Triple
T2364493
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Riemann surface |
E47348
|
entity |
| Predicate | hasTheorem |
P38252
|
FINISHED |
| Object |
uniformization theorem
The uniformization theorem is a fundamental result in complex analysis stating that every simply connected Riemann surface is conformally equivalent to either the Riemann sphere, the complex plane, or the unit disk.
|
E259768
|
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: uniformization theorem | Statement: [Riemann surface, hasTheorem, uniformization theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: uniformization theorem Context triple: [Riemann surface, hasTheorem, uniformization theorem]
-
A.
Riemann mapping theorem
The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
-
B.
Riemann–Hurwitz formula
The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
-
C.
Riemann surfaces
Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
-
D.
geometrization conjecture
The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
-
E.
Riemann–Roch theorem
The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
- 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: uniformization theorem Triple: [Riemann surface, hasTheorem, uniformization theorem]
Generated description
The uniformization theorem is a fundamental result in complex analysis stating that every simply connected Riemann surface is conformally equivalent to either the Riemann sphere, the complex plane, or the unit disk.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: uniformization theorem Target entity description: The uniformization theorem is a fundamental result in complex analysis stating that every simply connected Riemann surface is conformally equivalent to either the Riemann sphere, the complex plane, or the unit disk.
-
A.
Riemann mapping theorem
The Riemann mapping theorem is a fundamental result in complex analysis stating that any non-empty simply connected open subset of the complex plane (other than the whole plane) can be conformally mapped onto the open unit disk.
-
B.
Riemann–Hurwitz formula
The Riemann–Hurwitz formula is a fundamental result in algebraic geometry and complex analysis that relates the genera of two Riemann surfaces connected by a branched covering map, accounting for the ramification data.
-
C.
Riemann surfaces
Riemann surfaces are one-dimensional complex manifolds that provide the natural geometric setting for studying complex analytic functions and their multi-valued behavior.
-
D.
geometrization conjecture
The geometrization conjecture is a fundamental statement in 3-dimensional topology that classifies all closed 3-manifolds into pieces each admitting one of eight canonical geometric structures, a result proven by Grigori Perelman.
-
E.
Riemann–Roch theorem
The Riemann–Roch theorem is a fundamental result in algebraic geometry and complex analysis that relates the dimension of spaces of meromorphic sections of a line bundle on a curve to topological data such as genus and degree.
- F. None of above. chosen
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: hasTheorem Context triple: [Riemann surface, hasTheorem, uniformization theorem]
-
A.
hasTheoremNamedAfter
Indicates that a theorem is named in honor of or after a particular person or entity.
-
B.
hasTheoreticalStatus
Indicates that something possesses a particular theoretical standing, classification, or role within a conceptual or theoretical framework.
-
C.
appliesTheory
Indicates that an entity uses or implements a particular theory in analyzing, explaining, or addressing something.
-
D.
hasAxiom
Indicates that an entity is associated with, defined by, or governed through a specific axiom or set of axioms.
-
E.
hasTheoreticalJournal
Indicates that an entity is associated with or possesses a theoretical journal, typically as a publication, resource, or reference.
- 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_69a88a1a4a6081908645b0f2914521ab |
completed | March 4, 2026, 7:38 p.m. |
| NER | Named-entity recognition | batch_69abc7486cb48190acef1891cc87bdb1 |
completed | March 7, 2026, 6:35 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69aea896e0388190aabff2d70787dc43 |
completed | March 9, 2026, 11:01 a.m. |
| NEDg | Description generation | batch_69aea91ce164819091aa24b287f9fb8e |
completed | March 9, 2026, 11:03 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69aea999b864819084134c670e7c5d9c |
completed | March 9, 2026, 11:06 a.m. |
| PD | Predicate disambiguation | batch_69abc599b92c819093d9e15d4437705d |
completed | March 7, 2026, 6:28 a.m. |
| PDg | Predicate description generation | batch_69abc6a85e2c8190afec217ff29476be |
completed | March 7, 2026, 6:33 a.m. |
Created at: March 4, 2026, 7:55 p.m.