form is the canonical Kähler form on complex projective space, encoding its standard Hermitian and symplectic geometry.
- F. None of above.
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_69d822d9c0408190b9a2b3643e58bb4d |
completed | April 9, 2026, 10:06 p.m. |
| NER | Named-entity recognition | batch_69de94e40e44819084f323f8f9982b75 |
completed | April 14, 2026, 7:26 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69fd6da07ff481909fb2463b0ea92849 |
completed | May 8, 2026, 4:59 a.m. |
| NEDg | Description generation | batch_69fd6eca4ff48190b7c16d92234cb43c |
completed | May 8, 2026, 5:04 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69fd6f38ea788190a957419ca1971b15 |
completed | May 8, 2026, 5:06 a.m. |
Created at: April 10, 2026, 1:21 a.m.