Triple
T10313547
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Herbert Busemann |
E241955
|
entity |
| Predicate | hasConceptNamedAfter |
P3325
|
FINISHED |
| Object |
Busemann–Feller theorem
The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
|
E855798
|
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: Busemann–Feller theorem | Statement: [Herbert Busemann, hasConceptNamedAfter, Busemann–Feller theorem]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Busemann–Feller theorem Context triple: [Herbert Busemann, hasConceptNamedAfter, Busemann–Feller theorem]
-
A.
Hopf–Rinow theorem
The Hopf–Rinow theorem is a fundamental result in Riemannian geometry that characterizes when a Riemannian manifold is geodesically complete, relating metric completeness, compactness of closed and bounded sets, and the existence of minimizing geodesics between points.
-
B.
Bernstein theorem
Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
-
C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
D.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
E.
Carathéodory existence theorem
The Carathéodory existence theorem is a result in the theory of ordinary differential equations that guarantees the existence (and sometimes uniqueness) of solutions under weaker regularity conditions on the right-hand side than those required by classical theorems like Picard–Lindelöf.
- 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: Busemann–Feller theorem Triple: [Herbert Busemann, hasConceptNamedAfter, Busemann–Feller theorem]
Generated description
The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Busemann–Feller theorem Target entity description: The Busemann–Feller theorem is a result in geometric measure theory that characterizes when a metric space is geodesic by relating distance properties to the existence of shortest paths between points.
-
A.
Hopf–Rinow theorem
The Hopf–Rinow theorem is a fundamental result in Riemannian geometry that characterizes when a Riemannian manifold is geodesically complete, relating metric completeness, compactness of closed and bounded sets, and the existence of minimizing geodesics between points.
-
B.
Bernstein theorem
Bernstein theorem is a fundamental result in set theory stating that if each of two sets can be injected into the other, then there exists a bijection between them, so the sets have the same cardinality.
-
C.
Banach–Saks theorem
The Banach–Saks theorem is a result in functional analysis stating that every bounded sequence in a reflexive Banach space has a subsequence whose Cesàro means converge in norm.
-
D.
Banach–Mazur theorem
The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
-
E.
Carathéodory existence theorem
The Carathéodory existence theorem is a result in the theory of ordinary differential equations that guarantees the existence (and sometimes uniqueness) of solutions under weaker regularity conditions on the right-hand side than those required by classical theorems like Picard–Lindelöf.
- 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_69d381ac38808190a8ca7457c85b625b |
completed | April 6, 2026, 9:49 a.m. |
| NER | Named-entity recognition | batch_69d4d35a292c8190bc8c467e522bba92 |
completed | April 7, 2026, 9:50 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d71d86c7e481908a0d5e65f66ab2c0 |
completed | April 9, 2026, 3:31 a.m. |
| NEDg | Description generation | batch_69d73186831481909555e2205d8783a7 |
completed | April 9, 2026, 4:56 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69d732bfc76c819089287477b54a7b77 |
completed | April 9, 2026, 5:01 a.m. |
Created at: April 6, 2026, 11:48 a.m.